Product Name: Digits Accelerated Grade 7 Realize Edition
Product Version: v1.0


Source:     IMS Online Validator
Profile:    1.2.0
Identifier: realize-9ee1e8c8-7d44-3af0-8408-f026e5b89d03
Timestamp:  Friday, June 16, 2017 09:46 AM EDT
Status:     VALID!
Conformant: true

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Resource Validation Results
The document is valid.

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Schema Location Results
Schema locations are valid.

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Schema Validation Results
The document is valid.

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Schematron Validation Results
The document is valid.

Curriculum Standards:

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour. - 7.RP.A.1
Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. - 7.RP.A.3
Recognize and represent proportional relationships between quantities. - 7.RP.A.2
Apply properties of operations as strategies to multiply and divide rational numbers. - 7.NS.A.2c
Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. - 7.NS.A.2d
Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood? - 7.SP.C.8c
Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. - 7.SP.C.7
Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. - 8.EE.C.7b
Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. - 7.SP.C.8
Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. - 7.EE.B.4
Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. - 7.SP.C.5
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. - 7.EE.B.3
Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). - 8.EE.C.7a
Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. - 7.SP.C.6
Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. - 7.SP.A.1
Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. - 7.SP.C.8a
Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. - 7.SP.A.2
Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., rolling double sixes), identify the outcomes in the sample space which compose the event. - 7.SP.C.8b
Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. - 7.NS.A.2a
Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts. - 7.NS.A.2b
Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. - 7.G.B.6
Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. - 7.G.B.4
Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. - 7.G.B.5
Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. - 7.RP.A.2c
Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. - 7.RP.A.2b
Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. - 7.RP.A.2a
Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies? - 7.SP.C.7b
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. - 8.G.C.9
Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. - 7.RP.A.2d
Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. - 7.EE.B.4b
Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that the square root of 2 is irrational. - 8.EE.A.2
Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? - 7.EE.B.4a
Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27. - 8.EE.A.1
Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. - 8.EE.A.4
Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger. - 8.EE.A.3
Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two- dimensional figures, describe a sequence that exhibits the similarity between them. - 8.G.A.4
Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. - 8.G.A.5
Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. - 8.G.A.2
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. - 7.NS.A.1
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. - 7.NS.A.2
Verify experimentally the properties of rotations, reflections, and translations: Parallel lines are taken to parallel lines. - 8.G.A.1c
Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. - 8.G.A.3
Solve real-world and mathematical problems involving the four operations with rational numbers. - 7.NS.A.3
Verify experimentally the properties of rotations, reflections, and translations: Angles are taken to angles of the same measure. - 8.G.A.1b
Verify experimentally the properties of rotations, reflections, and translations: Lines are taken to lines, and line segments to line segments of the same length. - 8.G.A.1a
Solve linear equations in one variable. - 8.EE.C.7
Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. - 7.SP.C.7a
Verify experimentally the properties of rotations, reflections, and translations: - 8.G.A.1
Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book. - 7.SP.B.4
Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'. - 7.EE.A.2
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. - 7.EE.A.1
Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. - 7.G.A.1
Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable. - 7.SP.B.3
Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. - 7.G.A.2
Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. - 7.G.A.3
Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. - 7.NS.A.1b
Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. - 7.NS.A.1c
Apply properties of operations as strategies to add and subtract rational numbers. - 7.NS.A.1d
Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. - 8.NS.A.1
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. - 8.EE.B.5
Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., pi^2). For example, by truncating the decimal expansion of the square root of 2, show that the square root of 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. - 8.NS.A.2
Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. - 8.EE.B.6
Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged. - 7.NS.A.1a


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Title: digits Accelerated Grade 7 Realize Edition


         Tools

            Math Tools

            Grids & Organizers

            Student Companion v1 ACTIVe-book

            Student Companion v2 ACTIVe-book

            Multilingual Handbook

            Glossary

         Unit I: Rational Numbers and Exponents: Homework Helper Answer Key

            Unit I: Rational Numbers and Exponents: Enrichment Project

            Lesson i12-1: Mixed Numbers and Improper Fractions: Part 1

            Lesson i12-1: Mixed Numbers and Improper Fractions: Part 2

            Lesson i12-1: Mixed Numbers and Improper Fractions: Part 3

            Lesson i12-1: Mixed Numbers and Improper Fractions: Lesson Check

            i12-1 Journal

            i12-1 Practice

            Lesson i22-5: Comparing and Ordering Rational Numbers: Part 1

            Lesson i22-5: Comparing and Ordering Rational Numbers: Part 2

            Lesson i22-5: Comparing and Ordering Rational Numbers: Part 3

            Lesson i22-5: Comparing and Ordering Rational Numbers: Lesson Check

            i22-5 Journal

            i22-5 Practice

            Lesson i22-4: Rational Numbers on the Number Line: Part 1

            Lesson i22-4: Rational Numbers on the Number Line: Part 2

            Lesson i22-4: Rational Numbers on the Number Line: Part 3

            Lesson i22-4: Rational Numbers on the Number Line: Lesson Check

            i22-4 Journal

            i22-4 Practice

            Lesson i12-2: Adding Mixed Numbers: Part 1

            Lesson i12-2: Adding Mixed Numbers: Part 2

            Lesson i12-2: Adding Mixed Numbers: Part 3

            Lesson i12-2: Adding Mixed Numbers: Lesson Check

            i12-2 Journal

            i12-2 Practice

            Lesson i11-5: Dividing Fractions: Part 1

            Lesson i11-5: Dividing Fractions: Part 2

            Lesson i11-5: Dividing Fractions: Part 3

            Lesson i11-5: Dividing Fractions: Lesson Check

            i11-5 Journal

            i11-5 Practice

            Lesson i12-3: Subtracting Mixed Numbers: Part 1

            Lesson i12-3: Subtracting Mixed Numbers: Part 2

            Lesson i12-3: Subtracting Mixed Numbers: Part 3

            Lesson i12-3: Subtracting Mixed Numbers: Lesson Check

            i12-3 Journal

            i12-3 Practice

            Lesson i10-4: Subtracting with Unlike Denominators: Part 1

            Lesson i10-4: Subtracting with Unlike Denominators: Part 2

            Lesson i10-4: Subtracting with Unlike Denominators: Part 3

            Lesson i10-4: Subtracting with Unlike Denominators: Lesson Check

            i10-4 Journal

            i10-4 Practice

            Lesson i10-3: Adding Fractions with Unlike Denominators: Part 1

            Lesson i10-3: Adding Fractions with Unlike Denominators: Part 2

            Lesson i10-3: Adding Fractions with Unlike Denominators: Part 3

            Lesson i10-3: Adding Fractions with Unlike Denominators: Lesson Check

            i10-3 Journal

            i10-3 Practice

            Lesson i9-4: Fractions and Division: Part 1

            Lesson i9-4: Fractions and Division: Part 2

            Lesson i9-4: Fractions and Division: Part 3

            Lesson i9-4: Fractions and Division: Lesson Check

            i9-4 Journal

            i9-4 Practice

            Lesson i8-5: Dividing Decimals: Part 1

            Lesson i8-5: Dividing Decimals: Part 2

            Lesson i8-5: Dividing Decimals: Part 3

            Lesson i8-5: Dividing Decimals: Lesson Check

            i8-5 Practice

            i8-5 Journal

            Lesson i8-2: Multiplying Decimals: Part 1

            Lesson i8-2: Multiplying Decimals: Part 2

            Lesson i8-2: Multiplying Decimals: Part 3

            Lesson i8-2: Multiplying Decimals: Lesson Check

            i8-2 Journal

            i8-2 Practice

            Lesson i21-1: Understanding Integers: Part 1

            Lesson i21-1: Understanding Integers: Part 2

            Lesson i21-1: Understanding Integers: Part 3

            Lesson i21-1: Understanding Integers: Lesson Check

            i21-1 Journal

            i21-1 Practice

            Unit I: Rational Numbers and Exponents: Readiness Assessment

            Topic 1: Adding and Subtracting Rational Numbers

               Topic 1: Adding and Subtracting Rational Numbers: Enrichment Project

               Lesson 1-1: Rational Numbers, Opposites, and Absolute Value

                  Interactive Learning

                     1-1: Rational Numbers, Opposites, and Absolute Value: Topic Opener

                     1-1: Rational Numbers, Opposites, and Absolute Value: Launch
                       Curriculum Standards: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.

                     1-1: Rational Numbers, Opposites, and Absolute Value: Part 1
                       Curriculum Standards: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.

                     1-1: Rational Numbers, Opposites, and Absolute Value: Part 2
                       Curriculum Standards: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.

                     1-1: Rational Numbers, Opposites, and Absolute Value: Part 3
                       Curriculum Standards: Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.

                     1-1: Rational Numbers, Opposites, and Absolute Value: Key Concept
                       Curriculum Standards: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.

                     1-1: Rational Numbers, Opposites, and Absolute Value: Close and Check
                       Curriculum Standards: Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.

                  Practice

                     1-1: Rational Numbers, Opposites, and Absolute Value: Homework G
                       Curriculum Standards: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.

                     1-1: Rational Numbers, Opposites, and Absolute Value: Homework K
                       Curriculum Standards: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.

                     1-1: Rational Numbers, Opposites, and Absolute Value: Mixed Review

               Lesson 1-2: Adding Integers

                  Interactive Learning

                     1-2: Adding Integers: Launch
                       Curriculum Standards: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

                     1-2: Adding Integers: Key Concept
                       Curriculum Standards: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

                     1-2: Adding Integers: Part 1
                       Curriculum Standards: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

                     1-2: Adding Integers: Part 2
                       Curriculum Standards: Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

                     1-2: Adding Integers: Part 3
                       Curriculum Standards: Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

                     1-2: Adding Integers: Close and Check
                       Curriculum Standards: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

                  Practice

                     1-2: Adding Integers: Homework G
                       Curriculum Standards: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

                     1-2: Adding Integers: Homework K
                       Curriculum Standards: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

                     1-2: Adding Integers: Mixed Review

               Lesson 1-3: Adding Rational Numbers

                  Interactive Learning

                     1-3: Adding Rational Numbers: Launch
                       Curriculum Standards: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

                     1-3: Adding Rational Numbers: Part 1
                       Curriculum Standards: Apply properties of operations as strategies to add and subtract rational numbers.

                     1-3: Adding Rational Numbers: Key Concept
                       Curriculum Standards: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

                     1-3: Adding Rational Numbers: Part 2
                       Curriculum Standards: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

                     1-3: Adding Rational Numbers: Part 3
                       Curriculum Standards: Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

                     1-3: Adding Rational Numbers: Close and Check
                       Curriculum Standards: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

                  Practice

                     1-3: Adding Rational Numbers: Homework G
                       Curriculum Standards: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. Apply properties of operations as strategies to add and subtract rational numbers.

                     1-3: Adding Rational Numbers: Homework K
                       Curriculum Standards: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. Apply properties of operations as strategies to add and subtract rational numbers.

                     1-3: Adding Rational Numbers: Mixed Review

               Lesson 1-4: Subtracting Integers

                  Interactive Learning

                     1-4: Subtracting Integers: Launch
                       Curriculum Standards: Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

                     1-4: Subtracting Integers: Part 1
                       Curriculum Standards: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

                     1-4: Subtracting Integers: Part 2
                       Curriculum Standards: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

                     1-4: Subtracting Integers: Part 3
                       Curriculum Standards: Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

                     1-4: Subtracting Integers: Key Concept
                       Curriculum Standards: Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

                     1-4: Subtracting Integers: Close and Check
                       Curriculum Standards: Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

                  Practice

                     1-4: Subtracting Integers: Homework G
                       Curriculum Standards: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

                     1-4: Subtracting Integers: Homework K
                       Curriculum Standards: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

                     1-4: Subtracting Integers: Mixed Review

               Lesson 1-5: Subtracting Rational Numbers

                  Interactive Learning

                     1-5: Subtracting Rational Numbers: Launch
                       Curriculum Standards: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

                     1-5: Subtracting Rational Numbers: Key Concept
                       Curriculum Standards: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

                     1-5: Subtracting Rational Numbers: Part 1
                       Curriculum Standards: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

                     1-5: Subtracting Rational Numbers: Part 2
                       Curriculum Standards: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

                     1-5: Subtracting Rational Numbers: Part 3
                       Curriculum Standards: Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

                     1-5: Subtracting Rational Numbers: Close and Check
                       Curriculum Standards: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

                  Practice

                     1-5: Subtracting Rational Numbers: Homework G
                       Curriculum Standards: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

                     1-5: Subtracting Rational Numbers: Homework K
                       Curriculum Standards: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

                     1-5: Subtracting Rational Numbers: Mixed Review

               Lesson 1-6: Distance on a Number Line

                  Interactive Learning

                     1-6: Distance on a Number Line: Launch
                       Curriculum Standards: Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

                     1-6: Distance on a Number Line: Part 1
                       Curriculum Standards: Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

                     1-6: Distance on a Number Line: Part 2
                       Curriculum Standards: Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

                     1-6: Distance on a Number Line: Key Concept
                       Curriculum Standards: Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

                     1-6: Distance on a Number Line: Part 3
                       Curriculum Standards: Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

                     1-6: Distance on a Number Line: Close and Check
                       Curriculum Standards: Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

                  Practice

                     1-6: Distance on a Number Line: Homework G
                       Curriculum Standards: Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

                     1-6: Distance on a Number Line: Homework K
                       Curriculum Standards: Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

                     1-6: Distance on a Number Line: Mixed Review

               Lesson 1-7: Problem Solving

                  Interactive Learning

                     1-7: Problem Solving: Launch
                       Curriculum Standards: Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

                     1-7: Problem Solving: Part 1
                       Curriculum Standards: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

                     1-7: Problem Solving: Part 2
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

                     1-7: Problem Solving: Part 3
                       Curriculum Standards: Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

                     1-7: Problem Solving: Close and Check
                       Curriculum Standards: Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

                  Practice

                     1-7: Problem Solving: Homework G
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

                     1-7: Problem Solving: Homework K
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

                     1-7: Problem Solving: Mixed Review

               Topic 1 Review

                  Interactive Learning

                     Topic 1:  Adding and Subtracting Rational Numbers: Vocabulary Review
                     Topic 1: Adding and Subtracting Rational Numbers: Vocabulary Review

                     Topic 1: Adding and Subtracting Rational Numbers: Pull It All Together

                     Topic 1: Adding and Subtracting Rational Numbers: Close

                  Practice

                     Topic 1: Adding and Subtracting Rational Numbers: Review Homework
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

               Topic 1: Adding and Subtracting Rational Numbers: Topic Test
                 Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

            Topic 2: Multiplying and Dividing Rational Numbers

               Topic 2: Multiplying and Dividing Rational Numbers: Enrichment Project

               Lesson 2-1: Multiplying Integers

                  Interactive Learning

                     2-1: Multiplying Integers: Topic Opener

                     2-1: Multiplying Integers: Launch
                       Curriculum Standards: Apply properties of operations as strategies to multiply and divide rational numbers.

                     2-1: Multiplying Integers: Part 1

                     2-1: Multiplying Integers: Part 2
                       Curriculum Standards: Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

                     2-1: Multiplying Integers: Key Concept
                       Curriculum Standards: Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

                     2-1: Multiplying Integers: Part 3
                       Curriculum Standards: Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

                     2-1: Multiplying Integers: Close and Check
                       Curriculum Standards: Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

                  Practice

                     2-1: Multiplying Integers: Homework G
                       Curriculum Standards: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

                     2-1: Multiplying Integers: Homework K
                       Curriculum Standards: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

                     2-1: Multiplying Integers: Mixed Review

               Lesson 2-2: Multiplying Rational Numbers

                  Interactive Learning

                     2-2: Multiplying Rational Numbers: Launch

                     2-2: Multiplying Rational Numbers: Key Concept
                       Curriculum Standards: Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

                     2-2: Multiplying Rational Numbers: Part 1
                       Curriculum Standards: Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

                     2-2: Multiplying Rational Numbers: Part 2
                       Curriculum Standards: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

                     2-2: Multiplying Rational Numbers: Part 3
                       Curriculum Standards: Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

                     2-2: Multiplying Rational Numbers: Close and Check
                       Curriculum Standards: Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

                  Practice

                     2-2: Multiplying Rational Numbers: Homework G
                       Curriculum Standards: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

                     2-2: Multiplying Rational Numbers: Homework K
                       Curriculum Standards: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

                     2-2: Multiplying Rational Numbers: Mixed Review

               Lesson 2-3: Dividing Integers

                  Interactive Learning

                     2-3: Dividing Integers: Launch
                       Curriculum Standards: Apply properties of operations as strategies to multiply and divide rational numbers.

                     2-3: Dividing Integers: Key Concept
                       Curriculum Standards: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts.

                     2-3: Dividing Integers: Part 1
                       Curriculum Standards: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts.

                     2-3: Dividing Integers: Part 2
                       Curriculum Standards: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts.

                     2-3: Dividing Integers: Part 3
                       Curriculum Standards: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts.

                     2-3: Dividing Integers: Close and Check
                       Curriculum Standards: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts.

                  Practice

                     2-3: Dividing Integers: Homework G
                       Curriculum Standards: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts.

                     2-3: Dividing Integers: Homework K
                       Curriculum Standards: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts.

                     2-3: Dividing Integers: Mixed Review

               Lesson 2-4: Dividing Rational Numbers

                  Interactive Learning

                     2-4: Dividing Rational Numbers: Launch

                     2-4: Dividing Rational Numbers: Part 1

                     2-4: Dividing Rational Numbers: Part 2

                     2-4: Dividing Rational Numbers: Part 3
                       Curriculum Standards: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts.

                     2-4: Dividing Rational Numbers: Key Concept
                       Curriculum Standards: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts.

                     2-4: Dividing Rational Numbers: Close and Check

                  Practice

                     2-4: Dividing Rational Numbers: Homework G
                       Curriculum Standards: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts.

                     2-4: Dividing Rational Numbers: Homework K
                       Curriculum Standards: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts.

                     2-4: Dividing Rational Numbers: Mixed Review

               Lesson 2-5: Operations With Rational Numbers

                  Interactive Learning

                     2-5: Operations With Rational Numbers: Launch
                       Curriculum Standards: Apply properties of operations as strategies to multiply and divide rational numbers.

                     2-5: Operations With Rational Numbers: Key Concept
                       Curriculum Standards: Apply properties of operations as strategies to multiply and divide rational numbers.

                     2-5: Operations With Rational Numbers: Part 1
                       Curriculum Standards: Apply properties of operations as strategies to multiply and divide rational numbers.

                     2-5: Operations With Rational Numbers: Part 2
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                     2-5: Operations With Rational Numbers: Part 3

                     2-5: Operations With Rational Numbers: Close and Check
                       Curriculum Standards: Apply properties of operations as strategies to multiply and divide rational numbers.

                  Practice

                     2-5: Operations With Rational Numbers: Homework G
                       Curriculum Standards: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Apply properties of operations as strategies to multiply and divide rational numbers. Solve real-world and mathematical problems involving the four operations with rational numbers.

                     2-5: Operations With Rational Numbers: Homework K
                       Curriculum Standards: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Apply properties of operations as strategies to multiply and divide rational numbers. Solve real-world and mathematical problems involving the four operations with rational numbers.

                     2-5: Operations With Rational Numbers: Mixed Review

               Lesson 2-6: Problem Solving

                  Interactive Learning

                     2-6: Problem Solving: Launch
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                     2-6: Problem Solving: Part 1
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

                     2-6: Problem Solving: Part 2
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                     2-6: Problem Solving: Part 3
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

                     2-6: Problem Solving: Close and Check
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

                  Practice

                     2-6: Problem Solving: Homework G
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Solve real-world and mathematical problems involving the four operations with rational numbers.

                     2-6: Problem Solving: Homework K
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Solve real-world and mathematical problems involving the four operations with rational numbers.

                     2-6: Problem Solving: Mixed Review

               Topic 2 Review

                  Interactive Learning

                     Topic 2: Multiplying and Dividing Rational Numbers: Vocabulary Review

                     Topic 2: Multiplying and Dividing Rational Numbers: Pull It All Together

                     Topic 2: Multiplying and Dividing Rational Numbers: Close

                  Practice

                     Topic 2: Multiplying and Dividing Rational Numbers: Review Homework
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts. Apply properties of operations as strategies to multiply and divide rational numbers. Solve real-world and mathematical problems involving the four operations with rational numbers.

               Topic 2 Test
                 Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts. Apply properties of operations as strategies to multiply and divide rational numbers. Solve real-world and mathematical problems involving the four operations with rational numbers.

            Topic 3: Decimals and Percents

               Topic 3: Decimals and Percents: Enrichment Project

               Lesson 3-1: Repeating Decimals

                  Interactive Learning

                     3-1: Repeating Decimals: Topic Opener

                     3-1: Repeating Decimals: Launch
                       Curriculum Standards: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts.

                     3-1: Repeating Decimals: Part 1
                       Curriculum Standards: Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

                     3-1: Repeating Decimals: Key Concept
                       Curriculum Standards: Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

                     3-1: Repeating Decimals: Part 2
                       Curriculum Standards: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

                     3-1: Repeating Decimals: Part 3
                       Curriculum Standards: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

                     3-1: Repeating Decimals: Close and Check
                       Curriculum Standards: Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

                  Practice

                     3-1: Repeating Decimals: Homework G
                       Curriculum Standards: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

                     3-1: Repeating Decimals: Homework K
                       Curriculum Standards: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

                     3-1: Repeating Decimals: Mixed Review

               Lesson 3-2: Terminating Decimals

                  Interactive Learning

                     3-2: Terminating Decimals: Launch
                       Curriculum Standards: Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

                     3-2: Terminating Decimals: Key Concept
                       Curriculum Standards: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

                     3-2: Terminating Decimals: Part 1
                       Curriculum Standards: Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

                     3-2: Terminating Decimals: Part 2
                       Curriculum Standards: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

                     3-2: Terminating Decimals: Part 3
                       Curriculum Standards: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

                     3-2: Terminating Decimals: Close and Check
                       Curriculum Standards: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

                  Practice

                     3-2: Terminating Decimals: Homework G
                       Curriculum Standards: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

                     3-2: Terminating Decimals: Homework K
                       Curriculum Standards: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

                     3-2: Terminating Decimals: Mixed Review

               Lesson 3-3: Percents Greater Than 100

                  Interactive Learning

                     3-3: Percents Greater Than 100: Launch
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                     3-3: Percents Greater Than 100: Part 1
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                     3-3: Percents Greater Than 100: Key Concept
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                     3-3: Percents Greater Than 100: Part 2
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                     3-3: Percents Greater Than 100: Part 3
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                     3-3: Percents Greater Than 100: Close and Check
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                  Practice

                     3-3: Percents Greater Than 100: Homework G
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                     3-3: Percents Greater Than 100: Homework K
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                     3-3: Percents Greater Than 100: Mixed Review

               Lesson 3-4: Percents Less Than 1

                  Interactive Learning

                     3-4: Percents Less Than 1: Launch
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                     3-4: Percents Less Than 1: Part 1
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                     3-4: Percents Less Than 1: Key Concept
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                     3-4: Percents Less Than 1: Part 2
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                     3-4: Percents Less Than 1: Part 3
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                     3-4: Percents Less Than 1: Close and Check
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                  Practice

                     3-4: Percents Less Than 1: Homework G
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                     3-4: Percents Less Than 1: Homework K
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                     3-4: Percents Less Than 1: Mixed Review

               Lesson 3-5: Fractions, Decimals, and Percents

                  Interactive Learning

                     3-5: Fractions, Decimals, and Percents: Launch
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                     3-5: Fractions, Decimals, and Percents: Part 1
                       Curriculum Standards: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

                     3-5: Fractions, Decimals, and Percents: Part 2
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                     3-5: Fractions, Decimals, and Percents: Key Concept
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                     3-5:  Fractions, Decimals, and Percents: Part 3
                     3-5: Fractions, Decimals, and Percents: Part 3
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                     3-5: Fractions, Decimals, and Percents: Close and Check
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                  Practice

                     3-5: Fractions, Decimals, and Percents: Homework G
                       Curriculum Standards: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. Solve real-world and mathematical problems involving the four operations with rational numbers.

                     3-5: Fractions, Decimals, and Percents: Homework K
                       Curriculum Standards: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. Solve real-world and mathematical problems involving the four operations with rational numbers.

                     3-5: Fractions, Decimals, and Percents: Mixed Review

               Lesson 3-6: Percent Error

                  Interactive Learning

                     3-6: Percent Error: Launch
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     3-6: Percent Error: Key Concept
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     3-6: Percent Error: Part 1
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     3-6: Percent Error: Part 2
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     3-6: Percent Error: Part 3
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     3-6: Percent Error: Close and Check
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                  Practice

                     3-6: Percent Error: Homework G
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     3-6: Percent Error: Homework K
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     3-6: Percent Error: Mixed Review

               Lesson 3-7: Problem Solving

                  Interactive Learning

                     3-7: Problem Solving: Launch
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                     3-7: Problem Solving: Part 1
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                     3-7: Problem Solving: Part 2
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                     3-7: Problem Solving: Part 3
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                     3-7: Problem Solving: Close and Check
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                  Practice

                     3-7: Problem Solving: Homework G
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                     3-7: Problem Solving: Homework K
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                     3-7: Problem Solving: Mixed Review

               Topic 3 Review

                  Interactive Learning

                     Topic 3: Decimals and Percents: Vocabulary Review

                     Topic 3: Decimals and Percents: Pull It All Together

                     Topic 3: Decimals and Percents: Close

                  Practice

                     Topic 3: Decimals and Percents: Review Homework
                       Curriculum Standards: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. Solve real-world and mathematical problems involving the four operations with rational numbers. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

               Topic 3: Decimals and Percents: Test
                 Curriculum Standards: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. Solve real-world and mathematical problems involving the four operations with rational numbers. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

            Topic 4: Rational and Irrational Numbers

               Topic 4:  Rational and Irrational Numbers: Enrichment Project
               Topic 4: Rational and Irrational Numbers: Enrichment ProjectFor use with Topic 4: Rational and Irrational Numbers

               Lesson 4-1: Expressing Rational Numbers with Decimal Expansions

                  Interactive Learning

                     4-1: Expressing Rational Numbers with Decimal Expansions: Topic Opener

                     4-1: Expressing Rational Numbers with Decimal Expansions: Launch
                       Curriculum Standards: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

                     4-1: Expressing Rational Numbers with Decimal Expansions: Key Concept
                       Curriculum Standards: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

                     4-1: Expressing Rational Numbers with Decimal Expansions: Part 1
                       Curriculum Standards: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

                     4-1: Expressing Rational Numbers with Decimal Expansions: Part 2
                       Curriculum Standards: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

                     4-1: Expressing Rational Numbers with Decimal Expansions: Part 3
                       Curriculum Standards: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

                     4-1: Expressing Rational Numbers with Decimal Expansions: Close and Check
                       Curriculum Standards: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

                  Practice

                     4-1: Expressing Rational Numbers with Decimal Expansions: Homework G
                       Curriculum Standards: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

                     4-1: Expressing Rational Numbers with Decimal Expansions: Homework K
                       Curriculum Standards: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

                     4-1: Expressing Rational Numbers with Decimal Expansions: Mixed Review

               Lesson 4-2: Exploring Irrational Numbers

                  Interactive Learning

                     4-2:  Exploring Irrational Numbers: Launch
                     4-2: Exploring Irrational Numbers: Launch
                       Curriculum Standards: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

                     4-2: Exploring Irrational Numbers: Part 1
                       Curriculum Standards: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

                     4-2: Exploring Irrational Numbers: Part 2
                       Curriculum Standards: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

                     4-2: Exploring Irrational Numbers: Key Concept
                       Curriculum Standards: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

                     4-2: Exploring Irrational Numbers: Part 3
                       Curriculum Standards: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

                     4-2: Exploring Irrational Numbers: Close and Check
                       Curriculum Standards: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

                  Practice

                     4-2: Exploring Irrational Numbers: Homework G
                       Curriculum Standards: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

                     4-2: Exploring Irrational Numbers: Homework K
                       Curriculum Standards: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

                     4-2: Exploring Irrational Numbers: Mixed Review

               Lesson 4-3: Approximating Irrational Numbers

                  Interactive Learning

                     4-3: Approximating Irrational Numbers: Launch
                       Curriculum Standards: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., pi^2). For example, by truncating the decimal expansion of the square root of 2, show that the square root of 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

                     4-3: Approximating Irrational Numbers: Key Concept
                       Curriculum Standards: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., pi^2). For example, by truncating the decimal expansion of the square root of 2, show that the square root of 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

                     4-3: Approximating Irrational Numbers: Part 1
                       Curriculum Standards: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., pi^2). For example, by truncating the decimal expansion of the square root of 2, show that the square root of 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

                     4-3: Approximating Irrational Numbers: Part 3
                       Curriculum Standards: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., pi^2). For example, by truncating the decimal expansion of the square root of 2, show that the square root of 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

                     4-3: Approximating Irrational Numbers: Close and Check
                       Curriculum Standards: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., pi^2). For example, by truncating the decimal expansion of the square root of 2, show that the square root of 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

                     4-3: Approximating Irrational Numbers: Part 2
                       Curriculum Standards: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., pi^2). For example, by truncating the decimal expansion of the square root of 2, show that the square root of 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

                  Practice

                     4-3: Approximating Irrational Numbers: Homework G
                       Curriculum Standards: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., pi^2). For example, by truncating the decimal expansion of the square root of 2, show that the square root of 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

                     4-3: Approximating Irrational Numbers: Homework K
                       Curriculum Standards: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., pi^2). For example, by truncating the decimal expansion of the square root of 2, show that the square root of 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

                     4-3: Approximating Irrational Numbers: Mixed Review

               Lesson 4-4: Comparing and Ordering Rational and Irrational Numbers

                  Interactive Learning

                     4-4: Comparing and Ordering Rational and Irrational Numbers: Launch
                       Curriculum Standards: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., pi^2). For example, by truncating the decimal expansion of the square root of 2, show that the square root of 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

                     4-4: Comparing and Ordering Rational and Irrational Numbers: Key Concept
                       Curriculum Standards: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., pi^2). For example, by truncating the decimal expansion of the square root of 2, show that the square root of 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

                     4-4: Comparing and Ordering Rational and Irrational Numbers: Part 1
                       Curriculum Standards: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., pi^2). For example, by truncating the decimal expansion of the square root of 2, show that the square root of 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

                     4-4: Comparing and Ordering Rational and Irrational Numbers: Part 2
                       Curriculum Standards: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., pi^2). For example, by truncating the decimal expansion of the square root of 2, show that the square root of 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

                     4-4: Comparing and Ordering Rational and Irrational Numbers: Part 3
                       Curriculum Standards: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., pi^2). For example, by truncating the decimal expansion of the square root of 2, show that the square root of 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

                     4-4: Comparing and Ordering Rational and Irrational Numbers: Close and Check
                       Curriculum Standards: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., pi^2). For example, by truncating the decimal expansion of the square root of 2, show that the square root of 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

                  Practice

                     4-4: Comparing and Ordering Rational and Irrational Numbers: Homework G
                       Curriculum Standards: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., pi^2). For example, by truncating the decimal expansion of the square root of 2, show that the square root of 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

                     4-4: Comparing and Ordering Rational and Irrational Numbers: Homework K
                       Curriculum Standards: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., pi^2). For example, by truncating the decimal expansion of the square root of 2, show that the square root of 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

                     4-4: Comparing and Ordering Rational and Irrational Numbers: Mixed Review

               Lesson 4-5: Problem Solving

                  Interactive Learning

                     4-5: Problem Solving: Launch
                       Curriculum Standards: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., pi^2). For example, by truncating the decimal expansion of the square root of 2, show that the square root of 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

                     4-5: Problem Solving: Part 1
                       Curriculum Standards: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

                     4-5: Problem Solving: Part 2
                       Curriculum Standards: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., pi^2). For example, by truncating the decimal expansion of the square root of 2, show that the square root of 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

                     4-5: Problem Solving: Part 3
                       Curriculum Standards: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

                     4-5: Problem Solving: Close and Check
                       Curriculum Standards: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

                  Practice

                     4-5: Problem Solving: Homework G
                       Curriculum Standards: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., pi^2). For example, by truncating the decimal expansion of the square root of 2, show that the square root of 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

                     4-5: Problem Solving: Homework K
                       Curriculum Standards: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., pi^2). For example, by truncating the decimal expansion of the square root of 2, show that the square root of 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

                     4-5: Problem Solving: Mixed Review

               Topic 4 Review

                  Interactive Learning

                     Topic 4: Rational and Irrational Numbers: Vocabulary Review

                     Topic 4: Rational and Irrational Numbers: Pull It All Together

                     Topic 4: Rational and Irrational Numbers: Close

                  Practice

                     Topic 4: Rational and Irrational Numbers: Review Homework
                       Curriculum Standards: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., pi^2). For example, by truncating the decimal expansion of the square root of 2, show that the square root of 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

               Topic 4: Rational and Irrational Numbers: Test
                 Curriculum Standards: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., pi^2). For example, by truncating the decimal expansion of the square root of 2, show that the square root of 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

            Topic 5: Integer Exponents

               Topic 5: Integer Exponents: Enrichment Project

               Lesson 5-1: Perfect Squares, Square Roots, and Equations of the form x^2=p

                  Interactive Learning

                     5-1: Perfect Squares, Square Roots, and Equations of the form x^2 = p: Topic Opener

                     5-1: Perfect Squares, Square Roots, and Equations of the form x^2 = p: Launch
                       Curriculum Standards: Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that the square root of 2 is irrational.

                     5-1: Perfect Squares, Square Roots, and Equations of the form x^2 = p: Key Concept
                       Curriculum Standards: Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that the square root of 2 is irrational.

                     5-1: Perfect Squares, Square Roots, and Equations of the form x^2 = p: Part 1
                       Curriculum Standards: Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that the square root of 2 is irrational.

                     5-1: Perfect Squares, Square Roots, and Equations of the form x^2 = p: Part 2
                       Curriculum Standards: Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that the square root of 2 is irrational.

                     5-1: Perfect Squares, Square Roots, and Equations of the form x^2 = p: Part 3
                       Curriculum Standards: Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that the square root of 2 is irrational.

                     5-1: Perfect Squares, Square Roots, and Equations of the form x^2 = p: Close and Check
                       Curriculum Standards: Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that the square root of 2 is irrational.

                  Practice

                     5-1: Perfect Squares, Square Roots, and Equations of the form x^2 = p: Homework G
                       Curriculum Standards: Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that the square root of 2 is irrational.

                     5-1: Perfect Squares, Square Roots, and Equations of the form x^2 = p: Homework K
                       Curriculum Standards: Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that the square root of 2 is irrational.

                     5-1: Perfect Squares, Square Roots, and Equations of the form x^2 = p: Mixed Review

               Lesson 5-2: Perfect Cubes, Cube Roots, and Equations of the form x^3=p

                  Interactive Learning

                     5-2: Perfect Cubes, Cube Roots, and Equations of the form x^3 = p: Launch
                       Curriculum Standards: Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that the square root of 2 is irrational.

                     5-2: Perfect Cubes, Cube Roots, and Equations of the form x^3 = p: Key Concept
                       Curriculum Standards: Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that the square root of 2 is irrational.

                     5-2: Perfect Cubes, Cube Roots, and Equations of the form x^3 = p: Part 1
                       Curriculum Standards: Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that the square root of 2 is irrational.

                     5-2: Perfect Cubes, Cube Roots, and Equations of the form x^3 = p: Part 2
                       Curriculum Standards: Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that the square root of 2 is irrational.

                     5-2: Perfect Cubes, Cube Roots, and Equations of the form x^3 = p: Part 3
                       Curriculum Standards: Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that the square root of 2 is irrational.

                     5-2: Perfect Cubes, Cube Roots, and Equations of the form x^3 = p: Close and Check
                       Curriculum Standards: Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that the square root of 2 is irrational.

                  Practice

                     5-2: Perfect Cubes, Cube Roots, and Equations of the form x^3 = p: Homework G
                       Curriculum Standards: Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that the square root of 2 is irrational.

                     5-2: Perfect Cubes, Cube Roots, and Equations of the form x^3 = p: Homework K
                       Curriculum Standards: Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that the square root of 2 is irrational.

                     5-2: Perfect Cubes, Cube Roots, and Equations of the form x^3 = p: Mixed Review

               Lesson 5-3: Exponents and Multiplication

                  Interactive Learning

                     5-3: Exponents and Multiplication: Launch
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                     5-3: Exponents and Multiplication: Part 1
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                     5-3: Exponents and Multiplication: Part 2
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                     5-3: Exponents and Multiplication: Part 3
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                     5-3: Exponents and Multiplication: Key Concept
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                     5-3: Exponents and Multiplication: Close and Check
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                  Practice

                     5-3: Exponents and Multiplication: Homework G
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                     5-3: Exponents and Multiplication: Homework K
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                     5-3: Exponents and Multiplication: Mixed Review

               Lesson 5-4: Exponents and Division

                  Interactive Learning

                     5-4: Exponents and Division: Launch
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                     5-4: Exponents and Division: Part 1
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                     5-4: Exponents and Division: Part 2
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                     5-4: Exponents and Division: Key Concept
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                     5-4: Exponents and Division: Close and Check
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                  Practice

                     5-4: Exponents and Division: Homework G
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                     5-4: Exponents and Division: Homework K
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                     5-4: Exponents and Division: Mixed Review

               Lesson 5-5: Zero and Negative Exponents

                  Interactive Learning

                     5-5: Zero and Negative Exponents: Launch
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                     5-5: Zero and Negative Exponents: Part 1
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                     5-5: Zero and Negative Exponents: Part 2
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                     5-5: Zero and Negative Exponents: Part 3
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                     5-5: Zero and Negative Exponents: Key Concept
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                     5-5: Zero and Negative Exponents: Close and Check
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                  Practice

                     5-5: Zero and Negative Exponents: Homework G
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                     5-5: Zero and Negative Exponents: Homework K
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                     5-5: Zero and Negative Exponents:  Mixed Review
                     5-5: Zero and Negative Exponents: Mixed Review

               Lesson 5-6: Comparing Expressions with Exponents

                  Interactive Learning

                     5-6: Comparing Expressions with Exponents: Launch
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                     5-6: Comparing Expressions with Exponents: Part 1
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                     5-6: Comparing Expressions with Exponents: Part 2
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                     5-6: Comparing Expressions with Exponents: Part 3
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                     5-6: Comparing Expressions with Exponents: Close and Check
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                  Practice

                     5-6: Comparing Expressions with Exponents: Homework G
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                     5-6: Comparing Expressions with Exponents: Homework K
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                     5-6: Comparing Expressions with Exponents: Mixed Review

               Lesson 5-7: Problem Solving

                  Interactive Learning

                     5-7: Problem Solving: Launch
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                     5-7: Problem Solving: Part 1
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                     5-7: Problem Solving: Part 2
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                     5-7: Problem Solving: Close and Check
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                  Practice

                     5-7: Problem Solving: Homework G
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                     5-7: Problem Solving: Homework K
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                     5-7: Problem Solving: Mixed Review

               Topic 5 Review

                  Interactive Learning

                     Topic 5: Integer Exponents: Vocabulary Review

                     Topic 5: Integer Exponents: Pull It All Together

                     Topic 5: Integer Exponents: Close

                  Practice

                     Topic 5: Integer Exponents: Review Homework
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27. Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that the square root of 2 is irrational.

               Topic 5 Test
                 Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27. Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that the square root of 2 is irrational.

            Topic 6: Scientific Notation

               Topic 6:  Scientific Notation: Enrichment Project
               Topic 6: Scientific Notation: Enrichment ProjectFor use with Topic 6: Scientific Notation

               Lesson 6-1: Exploring Scientific Notation

                  Interactive Learning

                     6-1: Exploring Scientific Notation: Topic Opener

                     6-1: Exploring Scientific Notation: Launch
                       Curriculum Standards: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger.

                     6-1: Exploring Scientific Notation: Part 1
                       Curriculum Standards: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger.

                     6-1: Exploring Scientific Notation: Key Concept
                       Curriculum Standards: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger.

                     6-1: Exploring Scientific Notation: Part 2
                       Curriculum Standards: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger.

                     6-1: Exploring Scientific Notation: Part 3
                       Curriculum Standards: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

                     6-1: Exploring Scientific Notation: Close and Check
                       Curriculum Standards: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger.

                  Practice

                     6-1: Exploring Scientific Notation: Homework G
                       Curriculum Standards: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger.

                     6-1: Exploring Scientific Notation: Homework K
                       Curriculum Standards: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger.

                     6-1: Exploring Scientific Notation: Mixed Review

               Lesson 6-2: Using Scientific Notation to Describe Very Large Quantities

                  Interactive Learning

                     6-2: Using Scientific Notation to Describe Very Large Quantities: Launch
                       Curriculum Standards: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger.

                     6-2: Using Scientific Notation to Describe Very Large Quantities: Key Concept
                       Curriculum Standards: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger.

                     6-2: Using Scientific Notation to Describe Very Large Quantities: Part 1
                       Curriculum Standards: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger.

                     6-2: Using Scientific Notation to Describe Very Large Quantities: Part 2
                       Curriculum Standards: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger.

                     6-2: Using Scientific Notation to Describe Very Large Quantities: Part 3
                       Curriculum Standards: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger.

                     6-2: Using Scientific Notation to Describe Very Large Quantities: Close and Check
                       Curriculum Standards: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger.

                  Practice

                     6-2: Using Scientific Notation to Describe Very Large Quantities: Homework G
                       Curriculum Standards: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger.

                     6-2: Using Scientific Notation to Describe Very Large Quantities: Homework K
                       Curriculum Standards: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger.

                     6-2: Using Scientific Notation to Describe Very Large Quantities: Mixed Review

               Lesson 6-3: Using Scientific Notation to Describe Very Small Quantities

                  Interactive Learning

                     6-3: Using Scientific Notation to Describe Very Small Quantities: Launch
                       Curriculum Standards: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger.

                     6-3: Using Scientific Notation to Describe Very Small Quantities: Key Concept
                       Curriculum Standards: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger.

                     6-3: Using Scientific Notation to Describe Very Small Quantities: Part 1
                       Curriculum Standards: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger.

                     6-3: Using Scientific Notation to Describe Very Small Quantities: Part 2
                       Curriculum Standards: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger.

                     6-3: Using Scientific Notation to Describe Very Small Quantities: Part 3
                       Curriculum Standards: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger.

                     6-3: Using Scientific Notation to Describe Very Small Quantities: Close and Check
                       Curriculum Standards: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger.

                  Practice

                     6-3: Using Scientific Notation to Describe Very Small Quantities: Homework G
                       Curriculum Standards: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger.

                     6-3: Using Scientific Notation to Describe Very Small Quantities: Homework K
                       Curriculum Standards: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger.

                     6-3: Using Scientific Notation to Describe Very Small Quantities: Mixed Review

               Lesson 6-4: Operating with Numbers Expressed in Scientific Notation

                  Interactive Learning

                     6-4: Operating with Numbers Expressed in Scientific Notation: Launch
                       Curriculum Standards: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger.

                     6-4: Operating with Numbers Expressed in Scientific Notation: Part 1
                       Curriculum Standards: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

                     6-4: Operating with Numbers Expressed in Scientific Notation: Part 2
                       Curriculum Standards: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

                     6-4: Operating with Numbers Expressed in Scientific Notation: Part 3
                       Curriculum Standards: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

                     6-4: Operating with Numbers Expressed in Scientific Notation: Close and Check
                       Curriculum Standards: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

                  Practice

                     6-4: Operating with Numbers Expressed in Scientific Notation: Homework G
                       Curriculum Standards: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

                     6-4: Operating with Numbers Expressed in Scientific Notation: Homework K
                       Curriculum Standards: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

                     6-4: Operating with Numbers Expressed in Scientific Notation: Mixed Review

               Lesson 6-5: Problem Solving

                  Interactive Learning

                     6-5: Problem Solving: Launch
                       Curriculum Standards: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

                     6-5: Problem Solving: Part 1
                       Curriculum Standards: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

                     6-5: Problem Solving: Part 2
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

                     6-5: Problem Solving: Close and Check
                       Curriculum Standards: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

                  Practice

                     6-5: Problem Solving: Homework G
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

                     6-5: Problem Solving: Homework K
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

                     6-5: Problem Solving: Mixed Review

               Topic 6 Review

                  Interactive Learning

                     Topic 6: Scientific Notation: Vocabulary Review

                     Topic 6: Scientific Notation: Pull It All Together

                     Topic 6: Scientific Notation: Close

                  Practice

                     Topic 6: Scientific Notation: Review Homework
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger.

               Topic 6: Scientific Notation: Test
                 Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger.

            Unit I: Rational Numbers and Exponents: Test
              Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27. Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that the square root of 2 is irrational. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts. Apply properties of operations as strategies to multiply and divide rational numbers. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. Solve real-world and mathematical problems involving the four operations with rational numbers. Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., pi^2). For example, by truncating the decimal expansion of the square root of 2, show that the square root of 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

         Unit II: Proportionality and Linear Relationships

            Unit II: Proportionality and Linear Relationships: Enrichment Project

            Lesson i2-1: Addition and Multiplication Properties: Part 1

            Lesson i2-1: Addition and Multiplication Properties: Part 2

            Lesson i2-1: Addition and Multiplication Properties: Part 3

            Lesson i2-1: Addition and Multiplication Properties: Lesson Check

            i2-1 Journal

            i2-1 Practice

            Lesson i2-2: Distributive Property: Part 1

            Lesson i2-2: Distributive Property: Part 2

            Lesson i2-2: Distributive Property: Part 3

            Lesson i2-2: Distributive Property: Lesson Check

            i2-2 Journal

            i2-2 Practice

            Lesson i4-2: Estimating Quotients with 1-Digit Divisors: Part 1

            Lesson i4-2: Estimating Quotients with 1-Digit Divisors: Part 2

            Lesson i4-2: Estimating Quotients with 1-Digit Divisors: Part 3

            Lesson i4-2: Estimating Quotients with 1-Digit Divisors: Lesson Check

            i4-2 Journal

            i4-2 Practice

            Lesson i8-5: Dividing Decimals: Part 1

            Lesson i8-5: Dividing Decimals: Part 2

            Lesson i8-5: Dividing Decimals: Part 3

            Lesson i8-5: Dividing Decimals: Lesson Check

            i8-5 Journal

            i8-5 Practice

            Lesson i11-2: Multiplying Fractions: Part 1

            Lesson i11-2: Multiplying Fractions: Part 2

            Lesson i11-2: Multiplying Fractions: Part 3

            Lesson i11-2: Multiplying Fractions: Lesson Check

            i11-2 Journal

            i11-2 Practice

            Lesson i13-1: Ratios: Part 1

            Lesson i13-1: Ratios: Part 2

            Lesson i13-1: Ratios: Part 3

            Lesson i13-1: Ratios: Lesson Check

            i13-1 Journal

            i13-1 Practice
              Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

            Lesson i13-2: Equivalent Ratios: Part 1

            Lesson i13-2: Equivalent Ratios: Part 2

            Lesson i13-2: Equivalent Ratios: Part 3

            Lesson i13-2: Equivalent Ratios: Lesson Check

            i13-2 Journal

            i13-2 Practice

            Lesson i14-1: Unit Rates: Part 1

            Lesson i14-1: Unit Rates: Part 2

            Lesson i14-1: Unit Rates: Part 3

            Lesson i14-1: Unit Rates: Lesson Check

            i14-1 Journal

            i14-1 Practice
              Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

            Lesson i14-2: Converting Customary Measurements: Part 1

            Lesson i14-2: Converting Customary Measurements: Part 2

            Lesson i14-2: Converting Customary Measurements: Part 3

            Lesson i14-2: Converting Customary Measurements: Lesson Check

            i14-2 Journal

            i14-2 Practice

            Lesson i14-3: Converting Metric Measurements: Part 1

            Lesson i14-3: Converting Metric Measurements: Part 2

            Lesson i14-3: Converting Metric Measurements: Part 3

            Lesson i14-3: Converting Metric Measurements: Lesson Check

            i14-3 Journal

            i14-3 Practice

            Lesson i15-1: Graphing Ratios: Part 1

            Lesson i15-1: Graphing Ratios: Part 2

            Lesson i15-1: Graphing Ratios: Part 3

            Lesson i15-1: Graphing Ratios: Lesson Check

            i15-1 Journal

            i15-1 Practice

            Lesson i16-1: Understanding Percent: Part 1

            Lesson i16-1: Understanding Percent: Part 2

            Lesson i16-1: Understanding Percent: Part 3

            Lesson i16-1: Understanding Percent: Lesson Check

            i16-1 Journal

            i16-1 Practice

            Lesson i17-1: Finding a Percent of a Number: Part 1

            Lesson i17-1: Finding a Percent of a Number: Part 2

            Lesson i17-1: Finding a Percent of a Number: Part 3

            Lesson i17-1: Finding a Percent of a Number: Lesson Check

            i17-1 Journal

            i17-1 Practice

            Lesson i23-1: Order of Operations: Part 1

            Lesson i23-1: Order of Operations: Part 2

            Lesson i23-1: Order of Operations: Part 3

            Lesson i23-1: Order of Operations: Lesson Check

            i23-1 Journal

            i23-1 Practice

            Lesson i23-2: Variables and Expressions: Part 1

            Lesson i23-2: Variables and Expressions: Part 2

            Lesson i23-2: Variables and Expressions: Part 3

            Lesson i23-2: Variables and Expressions: Lesson Check

            i23-2 Journal

            i23-2 Practice

            Lesson i24-2: Equivalent Expressions: Part 1

            Lesson i24-2: Equivalent Expressions: Part 2

            Lesson i24-2: Equivalent Expressions: Part 3

            Lesson i24-2: Equivalent Expressions: Lesson Check

            i24-2 Journal

            i24-2 Practice

            Lesson i24-3: Simplifying Expressions: Part 1

            Lesson i24-3: Simplifying Expressions: Part 2

            Lesson i24-3: Simplifying Expressions: Part 3

            Lesson i24-3: Simplifying Expressions: Lesson Check

            i24-3 Journal

            i24-3 Practice

            Lesson i25-1: Writing Equations: Part 1

            Lesson i25-1: Writing Equations: Part 2

            Lesson i25-1: Writing Equations: Part 3

            Lesson i25-1: Writing Equations: Lesson Check

            i25-1 Journal

            i25-1 Practice

            Lesson i25-2: Principles of Solving Equations: Part 1

            Lesson i25-2: Principles of Solving Equations: Part 2

            Lesson i25-2: Principles of Solving Equations: Part 3

            Lesson i25-2: Principles of Solving Equations: Lesson Check

            i25-2 Journal

            i25-2 Practice

            Lesson i25-3: Solving Addition and Subtraction Equations: Part 1

            Lesson i25-3: Solving Addition and Subtraction Equations: Part 2

            Lesson i25-3: Solving Addition and Subtraction Equations: Part 3

            Lesson i25-3: Solving Addition and Subtraction Equations: Lesson Check

            i25-3 Journal

            i25-3 Practice

            Lesson i25-5: Solving Rational-Number Equations, Part 1: Part 1

            Lesson i25-5: Solving Rational-Number Equations, Part 1: Part 2

            Lesson i25-5: Solving Rational-Number Equations, Part 1: Part 3

            Lesson i25-5: Solving Rational-Number Equations, Part 1: Lesson Check

            i25-5 Journal

            i25-5 Practice

            Lesson i25-6: Solving Rational-Number Equations, Part 2: Part 1

            Lesson i25-6: Solving Rational-Number Equations, Part 2: Part 2

            Lesson i25-6: Solving Rational-Number Equations, Part 2: Part 3

            Lesson i25-6: Solving Rational-Number Equations, Part 2: Lesson Check

            i25-6 Journal

            i25-6 Practice

            Unit II: Proportionality and Linear Relationships: Readiness Assessment

            Topic 7: Ratios and Rates

               Topic 7: Ratios and Rates: Enrichment Project

               Lesson 7-1: Equivalent Ratios

                  Interactive Learning

                     7-1: Equivalent Ratios: Topic Opener

                     7-1: Equivalent Ratios: Launch
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                     7-1: Equivalent Ratios: Part 1
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                     7-1: Equivalent Ratios: Key Concept
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                     7-1: Equivalent Ratios: Part 2
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                     7-1: Equivalent Ratios: Part 3
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                     7-1: Equivalent Ratios: Close and Check
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                  Practice

                     7-1: Equivalent Ratios: Homework G
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                     7-1: Equivalent Ratios: Homework K
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                     7-1: Equivalent Ratios: Mixed Review

               Lesson 7-2: Unit Rates

                  Interactive Learning

                     7-2: Unit Rates: Launch
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                     7-2: Unit Rates: Key Concept
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                     7-2: Unit Rates: Part 1
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                     7-2: Unit Rates: Part 2
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                     7-2: Unit Rates: Part 3
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                     7-2: Unit Rates: Close and Check
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                  Practice

                     7-2: Unit Rates: Homework G
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                     7-2: Unit Rates: Homework K
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                     7-2: Unit Rates: Mixed Review

               Lesson 7-3: Ratios With Fractions

                  Interactive Learning

                     7-3: Ratios With Fractions: Launch
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                     7-3: Ratios With Fractions: Part 1
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                     7-3: Ratios With Fractions: Key Concept
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                     7-3: Ratios With Fractions: Part 2
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                     7-3: Ratios With Fractions: Part 3
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                     7-3: Ratios With Fractions: Close and Check
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                  Practice

                     7-3: Ratios With Fractions: Homework G
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                     7-3: Ratios With Fractions: Homework K
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                     7-3: Ratios With Fractions: Mixed Review

               Lesson 7-4: Unit Rates With Fractions

                  Interactive Learning

                     7-4: Unit Rates With Fractions: Launch
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                     7-4: Unit Rates With Fractions: Key Concept
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                     7-4: Unit Rates With Fractions: Part 1
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                     7-4: Unit Rates With Fractions: Part 2
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                     7-4: Unit Rates With Fractions: Part 3
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                     7-4: Unit Rates With Fractions: Close and Check
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                  Practice

                     7-4: Unit Rates With Fractions: Homework G
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                     7-4: Unit Rates With Fractions: Homework K
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                     7-4: Unit Rates With Fractions: Mixed Review

               Lesson 7-5: Problem Solving

                  Interactive Learning

                     7-5: Problem Solving: Launch
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                     7-5: Problem Solving: Part 1
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                     7-5: Problem Solving: Part 2
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                     7-5: Problem Solving: Part 3
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                     7-5: Problem Solving: Close and Check
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                  Practice

                     7-5: Problem Solving: Homework G
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                     7-5: Problem Solving: Homework K
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

                     7-5: Problem Solving: Mixed Review

               Topic 7 Review

                  Interactive Learning

                     Topic 7: Ratios and Rates: Vocabulary Review

                     Topic 7: Ratios and Rates: Pull It All Together

                     Topic 7: Ratios and Rates: Topic Close

                  Practice

                     Topic 7: Ratios and Rates: Review Homework
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

               Topic 7: Ratios and Rates: Test
                 Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

            Topic 8: Proportional Relationships

               Topic 8: Proportional Relationships: Enrichment Project

               Lesson 8-1: Proportional Relationships and Tables

                  Interactive Learning

                     8-1: Proportional Relationships and Tables: Topic Opener

                     8-1: Proportional Relationships and Tables: Launch
                       Curriculum Standards: Recognize and represent proportional relationships between quantities.

                     8-1: Proportional Relationships and Tables: Key Concept
                       Curriculum Standards: Recognize and represent proportional relationships between quantities.

                     8-1: Proportional Relationships and Tables: Part 1
                       Curriculum Standards: Recognize and represent proportional relationships between quantities.

                     8-1: Proportional Relationships and Tables: Part 2
                       Curriculum Standards: Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

                     8-1: Proportional Relationships and Tables: Part 3
                       Curriculum Standards: Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

                     8-1: Proportional Relationships and Tables: Close and Check
                       Curriculum Standards: Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

                  Practice

                     8-1: Proportional Relationships and Tables: Homework G
                       Curriculum Standards: Recognize and represent proportional relationships between quantities. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

                     8-1: Proportional Relationships and Tables: Homework K
                       Curriculum Standards: Recognize and represent proportional relationships between quantities. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

                     8-1: Proportional Relationships and Tables: Mixed Review
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

               Lesson 8-2: Proportional Relationships and Graphs

                  Interactive Learning

                     8-2: Proportional Relationships and Graphs: Launch
                       Curriculum Standards: Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

                     8-2: Proportional Relationships and Graphs: Key Concept
                       Curriculum Standards: Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

                     8-2: Proportional Relationships and Graphs: Part 1
                       Curriculum Standards: Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

                     8-2: Proportional Relationships and Graphs: Part 2
                       Curriculum Standards: Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

                     8-2: Proportional Relationships and Graphs: Part 3
                       Curriculum Standards: Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

                     8-2: Proportional Relationships and Graphs: Close and Check
                       Curriculum Standards: Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

                  Practice

                     8-2: Proportional Relationships and Graphs: Homework G
                       Curriculum Standards: Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

                     8-2: Proportional Relationships and Graphs: Homework K
                       Curriculum Standards: Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

                     8-2: Proportional Relationships and Graphs: Mixed Review
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

               Lesson 8-3: Constant of Proportionality

                  Interactive Learning

                     8-3: Constant of Proportionality: Launch
                       Curriculum Standards: Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

                     8-3: Constant of Proportionality: Key Concept
                       Curriculum Standards: Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

                     8-3: Constant of Proportionality: Part 1
                       Curriculum Standards: Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

                     8-3: Constant of Proportionality: Part 2
                       Curriculum Standards: Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

                     8-3: Constant of Proportionality: Part 3
                       Curriculum Standards: Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

                     8-3: Constant of Proportionality: Part 4
                       Curriculum Standards: Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

                     8-3: Constant of Proportionality: Close and Check
                       Curriculum Standards: Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

                  Practice

                     8-3: Constant of Proportionality: Homework G
                       Curriculum Standards: Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

                     8-3: Constant of Proportionality: Homework K
                       Curriculum Standards: Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

                     8-3: Constant of Proportionality: Mixed Review

               Lesson 8-4: Proportional Relationships and Equations

                  Interactive Learning

                     8-4: Proportional Relationships and Equations: Launch
                       Curriculum Standards: Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

                     8-4: Proportional Relationships and Equations: Key Concept
                       Curriculum Standards: Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

                     8-4: Proportional Relationships and Equations: Part 1
                       Curriculum Standards: Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

                     8-4: Proportional Relationships and Equations: Part 2
                       Curriculum Standards: Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

                     8-4: Proportional Relationships and Equations: Part 3
                       Curriculum Standards: Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

                     8-4: Proportional Relationships and Equations: Part 4
                       Curriculum Standards: Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

                     8-4: Proportional Relationships and Equations: Close and Check
                       Curriculum Standards: Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

                  Practice

                     8-4: Proportional Relationships and Equations: Homework G
                       Curriculum Standards: Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

                     8-4: Proportional Relationships and Equations: Homework K
                       Curriculum Standards: Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

                     8-4: Proportional Relationships and Equations: Mixed Review

               Lesson 8-5: Maps and Scale Drawings

                  Interactive Learning

                     8-5: Maps and Scale Drawings: Launch
                       Curriculum Standards: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

                     8-5: Maps and Scale Drawings: Key Concept
                       Curriculum Standards: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

                     8-5: Maps and Scale Drawings: Part 1
                       Curriculum Standards: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

                     8-5: Maps and Scale Drawings: Part 2
                       Curriculum Standards: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

                     8-5: Maps and Scale Drawings: Part 3
                       Curriculum Standards: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

                     8-5: Maps and Scale Drawings: Close and Check
                       Curriculum Standards: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

                  Practice

                     8-5: Maps and Scale Drawings: Homework G
                       Curriculum Standards: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

                     8-5: Maps and Scale Drawings: Homework K
                       Curriculum Standards: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

                     8-5: Maps and Scale Drawings: Mixed Review
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

               Lesson 8-6: Problem Solving

                  Interactive Learning

                     8-6: Problem Solving: Launch
                       Curriculum Standards: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

                     8-6: Problem Solving: Part 1
                       Curriculum Standards: Recognize and represent proportional relationships between quantities.

                     8-6: Problem Solving: Part 2
                       Curriculum Standards: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

                     8-6: Problem Solving: Part 3
                       Curriculum Standards: Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

                     8-6: Problem Solving: Close and Check
                       Curriculum Standards: Recognize and represent proportional relationships between quantities.

                  Practice

                     8-6: Problem Solving: Homework G
                       Curriculum Standards: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

                     8-6: Problem Solving: Homework K
                       Curriculum Standards: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

                     8-6: Problem Solving: Mixed Review
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

               Topic 8 Review

                  Interactive Learning

                     Topic 8: Proportional Relationships: Vocabulary Review

                     Topic 8: Proportional Relationships: Pull It All Together

                     Topic 8: Proportional Relationships: Topic Close

                  Practice

                     Topic 8: Proportional Relationships: Review Homework
                       Curriculum Standards: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. Recognize and represent proportional relationships between quantities. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

               Topic 8: Proportional Relationships: Test
                 Curriculum Standards: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. Recognize and represent proportional relationships between quantities. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

            Topic 9: Percents

               Topic 9: Percents: Enrichment Project

               Lesson 9-1: The Percent Equation

                  Interactive Learning

                     9-1: The Percent Equation: Topic Opener

                     9-1: The Percent Equation: Launch
                       Curriculum Standards: Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

                     9-1: The Percent Equation: Key Concept
                       Curriculum Standards: Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

                     9-1: The Percent Equation: Part 1
                       Curriculum Standards: Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

                     9-1: The Percent Equation: Part 2
                       Curriculum Standards: Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

                     9-1: The Percent Equation: Part 3
                       Curriculum Standards: Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

                     9-1: The Percent Equation: Close and Check
                       Curriculum Standards: Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

                  Practice

                     9-1: The Percent Equation: Homework G
                       Curriculum Standards: Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

                     9-1: The Percent Equation: Homework K
                       Curriculum Standards: Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

                     9-1: The Percent Equation: Mixed Review
                       Curriculum Standards: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. Solve real-world and mathematical problems involving the four operations with rational numbers. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

               Lesson 9-2: Using the Percent Equation

                  Interactive Learning

                     9-2: Using the Percent Equation: Launch
                       Curriculum Standards: Recognize and represent proportional relationships between quantities.

                     9-2: Using the Percent Equation: Key Concept
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     9-2: Using the Percent Equation: Part 1
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     9-2: Using the Percent Equation: Part 2
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     9-2: Using the Percent Equation: Part 3
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     9-2: Using the Percent Equation: Close and Check
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                  Practice

                     9-2: Using the Percent Equation: Homework G
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     9-2: Using the Percent Equation: Homework K
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     9-2: Using the Percent Equation: Mixed Review
                       Curriculum Standards: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. Solve real-world and mathematical problems involving the four operations with rational numbers. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

               Lesson 9-3: Simple Interest

                  Interactive Learning

                     9-3: Simple Interest: Launch
                       Curriculum Standards: Recognize and represent proportional relationships between quantities.

                     9-3: Simple Interest: Key Concept
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     9-3: Simple Interest: Part 1
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     9-3: Simple Interest: Part 2
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     9-3: Simple Interest: Part 3
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     9-3: Simple Interest: Close and Check
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                  Practice

                     9-3: Simple Interest: Homework G
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     9-3: Simple Interest: Homework K
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     9-3: Simple Interest: Mixed Review
                       Curriculum Standards: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Solve real-world and mathematical problems involving the four operations with rational numbers. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

               Lesson 9-4: Compound Interest

                  Interactive Learning

                     9-4: Compound Interest: Launch
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     9-4: Compound Interest: Part 1
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                     9-4: Compound Interest: Part 2
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                     9-4: Compound Interest: Key Concept
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                     9-4: Compound Interest: Part 3
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                     9-4: Compound Interest: Close and Check
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                  Practice

                     9-4: Compound Interest: Homework G
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                     9-4: Compound Interest: Homework K
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers.

                     9-4: Compound Interest: Mixed Review
                       Curriculum Standards: Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. Apply properties of operations as strategies to multiply and divide rational numbers. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

               Lesson 9-5: Percent Increase and Decrease

                  Interactive Learning

                     9-5: Percent Increase and Decrease: Launch
                       Curriculum Standards: Recognize and represent proportional relationships between quantities.

                     9-5: Percent Increase and Decrease: Key Concept
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     9-5: Percent Increase and Decrease: Part 1
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     9-5: Percent Increase and Decrease: Part 2
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     9-5: Percent Increase and Decrease: Part 3
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     9-5 Close and Check
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                  Practice

                     9-5: Percent Increase and Decrease: Homework G
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     9-5: Percent Increase and Decrease: Homework K
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     9-5: Percent Increase and Decrease: Mixed Review
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

               Lesson 9-6: Markups and Markdowns

                  Interactive Learning

                     9-6: Markups and Markdowns: Launch
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     9-6: Markups and Markdowns: Part 1
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     9-6: Markups and Markdowns: Part 2
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     9-6: Markups and Markdowns: Key Concept
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     9-6: Markups and Markdowns: Part 3
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     9-6: Markups and Markdowns: Close and Check
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                  Practice

                     9-6: Markups and Markdowns: Homework G
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     9-6: Markups and Markdowns: Homework K
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     9-6: Markups and Markdowns: Mixed Review
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers. Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

               Lesson 9-7: Problem Solving

                  Interactive Learning

                     9-7: Problem Solving: Launch
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     9-7: Problem Solving: Part 1
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     9-7: Problem Solving: Part 2
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     9-7: Problem Solving: Part 3
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     9-7: Problem Solving: Close and Check
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                  Practice

                     9-7: Problem Solving: Homework G
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     9-7: Problem Solving: Homework K
                       Curriculum Standards: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

                     9-7: Problem Solving: Mixed Review
                       Curriculum Standards: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

               Topic 9 Review

                  Interactive Learning

                     Topic 9: Percents: Vocabulary Review

                     Topic 9: Percents: Pull It All Together

                     Topic 9: Percents: Topic Close

                  Practice

                     Topic 9: Percents: Review Homework
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

               Topic 9: Percents: Test
                 Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

            Topic 10: Equivalent Expressions

               Topic 10: Equivalent Expressions: Enrichment Project

               Lesson 10-1: Expanding Algebraic Expressions

                  Interactive Learning

                     10-1: Expanding Algebraic Expressions: Topic Opener

                     10-1: Expanding Algebraic Expressions: Launch
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

                     10-1: Expanding Algebraic Expressions: Part 1
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

                     10-1: Expanding Algebraic Expressions: Key Concept
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

                     10-1: Expanding Algebraic Expressions: Part 2
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

                     10-1: Expanding Algebraic Expressions: Part 3
                       Curriculum Standards: Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'.

                     10-1: Expanding Algebraic Expressions: Close and Check
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

                  Practice

                     10-1: Expanding Algebraic Expressions: Homework G
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'.

                     10-1: Expanding Algebraic Expressions: Homework K
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'.

                     10-1: Expanding Algebraic Expressions: Mixed Review
                       Curriculum Standards: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Apply properties of operations as strategies to multiply and divide rational numbers. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

               Lesson 10-2: Factoring Algebraic Expressions

                  Interactive Learning

                     10-2: Factoring Algebraic Expressions: Launch
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

                     10-2: Factoring Algebraic Expressions: Part 1
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

                     10-2: Factoring Algebraic Expressions: Part 2
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

                     10-2: Factoring Algebraic Expressions: Part 3
                       Curriculum Standards: Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'.

                     10-2: Factoring Algebraic Expressions: Key Concept
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

                     10-2: Factoring Algebraic Expressions: Close and Check
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

                  Practice

                     10-2: Factoring Algebraic Expressions: Homework G
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'.

                     10-2: Factoring Algebraic Expressions: Homework K
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'.

                     10-2: Factoring Algebraic Expressions: Mixed Review
                       Curriculum Standards: Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts. Solve real-world and mathematical problems involving the four operations with rational numbers. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour. Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

               Lesson 10-3: Adding Algebraic Expressions

                  Interactive Learning

                     10-3: Adding Algebraic Expressions: Launch
                       Curriculum Standards: Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'.

                     10-3: Adding Algebraic Expressions: Part 1
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

                     10-3: Adding Algebraic Expressions: Part 2
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

                     10-3: Adding Algebraic Expressions: Key Concept
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

                     10-3: Adding Algebraic Expressions: Part 3
                       Curriculum Standards: Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'.

                     10-3: Adding Algebraic Expressions: Close and Check
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

                  Practice

                     10-3: Adding Algebraic Expressions: Homework G
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'.

                     10-3: Adding Algebraic Expressions: Homework K
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'.

                     10-3: Adding Algebraic Expressions: Mixed Review
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. Solve real-world and mathematical problems involving the four operations with rational numbers. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

               Lesson 10-4: Subtracting Algebraic Expressions

                  Interactive Learning

                     10-4: Subtracting Algebraic Expressions: Launch
                       Curriculum Standards: Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'.

                     10-4: Subtracting Algebraic Expressions: Key Concept
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

                     10-4: Subtracting Algebraic Expressions: Part 1
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

                     10-4: Subtracting Algebraic Expressions: Part 2
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

                     10-4: Subtracting Algebraic Expressions: Part 3
                       Curriculum Standards: Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'.

                     10-4: Subtracting Algebraic Expressions: Close and Check
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

                  Practice

                     10-4: Subtracting Algebraic Expressions: Homework G
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'.

                     10-4: Subtracting Algebraic Expressions: Homework K
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'.

                     10-4: Subtracting Algebraic Expressions: Mixed Review
                       Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

               Lesson 10-5: Problem Solving

                  Interactive Learning

                     10-5: Problem Solving: Launch
                       Curriculum Standards: Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'.

                     10-5: Problem Solving: Part 1
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

                     10-5: Problem Solving: Part 2
                       Curriculum Standards: Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'.

                     10-5: Problem Solving: Close and Check
                       Curriculum Standards: Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'.

                  Practice

                     10-5: Problem Solving: Homework G
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'.

                     10-5: Problem Solving: Homework K
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'.

                     10-5: Problem Solving: Mixed Review
                       Curriculum Standards: Solve real-world and mathematical problems involving the four operations with rational numbers. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

               Topic 10 Review

                  Interactive Learning

                     Topic 10: Equivalent Expressions: Vocabulary Review

                     Topic 10: Equivalent Expressions: Pull It All Together

                     Topic 10: Equivalent Expressions: Topic Close

                  Practice

                     Topic 10: Equivalent Expressions: Review Homework
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'.

               Topic 10: Equivalent Expressions: Test
                 Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'.

            Topic 11: Equations

               Topic 11: Equations: Enrichment Project

               Lesson 11-1: Solving Simple Equations

                  Interactive Learning

                     11-1: Solving Simple Equations: Topic Opener

                     11-1: Solving Simple Equations: Launch
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

                     11-1: Solving Simple Equations: Key Concept
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

                     11-1: Solving Simple Equations: Part 1
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

                     11-1 Key Concept
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

                     11-1: Solving Simple Equations: Part 2
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

                     11-1: Solving Simple Equations: Part 3
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

                     11-1: Solving Simple Equations: Close and Check
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

                  Practice

                     11-1: Solving Simple Equations: Homework G
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

                     11-1: Solving Simple Equations: Homework K
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

                     11-1: Solving Simple Equations: Mixed Review
                       Curriculum Standards: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Apply properties of operations as strategies to add and subtract rational numbers. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

               Lesson 11-2: Writing Two-Step Equations

                  Interactive Learning

                     11-2: Writing Two-Step Equations: Launch
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

                     11-2: Writing Two-Step Equations: Part 1
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

                     11-2: Writing Two-Step Equations: Part 2
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

                     11-2: Writing Two-Step Equations: Part 3
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

                     11-2: Writing Two-Step Equations: Close and Check
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

                  Practice

                     11-2: Writing Two-Step Equations: Homework G
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

                     11-2: Writing Two-Step Equations: Homework K
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

                     11-2: Writing Two-Step Equations: Mixed Review
                       Curriculum Standards: Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'. Recognize and represent proportional relationships between quantities. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

               Lesson 11-3: Solving Two-Step Equations

                  Interactive Learning

                     11-3: Solving Two-Step Equations: Launch
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

                     11-3: Solving Two-Step Equations: Part 1
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

                     11-3: Solving Two-Step Equations: Key Concept
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

                     11-3: Solving Two-Step Equations: Part 2
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

                     11-3: Solving Two-Step Equations: Part 3
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

                     11-3: Solving Two-Step Equations: Close and Check
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

                  Practice

                     11-3: Solving Two-Step Equations: Homework G
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

                     11-3: Solving Two-Step Equations: Homework K
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

                     11-3: Solving Two-Step Equations: Mixed Review
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

               Lesson 11-4: Solving Equations Using the Distributive Property

                  Interactive Learning

                     11-4: Solving Equations Using the Distributive Property: Launch
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

                     11-4: Solving Equations Using the Distributive Property: Part 1
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

                     11-4: Solving Equations Using the Distributive Property: Part 2
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

                     11-4: Solving Equations Using the Distributive Property: Part 3
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

                     11-4: Solving Equations Using the Distributive Property: Close and Check
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

                  Practice

                     11-4: Solving Equations Using the Distributive Property: Homework G
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

                     11-4: Solving Equations Using the Distributive Property: Homework K
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

                     11-4: Solving Equations Using the Distributive Property: Mixed Review
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'. Apply properties of operations as strategies to multiply and divide rational numbers.

               Lesson 11-5: Problem Solving

                  Interactive Learning

                     11-5: Problem Solving: Launch
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

                     11-5: Problem Solving: Part 1
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

                     11-5: Problem Solving: Part 2
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

                     11-5: Problem Solving: Part 3
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

                     11-5: Problem Solving: Close and Check
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

                  Practice

                     11-5: Problem Solving: Homework G
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

                     11-5: Problem Solving: Homework K
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

                     11-5: Problem Solving: Mixed Review
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

               Topic 11 Review

                  Interactive Learning

                     Topic 11: Equations: Vocabulary Review

                     Topic 11: Equations: Pull It All Together

                     Topic 11: Equations: Topic Close

                  Practice

                     Topic 11: Equations: Review Homework
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

               Topic 11: Equations: Test
                 Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

            Topic 12: Linear Equations in One Variable

               Topic 12: Linear Equations in One Variable: Enrichment Project

               Lesson 12-1: Solving Two-Step Equations

                  Interactive Learning

                     12-1: Solving Two-Step Equations: Topic Opener

                     12-1: Solving Two-Step Equations: Launch
                       Curriculum Standards: Solve linear equations in one variable.

                     12-1: Solving Two-Step Equations: Key Concept
                       Curriculum Standards: Solve linear equations in one variable.

                     12-1: Solving Two-Step Equations: Part 1
                       Curriculum Standards: Solve linear equations in one variable.

                     12-1: Solving Two-Step Equations: Part 2
                       Curriculum Standards: Solve linear equations in one variable.

                     12-1: Solving Two-Step Equations: Part 3
                       Curriculum Standards: Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

                     12-1: Solving Two-Step Equations: Close and Check
                       Curriculum Standards: Solve linear equations in one variable.

                  Practice

                     12-1: Solving Two-Step Equations: Homework G
                       Curriculum Standards: Solve linear equations in one variable. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

                     12-1: Solving Two-Step Equations: Homework K
                       Curriculum Standards: Solve linear equations in one variable. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

                     12-1: Solving Two-Step Equations: Mixed Review
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

               Lesson 12-2: Solving Equations with Variables on Both Sides

                  Interactive Learning

                     12-2: Solving Equations with Variables on Both Sides: Launch
                       Curriculum Standards: Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

                     12-2: Solving Equations with Variables on Both Sides: Key Concept
                       Curriculum Standards: Solve linear equations in one variable.

                     12-2: Solving Equations with Variables on Both Sides: Part 1
                       Curriculum Standards: Solve linear equations in one variable.

                     12-2: Solving Equations with Variables on Both Sides: Part 2
                       Curriculum Standards: Solve linear equations in one variable.

                     12-2: Solving Equations with Variables on Both Sides: Part 3
                       Curriculum Standards: Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

                     12-2: Solving Equations with Variables on Both Sides: Close and Check
                       Curriculum Standards: Solve linear equations in one variable.

                  Practice

                     12-2: Solving Equations with Variables on Both Sides: Homework G
                       Curriculum Standards: Solve linear equations in one variable. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

                     12-2: Solving Equations with Variables on Both Sides: Homework K
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

                     12-2: Solving Equations with Variables on Both Sides: Mixed Review

               Lesson 12-3: Solving Equations Using the Distributive Property

                  Interactive Learning

                     12-3: Solving Equations Using the Distributive Property: Launch
                       Curriculum Standards: Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

                     12-3: Solving Equations Using the Distributive Property: Part 1
                       Curriculum Standards: Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

                     12-3: Solving Equations Using the Distributive Property: Part 2
                       Curriculum Standards: Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

                     12-3: Solving Equations Using the Distributive Property: Part 3
                       Curriculum Standards: Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

                     12-3: Solving Equations Using the Distributive Property: Close and Check
                       Curriculum Standards: Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

                  Practice

                     12-3: Solving Equations Using the Distributive Property: Homework G
                       Curriculum Standards: Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

                     12-3: Solving Equations Using the Distributive Property: Homework K
                       Curriculum Standards: Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

                     12-3: Solving Equations Using the Distributive Property: Mixed Review
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'. Solve real-world and mathematical problems involving the four operations with rational numbers.

               Lesson 12-4: Solutions – One, None, or Infinitely Many

                  Interactive Learning

                     12-4: Solutions – One, None, or Infinitely Many: Launch
                       Curriculum Standards: Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

                     12-4: Solutions – One, None, or Infinitely Many: Key Concept
                       Curriculum Standards: Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

                     12-4: Solutions – One, None, or Infinitely Many: Part 1
                       Curriculum Standards: Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

                     12-4: Solutions – One, None, or Infinitely Many: Part 2
                       Curriculum Standards: Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

                     12-4: Solutions – One, None, or Infinitely Many: Part 3
                       Curriculum Standards: Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

                     12-4: Solutions – One, None, or Infinitely Many: Close and Check
                       Curriculum Standards: Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

                  Practice

                     12-4: Solutions – One, None, or Infinitely Many: Homework G
                       Curriculum Standards: Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

                     12-4: Solutions – One, None, or Infinitely Many: Homework K
                       Curriculum Standards: Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

                     12-4: Solutions – One, None, or Infinitely Many: Mixed Review
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

               Lesson 12-5: Problem Solving

                  Interactive Learning

                     12-5: Problem Solving: Launch
                       Curriculum Standards: Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

                     12-5: Problem Solving: Part 1
                       Curriculum Standards: Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

                     12-5: Problem Solving: Part 2
                       Curriculum Standards: Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

                     12-5: Problem Solving: Part 3
                       Curriculum Standards: Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

                     12-5: Problem Solving: Close and Check
                       Curriculum Standards: Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

                  Practice

                     12-5: Problem Solving: Homework G
                       Curriculum Standards: Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

                     12-5: Problem Solving: Homework K
                       Curriculum Standards: Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

                     12-5: Problem Solving: Mixed Review
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts. Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

               Topic 12 Review

                  Interactive Learning

                     Topic 12: Linear Equations in One Variable: Vocabulary Review

                     Topic 12 Pull It All Together

                     Topic 12: Linear Equations in One Variable: Topic Close

                  Practice

                     Topic 12: Linear Equations in One Variable: Review Homework
                       Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

               Topic 12: Linear Equations in One Variable: Test
                 Curriculum Standards: Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

            Topic 13: Inequalities

               Topic 13: Inequalities: Enrichment Project

               Lesson 13-1: Solving Inequalities Using Addition or Subtraction

                  Interactive Learning

                     13-1: Solving Inequalities Using Addition or Subtraction: Topic Opener

                     13-1: Solving Inequalities Using Addition or Subtraction: Launch
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                     13-1: Solving Inequalities Using Addition or Subtraction: Part 1
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                     13-1: Solving Inequalities Using Addition or Subtraction: Key Concept
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                     13-1: Solving Inequalities Using Addition or Subtraction: Part 2
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                     13-1: Solving Inequalities Using Addition or Subtraction: Part 3
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                     13-1: Solving Inequalities Using Addition or Subtraction: Close and Check
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                  Practice

                     13-1: Solving Inequalities Using Addition or Subtraction: Homework G
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                     13-1: Solving Inequalities Using Addition or Subtraction: Homework K
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                     13-1: Solving Inequalities Using Addition or Subtraction: Mixed Review
                       Curriculum Standards: Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Apply properties of operations as strategies to add and subtract rational numbers.

               Lesson 13-2: Solving Inequalities Using Multiplication or Division

                  Interactive Learning

                     13-2: Solving Inequalities Using Multiplication or Division: Launch
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                     13-2: Solving Inequalities Using Multiplication or Division: Key Concept
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                     13-2: Solving Inequalities Using Multiplication or Division: Part 1
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                     13-2: Solving Inequalities Using Multiplication or Division: Key Concept
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                     13-2: Solving Inequalities Using Multiplication or Division: Part 2
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                     13-2: Solving Inequalities Using Multiplication or Division: Part 3
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                     13-2: Solving Inequalities Using Multiplication or Division: Close and Check
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                  Practice

                     13-2: Solving Inequalities Using Multiplication or Division: Homework G
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                     13-2: Solving Inequalities Using Multiplication or Division: Homework K
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                     13-2: Solving Inequalities Using Multiplication or Division: Mixed Review
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts.

               Lesson 13-3: Solving Two-Step Inequalities

                  Interactive Learning

                     13-3: Solving Two-Step Inequalities: Launch
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                     13-3: Solving Two-Step Inequalities: Part 1
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                     13-3: Solving Two-Step Inequalities: Key Concept
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                     13-3: Solving Two-Step Inequalities: Part 2
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                     13-3: Solving Two-Step Inequalities: Part 3
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                     13-3: Solving Two-Step Inequalities: Close and Check
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                  Practice

                     13-3: Solving Two-Step Inequalities: Homework G
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                     13-3: Solving Two-Step Inequalities: Homework K
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                     13-3: Solving Two-Step Inequalities: Mixed Review
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

               Lesson 13-4: Solving Multi-Step Inequalities

                  Interactive Learning

                     13-4: Solving Multi-Step Inequalities: Launch
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                     13-4: Solving Multi-Step Inequalities: Part 1
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                     13-4: Solving Multi-Step Inequalities: Part 2
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                     13-4: Solving Multi-Step Inequalities: Part 3
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                     13-4: Solving Multi-Step Inequalities: Close and Check
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                  Practice

                     13-4: Solving Multi-Step Inequalities: Homework G
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                     13-4: Solving Multi-Step Inequalities: Homework K
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                     13-4: Solving Multi-Step Inequalities: Mixed Review
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Solve linear equations in one variable. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

               Lesson 13-5: Problem Solving

                  Interactive Learning

                     13-5: Problem Solving: Launch
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                     13-5: Problem Solving: Part 1
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                     13-5: Problem Solving: Part 2
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                     13-5: Problem Solving: Part 3
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                     13-5: Problem Solving: Close and Check
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                  Practice

                     13-5: Problem Solving: Homework G
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                     13-5: Problem Solving: Homework K
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

                     13-5: Problem Solving: Mixed Review
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Solve linear equations in one variable. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

               Topic 13 Review

                  Interactive Learning

                     Topic 13: Inequalities: Vocabulary Review

                     Topic 13: Inequalities: Pull It All Together

                     Topic 13: Inequalities: Topic Close

                  Practice

                     Topic 13: Inequalities: Review Homework
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

               Topic 13: Inequalities: Test
                 Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

            Topic 14: Proportional Relationships, Lines, and Linear Equations

               Topic 14: Proportional Relationships, Lines, and Linear Equations: Enrichment Project

               Lesson 14-1: Graphing Proportional Relationships

                  Interactive Learning

                     14-1: Graphing Proportional Relationships: Topic Opener

                     14-1: Graphing Proportional Relationships: Launch
                       Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

                     14-1: Graphing Proportional Relationships: Part 1
                       Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

                     14-1: Graphing Proportional Relationships: Key Concept
                       Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

                     14-1: Graphing Proportional Relationships: Part 2
                       Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

                     14-1: Graphing Proportional Relationships: Part 3
                       Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

                     14-1: Graphing Proportional Relationships: Close and Check
                       Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

                  Practice

                     14-1: Graphing Proportional Relationships: Homework G
                       Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

                     14-1: Graphing Proportional Relationships: Homework K
                       Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

                     14-1: Graphing Proportional Relationships: Mixed Review
                       Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

               Lesson 14-2: Linear Equations: y = mx

                  Interactive Learning

                     14-2: Linear Equations: y = mx: Launch
                       Curriculum Standards: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

                     14-2: Linear Equations: y = mx: Part 1
                       Curriculum Standards: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

                     14-2: Linear Equations: y = mx: Key Concept
                       Curriculum Standards: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

                     14-2: Linear Equations: y = mx: Part 2
                       Curriculum Standards: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

                     14-2: Linear Equations: y = mx: Part 3
                       Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

                     14-2: Linear Equations: y = mx: Close and Check
                       Curriculum Standards: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

                  Practice

                     14-2: Linear Equations: y = mx: Homework G
                       Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

                     14-2: Linear Equations: y = mx: Homework K
                       Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

                     14-2: Linear Equations: y = mx: Mixed Review
                       Curriculum Standards: Solve linear equations in one variable. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

               Lesson 14-3: The Slope of a Line

                  Interactive Learning

                     14-3: The Slope of a Line: Launch
                       Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

                     14-3: The Slope of a Line: Part 1
                       Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

                     14-3: The Slope of a Line: Part 2
                       Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

                     14-3: The Slope of a Line: Key Concept
                       Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

                     14-3: The Slope of a Line: Part 3
                       Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

                     14-3: The Slope of a Line: Close and Check
                       Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

                  Practice

                     14-3: The Slope of a Line: Homework G
                       Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

                     14-3: The Slope of a Line: Homework K
                       Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

                     14-3: The Slope of a Line: Mixed Review
                       Curriculum Standards: Solve linear equations in one variable. Recognize and represent proportional relationships between quantities. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

               Lesson 14-4: Unit Rates and Slope

                  Interactive Learning

                     14-4: Unit Rates and Slope: Launch
                       Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

                     14-4: Unit Rates and Slope: Key Concept
                       Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

                     14-4: Unit Rates and Slope: Part 1
                       Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

                     14-4: Unit Rates and Slope: Part 2
                       Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

                     14-4: Unit Rates and Slope: Part 3
                       Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

                     14-4: Unit Rates and Slope: Close and Check
                       Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

                  Practice

                     14-4: Unit Rates and Slope: Homework G
                       Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

                     14-4: Unit Rates and Slope: Homework K
                       Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

                     14-4: Unit Rates and Slope: Mixed Review
                       Curriculum Standards: Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour. Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

               Lesson 14-5: The y-intercept of a Line

                  Interactive Learning

                     14-5: The y-intercept of a Line: Launch
                       Curriculum Standards: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

                     14-5: The y-intercept of a Line: Key Concept
                       Curriculum Standards: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

                     14-5: The y-intercept of a Line: Part 1
                       Curriculum Standards: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

                     14-5: The y-intercept of a Line: Part 2
                       Curriculum Standards: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

                     14-5: The y-intercept of a Line: Part 3
                       Curriculum Standards: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

                     14-5: The y-intercept of a Line: Close and Check
                       Curriculum Standards: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

                  Practice

                     14-5: The y-intercept of a Line: Homework G
                       Curriculum Standards: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

                     14-5: The y-intercept of a Line: Homework K
                       Curriculum Standards: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

                     14-5: The y-intercept of a Line: Mixed Review
                       Curriculum Standards: Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

               Lesson 14-6: Linear Equations: y = mx + b

                  Interactive Learning

                     14-6: Linear Equations: y = mx + b: Launch
                       Curriculum Standards: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

                     14-6: Linear Equations: y = mx + b: Part 1
                       Curriculum Standards: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

                     14-6: Linear Equations: y = mx + b: Part 2
                       Curriculum Standards: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

                     14-6: Linear Equations: y = mx + b: Part 3
                       Curriculum Standards: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

                     14-6: Linear Equations: y = mx + b: Key Concept
                       Curriculum Standards: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

                     14-6: Linear Equations: y = mx + b: Close and Check
                       Curriculum Standards: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

                  Practice

                     14-6: Linear Equations: y = mx + b: Homework G
                       Curriculum Standards: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

                     14-6: Linear Equations: y = mx + b: Homework K
                       Curriculum Standards: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

                     14-6: Linear Equations: y = mx + b: Mixed Review
                       Curriculum Standards: Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

               Lesson 14-7: Problem Solving

                  Interactive Learning

                     14-7: Problem Solving: Launch
                       Curriculum Standards: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

                     14-7: Problem Solving: Part 1
                       Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

                     14-7: Problem Solving: Part 2
                       Curriculum Standards: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

                     14-7: Problem Solving: Close and Check
                       Curriculum Standards: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

                  Practice

                     14-7: Problem Solving: Homework G
                       Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

                     14-7: Problem Solving: Homework K
                       Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

                     14-7: Problem Solving: Mixed Review
                       Curriculum Standards: Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour. Recognize and represent proportional relationships between quantities. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

               Topic 14 Review

                  Interactive Learning

                     Topic 14: Proportional Relationships, Lines, and Linear Equations: Vocabulary Review

                     Topic 14: Proportional Relationships, Lines, and Linear Equations: Pull It All Together

                     Topic 14: Proportional Relationships, Lines, and Linear Equations: Topic Close

                  Practice

                     Topic 14: Proportional Relationships, Lines, and Linear Equations: Review Homework
                       Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

               Topic 14: Proportional Relationships, Lines, and Linear Equations: Test
                 Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

            Unit II: Proportionality and Linear Relationships: Test
              Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. Solve real-world and mathematical problems involving the four operations with rational numbers. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

         Unit III: Introduction to Sampling and Inference

            Unit III: Introduction to Sampling and Inference: Enrichment Project

            Lesson i11-1: Multiplying a Whole Number and a Fraction: Part 1

            Lesson i11-1: Multiplying a Whole Number and a Fraction: Part 2

            Lesson i11-1: Multiplying a Whole Number and a Fraction: Part 3

            i11-1 Journal

            i11-1 Practice

            Lesson i13-1: Ratios: Part 1

            Lesson i13-1: Ratios: Part 2

            Lesson i13-1: Ratios: Part 3

            Lesson i13-1: Ratios: Lesson Check

            i13-1 Journal

            i13-1 Practice

            Lesson i16-1: Understanding Percent: Part 1

            Lesson i16-1: Understanding Percent: Part 2

            Lesson i16-1: Understanding Percent: Part 3

            Lesson i16-1: Understanding Percent: Lesson Check

            i16-1 Journal

            i16-1 Practice

            Lesson i16-2: Estimating Percent: Part 1

            Lesson i16-2: Estimating Percent: Part 2

            Lesson i16-2: Estimating Percent: Part 3

            Lesson i16-2: Estimating Percent: Lesson Check

            i16-2 Journal

            i16-2 Practice

            Lesson i17-1: Finding a Percent of a Number: Part 1

            Lesson i17-1: Finding a Percent of a Number: Part 2

            Lesson i17-1: Finding a Percent of a Number: Part 3

            Lesson i17-1: Finding a Percent of a Number: Lesson Check

            i17-1 Journal

            i17-1 Practice

            Lesson i17-2: Finding a Percent: Part 1

            Lesson i17-2: Finding a Percent: Part 2

            Lesson i17-2: Finding a Percent: Part 3

            Lesson i17-2: Finding a Percent: Lesson Check

            i17-2 Journal

            i17-2 Practice

            Lesson i17-3: Finding the Whole Given a Percent: Part 1

            Lesson i17-3: Finding the Whole Given a Percent: Part 2

            Lesson i17-3: Finding the Whole Given a Percent: Part 3

            Lesson i17-3: Finding the Whole Given a Percent: Lesson Check

            i17-3 Journal

            i17-3 Practice

            Lesson i8-2: Multiplying Decimals: Part 1

            Lesson i8-2: Multiplying Decimals: Part 2

            Lesson i8-2: Multiplying Decimals: Part 3

            Lesson i8-2: Multiplying Decimals: Lesson Check

            i18-2 Journal

            i8-2 Practice

            Lesson i9-1: Equivalent Fractions: Part 1

            Lesson i9-1: Equivalent Fractions: Part 2

            Lesson i9-1: Equivalent Fractions: Part 3

            Lesson i9-1: Equivalent Fractions: Lesson Check

            i9-1 Journal

            i9-1 Practice

            Lesson i9-2: Fractions in Simplest Form: Part 1

            Lesson i9-2: Fractions in Simplest Form: Part 2

            Lesson i9-2: Fractions in Simplest Form: Part 3

            Lesson i9-2: Fractions in Simplest Form: Lesson Check

            i9-2 Journal

            i9-2 Practice

            Lesson i9-3: Comparing and Ordering Fractions: Part 1

            Lesson i9-3: Comparing and Ordering Fractions: Part 2

            Lesson i9-3: Comparing and Ordering Fractions: Part 3

            Lesson i9-3: Comparing and Ordering Fractions: Lesson Check

            i9-3 Journal

            i9-3 Practice

            Lesson i9-5: Fractions and Decimals: Part 1

            Lesson i9-5: Fractions and Decimals: Part 2

            Lesson i9-5: Fractions and Decimals: Part 3

            Lesson i9-5: Fractions and Decimals: Lesson Check

            i9-5 Journal

            i9-5 Practice

            Lesson i11-1: Multiplying a Whole Number and a Fraction: Lesson Check

            Unit III: Introduction to Sampling and Inference: Readiness Assessment

            Topic 15: Sampling

               Topic 15: Sampling: Enrichment Project

               Lesson 15-1: Populations and Samples

                  Interactive Learning

                     Lesson 15-1: Populations and Samples: Topic Opener

                     15-1: Populations and Samples: Launch
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-1: Populations and Samples: Part 1
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-1: Populations and Samples: Part 2
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-1: Populations and Samples: Key Concept
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-1: Populations and Samples: Part 3
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-1: Populations and Samples: Close and Check
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                  Practice

                     15-1: Populations and Samples: Homework G
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-1: Populations and Samples: Homework K
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-1: Populations and Samples: Mixed Review
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. Solve linear equations in one variable. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Solve real-world and mathematical problems involving the four operations with rational numbers. Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

               Lesson 15-2: Estimating a Population

                  Interactive Learning

                     15-2: Estimating a Population: Launch
                       Curriculum Standards: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

                     15-2: Estimating a Population: Key Concept
                       Curriculum Standards: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

                     15-2: Estimating a Population: Part 1
                       Curriculum Standards: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

                     15-2: Estimating a Population: Part 2
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-2: Estimating a Population: Part 3
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-2: Estimating a Population: Close and Check
                       Curriculum Standards: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

                  Practice

                     15-2: Estimating a Population: Homework G
                       Curriculum Standards: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-2: Estimating a Population: Homework K
                       Curriculum Standards: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-2: Estimating a Population: Mixed Review
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. Solve linear equations in one variable. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Solve real-world and mathematical problems involving the four operations with rational numbers. Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

               Lesson 15-3: Convenience Sampling

                  Interactive Learning

                     15-3: Convenience Sampling: Launch
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-3: Convenience Sampling: Key Concept
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-3: Convenience Sampling: Part 1
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-3: Convenience Sampling: Part 2
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-3: Convenience Sampling: Part 3
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-3: Convenience Sampling: Close and Check
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                  Practice

                     15-3: Convenience Sampling: Homework G
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-3: Convenience Sampling: Homework K
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-3: Convenience Sampling: Mixed Review
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

               Lesson 15-4: Systematic Sampling

                  Interactive Learning

                     15-4: Systematic Sampling: Launch
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-4: Systematic Sampling: Key Concept
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-4: Systematic Sampling: Part 1
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-4: Systematic Sampling: Part 2
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-4: Systematic Sampling: Part 3
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-4: Systematic Sampling: Close and Check
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                  Practice

                     15-4: Systematic Sampling: Homework G
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-4: Systematic Sampling: Homework K
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-4: Systematic Sampling: Mixed Review
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts.

               Lesson 15-5: Simple Random Sampling

                  Interactive Learning

                     15-5: Simple Random Sampling: Launch
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-5: Simple Random Sampling: Key Concept
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-5: Simple Random Sampling: Part 1
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-5: Simple Random Sampling: Part 2
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-5: Simple Random Sampling: Part 3
                       Curriculum Standards: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

                     15-5: Simple Random Sampling: Close and Check
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                  Practice

                     15-5: Simple Random Sampling: Homework G
                       Curriculum Standards: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-5: Simple Random Sampling: Homework K
                       Curriculum Standards: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-5: Simple Random Sampling: Mixed Review
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

               Lesson 15-6: Comparing Sampling Methods

                  Interactive Learning

                     15-6: Comparing Sampling Methods: Launch
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-6: Comparing Sampling Methods: Key Concept
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-6: Comparing Sampling Methods: Part 1
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-6: Comparing Sampling Methods: Part 2
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-6: Comparing Sampling Methods: Part 3
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-6: Comparing Sampling Methods: Close and Check
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                  Practice

                     15-6: Comparing Sampling Methods: Homework G
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-6: Comparing Sampling Methods: Homework K
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-6: Comparing Sampling Methods: Mixed Review
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

               Lesson 15-7: Problem Solving

                  Interactive Learning

                     15-7: Problem Solving: Launch
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-7: Problem Solving: Part 1
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-7: Problem Solving: Part 2
                       Curriculum Standards: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

                     15-7: Problem Solving: Part 3
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-7: Problem Solving: Close and Check
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                  Practice

                     15-7: Problem Solving: Homework G
                       Curriculum Standards: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-7: Problem Solving: Homework K
                       Curriculum Standards: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     15-7: Problem Solving: Mixed Review
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

               Topic 15 Review

                  Interactive Learning

                     Topic 15: Sampling: Vocabulary Review

                     Topic 15: Sampling: Pull It All Together

                     Topic 15: Sampling: Topic Close

                  Practice

                     Topic 15: Sampling: Review Homework
                       Curriculum Standards: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

               Topic 15: Sampling: Test
                 Curriculum Standards: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

            Topic 16: Comparing Two Populations

               Topic 16: Comparing Two Populations: Enrichment Project

               Lesson 16-1: Statistical Measures

                  Interactive Learning

                     16-1: Statistical Measures: Topic Opener

                     16-1: Statistical Measures: Launch
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     16-1: Statistical Measures: Part 1
                       Curriculum Standards: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

                     16-1: Statistical Measures: Part 2
                       Curriculum Standards: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

                     16-1: Statistical Measures: Part 3
                       Curriculum Standards: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

                     16-1: Statistical Measures: Close and Check
                       Curriculum Standards: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

                  Practice

                     16-1: Statistical Measures: Homework G
                       Curriculum Standards: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

                     16-1: Statistical Measures: Homework K
                       Curriculum Standards: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

                     16-1: Statistical Measures: Mixed Review
                       Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Solve real-world and mathematical problems involving the four operations with rational numbers. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

               Lesson 16-2: Multiple Populations and Inferences

                  Interactive Learning

                     16-2: Multiple Populations and Inferences: Launch
                       Curriculum Standards: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

                     16-2: Multiple Populations and Inferences: Part 1
                       Curriculum Standards: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.

                     16-2: Multiple Populations and Inferences: Part 2
                       Curriculum Standards: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.

                     16-2: Multiple Populations and Inferences: Key Concept
                       Curriculum Standards: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

                     16-2: Multiple Populations and Inferences: Part 3
                       Curriculum Standards: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

                     16-2: Multiple Populations and Inferences: Close and Check
                       Curriculum Standards: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.

                  Practice

                     16-2: Multiple Populations and Inferences: Homework G
                       Curriculum Standards: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.

                     16-2: Multiple Populations and Inferences: Homework K
                       Curriculum Standards: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.

                     16-2: Multiple Populations and Inferences: Mixed Review
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Solve real-world and mathematical problems involving the four operations with rational numbers. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

               Lesson 16-3: Using Measures of Center

                  Interactive Learning

                     16-3: Using Measures of Center: Launch
                       Curriculum Standards: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

                     16-3: Using Measures of Center: Key Concept
                       Curriculum Standards: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

                     16-3: Using Measures of Center: Part 1
                       Curriculum Standards: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

                     16-3: Using Measures of Center: Part 2
                       Curriculum Standards: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

                     16-3: Using Measures of Center: Part 3
                       Curriculum Standards: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

                     16-3: Using Measures of Center: Close and Check
                       Curriculum Standards: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

                  Practice

                     16-3: Using Measures of Center: Homework G
                       Curriculum Standards: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

                     16-3: Using Measures of Center: Homework K
                       Curriculum Standards: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

                     16-3: Using Measures of Center: Mixed Review
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

               Lesson 16-4: Using Measures of Variability

                  Interactive Learning

                     16-4: Using Measures of Variability: Launch
                       Curriculum Standards: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

                     16-4: Using Measures of Variability: Key Concept
                       Curriculum Standards: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

                     16-4: Using Measures of Variability: Part 1
                       Curriculum Standards: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

                     16-4: Using Measures of Variability: Part 2
                       Curriculum Standards: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

                     16-4: Using Measures of Variability: Part 3
                       Curriculum Standards: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

                     16-4: Using Measures of Variability: Close and Check
                       Curriculum Standards: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

                  Practice

                     16-4: Using Measures of Variability: Homework G
                       Curriculum Standards: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

                     16-4: Using Measures of Variability: Homework K
                       Curriculum Standards: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

                     16-4: Using Measures of Variability: Mixed Review
                       Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., pi^2). For example, by truncating the decimal expansion of the square root of 2, show that the square root of 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

               Lesson 16-5: Exploring Overlap in Data Sets

                  Interactive Learning

                     16-5: Exploring Overlap in Data Sets: Launch
                       Curriculum Standards: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

                     16-5: Exploring Overlap in Data Sets: Part 1
                       Curriculum Standards: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.

                     16-5: Exploring Overlap in Data Sets: Key Concept
                       Curriculum Standards: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.

                     16-5: Exploring Overlap in Data Sets: Part 2
                       Curriculum Standards: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.

                     16-5: Exploring Overlap in Data Sets: Part 3
                       Curriculum Standards: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.

                     16-5: Exploring Overlap in Data Sets: Close and Check
                       Curriculum Standards: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.

                  Practice

                     16-5: Exploring Overlap in Data Sets: Homework G
                       Curriculum Standards: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.

                     16-5: Exploring Overlap in Data Sets: Homework K
                       Curriculum Standards: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.

                     16-5: Exploring Overlap in Data Sets: Mixed Review
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

               Lesson 16-6: Problem Solving

                  Interactive Learning

                     16-6: Problem Solving: Launch
                       Curriculum Standards: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

                     16-6: Problem Solving: Part 1
                       Curriculum Standards: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

                     16-6: Problem Solving: Part 2
                       Curriculum Standards: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

                     16-6: Problem Solving: Close and Check
                       Curriculum Standards: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

                  Practice

                     16-6: Problem Solving: Homework G
                       Curriculum Standards: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

                     16-6: Problem Solving: Homework K
                       Curriculum Standards: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

                     16-6: Problem Solving: Mixed Review
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

               Topic 16 Review

                  Interactive Learning

                     Topic 16: Comparing Two Populations: Vocabulary Review

                     Topic 16: Comparing Two Populations: Pull It All Together

                     Topic 16: Comparing Two Populations: Topic Close

                  Practice

                     Topic 16: Comparing Two Populations: Review Homework
                       Curriculum Standards: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

               Topic 16: Comparing Two Populations: Test
                 Curriculum Standards: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

            Topic 17: Probability Concepts

               Topic 17: Probability Concepts: Enrichment Project

               Lesson 17-1: Likelihood and Probability

                  Interactive Learning

                     17-1: Likelihood and Probability: Topic Opener

                     17-1: Likelihood and Probability: Launch
                       Curriculum Standards: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

                     17-1: Likelihood and Probability: Part 1
                       Curriculum Standards: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

                     17-1: Likelihood and Probability: Key Concept
                       Curriculum Standards: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

                     17-1: Likelihood and Probability: Part 2
                       Curriculum Standards: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

                     17-1: Likelihood and Probability: Part 3
                       Curriculum Standards: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.

                     17-1: Likelihood and Probability: Close and Check
                       Curriculum Standards: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

                  Practice

                     17-1: Likelihood and Probability: Homework G
                       Curriculum Standards: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.

                     17-1: Likelihood and Probability: Homework K
                       Curriculum Standards: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.

                     17-1: Likelihood and Probability: Mixed Review
                       Curriculum Standards: Solve linear equations in one variable. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. Recognize and represent proportional relationships between quantities. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

               Lesson 17-2: Sample Space

                  Interactive Learning

                     17-2: Sample Space: Launch
                       Curriculum Standards: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

                     17-2: Sample Space: Part 1
                       Curriculum Standards: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

                     17-2: Sample Space: Part 2
                       Curriculum Standards: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

                     17-2: Sample Space: Part 3
                       Curriculum Standards: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

                     17-2: Sample Space: Key Concept
                       Curriculum Standards: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

                     17-2: Sample Space: Close and Check
                       Curriculum Standards: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

                  Practice

                     17-2: Sample Space: Homework G
                       Curriculum Standards: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

                     17-2: Sample Space: Homework K
                       Curriculum Standards: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

                     17-2: Sample Space: Mixed Review
                       Curriculum Standards: Solve linear equations in one variable. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

               Lesson 17-3: Relative Frequency and Experimental Probability

                  Interactive Learning

                     17-3: Relative Frequency and Experimental Probability: Launch
                       Curriculum Standards: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.

                     17-3: Relative Frequency and Experimental Probability: Part 1
                       Curriculum Standards: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.

                     17-3: Relative Frequency and Experimental Probability: Key Concept
                       Curriculum Standards: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.

                     17-3: Relative Frequency and Experimental Probability: Part 2
                       Curriculum Standards: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.

                     17-3: Relative Frequency and Experimental Probability: Close and Check
                       Curriculum Standards: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.

                  Practice

                     17-3: Relative Frequency and Experimental Probability: Homework G
                       Curriculum Standards: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.

                     17-3: Relative Frequency and Experimental Probability: Homework K
                       Curriculum Standards: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.

                     17-3: Relative Frequency and Experimental Probability: Mixed Review
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

               Lesson 17-4: Theoretical Probability

                  Interactive Learning

                     17-4: Theoretical Probability: Launch
                       Curriculum Standards: Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.

                     17-4: Theoretical Probability: Key Concept
                       Curriculum Standards: Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.

                     17-4: Theoretical Probability: Part 1
                       Curriculum Standards: Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.

                     17-4: Theoretical Probability: Part 2
                       Curriculum Standards: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

                     17-4: Theoretical Probability: Part 3
                       Curriculum Standards: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

                     17-4: Theoretical Probability: Close and Check
                       Curriculum Standards: Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.

                  Practice

                     17-4: Theoretical Probability: Homework G
                       Curriculum Standards: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.

                     17-4: Theoretical Probability: Homework K
                       Curriculum Standards: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.

                     17-4: Theoretical Probability: Mixed Review
                       Curriculum Standards: Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

               Lesson 17-5: Probability Models

                  Interactive Learning

                     17-5: Probability Models: Launch
                       Curriculum Standards: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

                     17-5: Probability Models: Key Concept
                       Curriculum Standards: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

                     17-5: Probability Models: Part 1
                       Curriculum Standards: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

                     17-5: Probability Models: Part 2
                       Curriculum Standards: Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.

                     17-5: Probability Models: Part 3
                       Curriculum Standards: Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?

                     17-5: Probability Models: Close and Check
                       Curriculum Standards: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

                  Practice

                     17-5: Probability Models: Homework G
                       Curriculum Standards: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?

                     17-5: Probability Models: Homework K
                       Curriculum Standards: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?

                     17-5: Probability Models: Mixed Review
                       Curriculum Standards: Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

               Lesson 17-6: Problem Solving

                  Interactive Learning

                     17-6: Problem Solving: Launch
                       Curriculum Standards: Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?

                     17-6: Problem Solving: Part 1
                       Curriculum Standards: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

                     17-6: Problem Solving: Part 2
                       Curriculum Standards: Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?

                     17-6: Problem Solving: Close and Check
                       Curriculum Standards: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

                  Practice

                     17-6: Problem Solving: Homework G
                       Curriculum Standards: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?

                     17-6: Problem Solving: Homework K
                       Curriculum Standards: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?

                     17-6: Problem Solving: Mixed Review
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

               Topic 17 Review

                  Interactive Learning

                     Topic 17: Probability Concepts: Vocabulary Review

                     Topic 17: Probability Concepts: Topic Close

                     Topic 17: Probability Concepts: Pull It All Together

                  Practice

                     Topic 17: Probability Concepts: Review Homework
                       Curriculum Standards: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?

               Topic 17: Probability Concepts: Test
                 Curriculum Standards: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?

            Topic 18: Compound Events

               Topic 18: Compound Events: Enrichment Project

               Lesson 18-1: Compound Events

                  Interactive Learning

                     18-1: Compound Events: Topic Opener

                     18-1: Compound Events: Launch
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., rolling double sixes), identify the outcomes in the sample space which compose the event.

                     18-1: Compound Events: Part 1
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., rolling double sixes), identify the outcomes in the sample space which compose the event.

                     18-1: Compound Events: Part 2
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., rolling double sixes), identify the outcomes in the sample space which compose the event.

                     18-1: Compound Events: Part 3
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., rolling double sixes), identify the outcomes in the sample space which compose the event.

                     18-1: Compound Events: Key Concept
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., rolling double sixes), identify the outcomes in the sample space which compose the event.

                     18-1: Compound Events: Close and Check
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., rolling double sixes), identify the outcomes in the sample space which compose the event.

                  Practice

                     18-1: Compound Events: Homework G
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., rolling double sixes), identify the outcomes in the sample space which compose the event.

                     18-1: Compound Events: Homework K
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., rolling double sixes), identify the outcomes in the sample space which compose the event.

                     18-1: Compound Events: Mixed Review
                       Curriculum Standards: Solve linear equations in one variable. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

               Lesson 18-2: Sample Spaces

                  Interactive Learning

                     18-2: Sample Spaces: Launch
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., rolling double sixes), identify the outcomes in the sample space which compose the event.

                     18-2: Sample Spaces: Part 1
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., rolling double sixes), identify the outcomes in the sample space which compose the event.

                     18-2: Sample Spaces: Part 3
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., rolling double sixes), identify the outcomes in the sample space which compose the event.

                     18-2: Sample Spaces: Key Concept
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., rolling double sixes), identify the outcomes in the sample space which compose the event.

                     18-2: Sample Spaces: Close and Check
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., rolling double sixes), identify the outcomes in the sample space which compose the event.

                     18-2: Sample Spaces: Part 2
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., rolling double sixes), identify the outcomes in the sample space which compose the event.

                  Practice

                     18-2: Sample Spaces: Homework G
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., rolling double sixes), identify the outcomes in the sample space which compose the event.

                     18-2: Sample Spaces: Homework K
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., rolling double sixes), identify the outcomes in the sample space which compose the event.

                     18-2: Sample Spaces: Mixed Review
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

               Lesson 18-3: Counting Outcomes

                  Interactive Learning

                     18-3: Counting Outcomes: Launch
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

                     18-3: Counting Outcomes: Key Concept
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

                     18-3: Counting Outcomes: Part 1
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

                     18-3: Counting Outcomes: Part 2
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., rolling double sixes), identify the outcomes in the sample space which compose the event.

                     18-3: Counting Outcomes: Part 3
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

                     18-3: Counting Outcomes: Close and Check
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

                  Practice

                     18-3: Counting Outcomes: Homework G
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., rolling double sixes), identify the outcomes in the sample space which compose the event.

                     18-3: Counting Outcomes: Homework K
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., rolling double sixes), identify the outcomes in the sample space which compose the event.

                     18-3: Counting Outcomes: Mixed Review
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

               Lesson 18-4: Finding Theoretical Probabilities

                  Interactive Learning

                     18-4: Finding Theoretical Probabilities: Launch
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

                     18-4: Finding Theoretical Probabilities: Key Concept
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

                     18-4: Finding Theoretical Probabilities: Part 1
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

                     18-4: Finding Theoretical Probabilities: Part 2
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

                     18-4: Finding Theoretical Probabilities: Part 3
                       Curriculum Standards: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.

                     18-4: Finding Theoretical Probabilities: Close and Check
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

                  Practice

                     18-4: Finding Theoretical Probabilities: Homework G
                       Curriculum Standards: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

                     18-4: Finding Theoretical Probabilities: Homework K
                       Curriculum Standards: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

                     18-4: Finding Theoretical Probabilities: Mixed Review
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

               Lesson 18-5: Simulation With Random Numbers

                  Interactive Learning

                     18-5: Simulation With Random Numbers: Launch
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

                     18-5: Simulation With Random Numbers: Key Concept
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

                     18-5: Simulation With Random Numbers: Part 1
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

                     18-5: Simulation With Random Numbers: Part 2
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

                     18-5: Simulation With Random Numbers: Part 3
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

                     18-5: Simulation With Random Numbers: Close and Check
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

                  Practice

                     18-5: Simulation With Random Numbers: Homework G
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

                     18-5: Simulation With Random Numbers: Homework K
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

                     18-5: Simulation With Random Numbers: Mixed Review
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.

               Lesson 18-6: Finding Probabilities Using Simulation

                  Interactive Learning

                     18-6: Finding Probabilities Using Simulation: Launch
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

                     18-6: Finding Probabilities Using Simulation: Key Concept
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

                     18-6: Finding Probabilities Using Simulation: Part 1
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

                     18-6: Finding Probabilities Using Simulation: Part 2
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

                     18-6: Finding Probabilities Using Simulation: Close and Check
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

                  Practice

                     18-6: Finding Probabilities Using Simulation: Homework G
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

                     18-6: Finding Probabilities Using Simulation: Homework K
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

                     18-6: Finding Probabilities Using Simulation: Mixed Review
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.

               Lesson 18-7: Problem Solving

                  Interactive Learning

                     18-7: Problem Solving: Launch
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

                     18-7: Problem Solving: Part 1
                       Curriculum Standards: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

                     18-7: Problem Solving: Part 2
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

                     18-7: Problem Solving: Close and Check
                       Curriculum Standards: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

                  Practice

                     18-7: Problem Solving: Homework G
                       Curriculum Standards: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

                     18-7: Problem Solving: Homework K
                       Curriculum Standards: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

                     18-7: Problem Solving: Mixed Review
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

               Topic 18 Review

                  Interactive Learning

                     Topic 18: Compound Events: Vocabulary Review

                     Topic 18: Compound Events: Pull It All Together

                     Topic 18: Compound Events: Topic Close

                  Practice

                     Topic 18: Compound Events: Review Homework
                       Curriculum Standards: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., rolling double sixes), identify the outcomes in the sample space which compose the event. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

               Topic 18: Compound Events: Test
                 Curriculum Standards: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., rolling double sixes), identify the outcomes in the sample space which compose the event. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

            Unit III: Introduction to Sampling and Inference: Test
              Curriculum Standards: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies? Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., rolling double sixes), identify the outcomes in the sample space which compose the event. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

         Unit IV: Creating, Comparing, and Analyzing Geometric Figures

            Unit IV: Creating, Comparing, and Analyzing Geometric Figures: Enrichment Project

            Lesson i19-1: Classifying Triangles: Part 1

            Lesson i19-1: Classifying Triangles: Part 2

            Lesson i19-1: Classifying Triangles: Part 3

            Lesson i19-1: Classifying Triangles: Lesson Check

            i19-1 Journal

            i19-1 Practice

            Lesson i19-2: Classifying Quadrilaterals: Part 1

            Lesson i19-2: Classifying Quadrilaterals: Part 2

            Lesson i19-2: Classifying Quadrilaterals: Part 3

            Lesson i19-2: Classifying Quadrilaterals: Lesson Check

            i19-2 Journal

            i19-2 Practice

            Lesson i20-2: Area of Rectangles and Squares: Part 1

            Lesson i20-2: Area of Rectangles and Squares: Part 2

            Lesson i20-2: Area of Rectangles and Squares: Part 3

            Lesson i20-2: Area of Rectangles and Squares: Lesson Check

            i20-2 Journal

            i20-2 Practice

            Lesson i20-3: Area of Parallelograms and Triangles: Part 1

            Lesson i20-3: Area of Parallelograms and Triangles: Part 2

            Lesson i20-3: Area of Parallelograms and Triangles: Part 3

            Lesson i20-3: Area of Parallelograms and Triangles: Lesson Check

            i20-3 Journal

            i20-3 Practice

            Lesson i20-4: Nets and Surface Area: Part 1

            Lesson i20-4: Nets and Surface Area: Part 2

            Lesson i20-4: Nets and Surface Area: Lesson Check

            i20-4 Journal

            i20-4 Practice

            Lesson i20-5: Volume of Prisms: Part 1

            Lesson i20-5: Volume of Prisms: Part 2

            Lesson i20-5: Volume of Prisms: Part 3

            Lesson i20-5: Volume of Prisms: Lesson Check

            i20-5 Journal

            i20-5 Practice

            Lesson i23-4: Evaluating Expressions: Whole Numbers: Part 1

            Lesson i23-4: Evaluating Expressions: Whole Numbers: Part 2

            Lesson i23-4: Evaluating Expressions: Whole Numbers: Part 3

            Lesson i23-4: Evaluating Expressions: Whole Numbers: Lesson Check

            i23-4 Journal

            i23-4 Practice

            Lesson i24-1: Evaluating Expressions: Rational Numbers: Part 1

            Lesson i24-1: Evaluating Expressions: Rational Numbers: Part 2

            Lesson i24-1: Evaluating Expressions: Rational Numbers: Part 3

            Lesson i24-1: Evaluating Expressions: Rational Numbers: Lesson Check

            i24-1 Journal

            i24-1 Practice

            Lesson i25-2: Principles of Solving Equations: Part 1

            Lesson i25-2: Principles of Solving Equations: Part 2

            Lesson i25-2: Principles of Solving Equations: Part 3

            Lesson i25-2: Principles of Solving Equations: Lesson Check

            i25-2 Journal

            i25-2 Practice

            Lesson i8-2: Multiplying Decimals: Part 1

            Lesson i8-2: Multiplying Decimals: Part 2

            Lesson i8-2: Multiplying Decimals: Part 3

            Lesson i8-2: Multiplying Decimals: Lesson Check

            i8-2 Journal

            i8-2 Practice

            Unit IV: Creating, Comparing, and Analyzing Geometric Figures: Readiness Assessment

            Topic 19: Angles

               Topic 19: Angles: Enrichment Project

               Lesson 19-1: Measuring Angles

                  Interactive Learning

                     19-1: Measuring Angles: Topic Opener

                     19-1: Measuring Angles: Launch
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     19-1: Measuring Angles: Part 1
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     19-1: Measuring Angles: Part 2
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     19-1: Measuring Angles: Part 3
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

                     19-1: Measuring Angles: Close and Check
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                  Practice

                     19-1: Measuring Angles: Homework G
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     19-1: Measuring Angles: Homework K
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     19-1: Measuring Angles: Mixed Review
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

               Lesson 19-2: Adjacent Angles

                  Interactive Learning

                     19-2: Adjacent Angles: Launch
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     19-2: Adjacent Angles: Key Concept
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     19-2: Adjacent Angles: Part 1
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     19-2: Adjacent Angles: Part 2
                       Curriculum Standards: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

                     19-2: Adjacent Angles: Close and Check
                       Curriculum Standards: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

                  Practice

                     19-2: Adjacent Angles: Homework G
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

                     19-2: Adjacent Angles: Homework K
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

                     19-2: Adjacent Angles: Mixed Review
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

               Lesson 19-3: Complementary Angles

                  Interactive Learning

                     19-3: Complementary Angles: Launch
                       Curriculum Standards: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

                     19-3: Complementary Angles: Key Concept
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     19-3: Complementary Angles: Part 1
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     19-3: Complementary Angles: Part 2
                       Curriculum Standards: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

                     19-3: Complementary Angles: Close and Check
                       Curriculum Standards: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

                  Practice

                     19-3: Complementary Angles: Homework G
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

                     19-3: Complementary Angles: Homework K
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

                     19-3: Complementary Angles: Mixed Review
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. Recognize and represent proportional relationships between quantities.

               Lesson 19-4: Supplementary Angles

                  Interactive Learning

                     19-4: Supplementary Angles: Launch
                       Curriculum Standards: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

                     19-4: Supplementary Angles: Key Concept
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     19-4: Supplementary Angles: Part 1
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     19-4: Supplementary Angles: Part 2
                       Curriculum Standards: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

                     19-4: Supplementary Angles: Close and Check
                       Curriculum Standards: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

                  Practice

                     19-4: Supplementary Angles: Homework G
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

                     19-4: Supplementary Angles: Homework K
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

                     19-4: Supplementary Angles: Mixed Review
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

               Lesson 19-5: Vertical Angles

                  Interactive Learning

                     19-5: Vertical Angles: Launch
                       Curriculum Standards: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

                     19-5: Vertical Angles: Key Concept
                       Curriculum Standards: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

                     19-5: Vertical Angles: Part 1
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     19-5: Vertical Angles: Part 2
                       Curriculum Standards: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

                     19-5: Vertical Angles: Close and Check
                       Curriculum Standards: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

                  Practice

                     19-5: Vertical Angles: Homework G
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

                     19-5: Vertical Angles: Mixed Review
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Solve real-world and mathematical problems involving the four operations with rational numbers.

                     19-5: Vertical Angles: Homework K
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

               Lesson 19-6: Problem Solving

                  Interactive Learning

                     19-6: Problem Solving: Launch
                       Curriculum Standards: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

                     19-6: Problem Solving: Part 1
                       Curriculum Standards: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

                     19-6: Problem Solving: Part 2
                       Curriculum Standards: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

                     19-6: Problem Solving: Close and Check
                       Curriculum Standards: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

                  Practice

                     19-6: Problem Solving: Homework G
                       Curriculum Standards: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

                     19-6: Problem Solving: Homework K
                       Curriculum Standards: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

                     19-6: Problem Solving: Mixed Review
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

               Topic 19 Review

                  Interactive Learning

                     Topic 19: Angles: Vocabulary Review

                     Topic 19: Angles: Topic Close

                     Topic 19: Angles: Pull It All Together

                  Practice

                     Topic 19: Angles: Review Homework
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

               Topic 19: Angles: Test
                 Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

            Topic 20: Circles

               Topic 20: Circles: Enrichment Project

               Lesson 20-1: Center, Radius, and Diameter

                  Interactive Learning

                     20-1: Center, Radius, and Diameter: Topic Opener

                     20-1: Center, Radius, and Diameter: Launch
                       Curriculum Standards: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

                     20-1: Center, Radius, and Diameter: Key Concept
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     20-1: Center, Radius, and Diameter: Part 1
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     20-1: Center, Radius, and Diameter: Part 2
                       Curriculum Standards: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

                     20-1: Center, Radius, and Diameter: Part 3
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

                     20-1: Center, Radius, and Diameter: Close and Check
                       Curriculum Standards: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

                  Practice

                     20-1: Center, Radius, and Diameter: Homework G
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

                     20-1: Center, Radius, and Diameter: Homework K
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

                     20-1: Center, Radius, and Diameter: Mixed Review
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Solve real-world and mathematical problems involving the four operations with rational numbers.

               Lesson 20-2: Circumference of a Circle

                  Interactive Learning

                     20-2: Circumference of a Circle: Launch
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     20-2: Circumference of a Circle: Key Concept
                       Curriculum Standards: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

                     20-2: Circumference of a Circle: Part 1
                       Curriculum Standards: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

                     20-2: Circumference of a Circle: Part 2
                       Curriculum Standards: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

                     20-2: Circumference of a Circle: Part 3
                       Curriculum Standards: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

                     20-2: Circumference of a Circle: Close and Check
                       Curriculum Standards: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

                  Practice

                     20-2: Circumference of a Circle: Homework G
                       Curriculum Standards: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

                     20-2: Circumference of a Circle: Homework K
                       Curriculum Standards: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

                     20-2: Circumference of a Circle: Mixed Review
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

               Lesson 20-3: Area of a Circle

                  Interactive Learning

                     20-3: Area of a Circle: Launch
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     20-3: Area of a Circle: Key Concept
                       Curriculum Standards: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

                     20-3: Area of a Circle: Part 1
                       Curriculum Standards: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

                     20-3: Area of a Circle: Part 2
                       Curriculum Standards: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

                     20-3: Area of a Circle: Part 3
                       Curriculum Standards: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

                     20-3: Area of a Circle: Close and Check
                       Curriculum Standards: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

                  Practice

                     20-3: Area of a Circle: Homework G
                       Curriculum Standards: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

                     20-3: Area of a Circle: Homework K
                       Curriculum Standards: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

                     20-3: Area of a Circle: Mixed Review
                       Curriculum Standards: Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

               Lesson 20-4: Relating Circumference and Area of a Circle

                  Interactive Learning

                     20-4: Relating Circumference and Area of a Circle: Launch
                       Curriculum Standards: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

                     20-4: Relating Circumference and Area of a Circle: Part 1
                       Curriculum Standards: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

                     20-4: Relating Circumference and Area of a Circle: Part 2
                       Curriculum Standards: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

                     20-4: Relating Circumference and Area of a Circle: Close and Check
                       Curriculum Standards: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

                  Practice

                     20-4: Relating Circumference and Area of a Circle: Homework G
                       Curriculum Standards: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

                     20-4: Relating Circumference and Area of a Circle: Homework K
                       Curriculum Standards: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

                     20-4: Relating Circumference and Area of a Circle: Mixed Review
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

               Lesson 20-5: Problem Solving

                  Interactive Learning

                     20-5: Problem Solving: Launch
                       Curriculum Standards: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

                     20-5: Problem Solving: Part 1
                       Curriculum Standards: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

                     20-5: Problem Solving: Part 2
                       Curriculum Standards: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

                     20-5: Problem Solving: Part 3
                       Curriculum Standards: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

                     20-5: Problem Solving: Close and Check
                       Curriculum Standards: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

                  Practice

                     20-5: Problem Solving: Homework G
                       Curriculum Standards: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

                     20-5: Problem Solving: Homework K
                       Curriculum Standards: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

                     20-5: Problem Solving: Mixed Review
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

               Topic 20 Review

                  Interactive Learning

                     Topic 20: Circles: Vocabulary Review

                     Topic 20: Circles: Pull It All Together

                     Topic 20: Circles: Topic Close

                  Practice

                     Topic 20: Circles: Review Homework
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

               Topic 20: Circles: Test
                 Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

            Topic 21: 2- and 3-Dimensional Shapes

               Topic 21: 2- and 3- Dimensional Shapes

               Lesson 21-1: Geometry Drawing Tools

                  Interactive Learning

                     21-1: Geometry Drawing Tools: Topic Opener

                     21-1: Geometry Drawing Tools: Launch
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     21-1: Geometry Drawing Tools: Part 1
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     21-1: Geometry Drawing Tools: Part 2
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     21-1: Geometry Drawing Tools: Part 3
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     21-1: Geometry Drawing Tools: Close and Check
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                  Practice

                     21-1: Geometry Drawing Tools: Homework G
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     21-1: Geometry Drawing Tools: Homework K
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     21-1: Geometry Drawing Tools: Mixed Review
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Solve real-world and mathematical problems involving the four operations with rational numbers.

               Lesson 21-2: Drawing Triangles with Given Conditions 1

                  Interactive Learning

                     21-2: Drawing Triangles with Given Conditions 1: Launch
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     21-2: Drawing Triangles with Given Conditions 1: Part 1
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     21-2: Drawing Triangles with Given Conditions 1: Part 2
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     21-2: Drawing Triangles with Given Conditions 1: Part 3
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     21-2: Drawing Triangles with Given Conditions 1: Key Concept
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     21-2: Drawing Triangles with Given Conditions 1: Close and Check
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                  Practice

                     21-2: Drawing Triangles with Given Conditions 1: Homework G
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     21-2: Drawing Triangles with Given Conditions 1: Homework K
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     21-2: Drawing Triangles with Given Conditions 1: Mixed Review
                       Curriculum Standards: Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts.

               Lesson 21-3: Drawing Triangles with Given Conditions 2

                  Interactive Learning

                     21-3: Drawing Triangles with Given Conditions 2: Launch
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     21-3: Drawing Triangles with Given Conditions 2: Part 1
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     21-3: Drawing Triangles with Given Conditions 2: Part 2
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     21-3: Drawing Triangles with Given Conditions 2: Part 3
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     21-3: Drawing Triangles with Given Conditions 2: Key Concept
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     21-3: Drawing Triangles with Given Conditions 2: Close and Check
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                  Practice

                     21-3: Drawing Triangles with Given Conditions 2: Homework G
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     21-3: Drawing Triangles with Given Conditions 2: Homework K
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     21-3: Drawing Triangles with Given Conditions 2: Mixed Review
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

               Lesson 21-4: 2-D Slices of Right Rectangular Prisms

                  Interactive Learning

                     21-4: 2-D Slices of Right Rectangular Prisms: Launch
                       Curriculum Standards: Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

                     21-4: 2-D Slices of Right Rectangular Prisms: Key Concept
                       Curriculum Standards: Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

                     21-4: 2-D Slices of Right Rectangular Prisms: Part 1
                       Curriculum Standards: Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

                     21-4: 2-D Slices of Right Rectangular Prisms: Part 2
                       Curriculum Standards: Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

                     21-4: 2-D Slices of Right Rectangular Prisms: Close and Check
                       Curriculum Standards: Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

                  Practice

                     21-4: 2-D Slices of Right Rectangular Prisms: Homework G
                       Curriculum Standards: Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

                     21-4: 2-D Slices of Right Rectangular Prisms: Homework K
                       Curriculum Standards: Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

                     21-4: 2-D Slices of Right Rectangular Prisms: Mixed Review
                       Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. Solve real-world and mathematical problems involving the four operations with rational numbers.

               Lesson 21-5: 2-D Slices of Right Rectangular Pyramids

                  Interactive Learning

                     21-5: 2-D Slices of Right Rectangular Pyramids: Launch
                       Curriculum Standards: Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

                     21-5: 2-D Slices of Right Rectangular Pyramids: Part 1
                       Curriculum Standards: Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

                     21-5: 2-D Slices of Right Rectangular Pyramids: Part 2
                       Curriculum Standards: Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

                     21-5: 2-D Slices of Right Rectangular Pyramids: Close and Check
                       Curriculum Standards: Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

                     21-5: 2-D Slices of Right Rectangular Pyramids: Key Concept
                       Curriculum Standards: Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

                  Practice

                     21-5: 2-D Slices of Right Rectangular Pyramids: Homework G
                       Curriculum Standards: Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

                     21-5: 2-D Slices of Right Rectangular Pyramids: Homework K
                       Curriculum Standards: Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

                     21-5: 2-D Slices of Right Rectangular Pyramids: Mixed Review
                       Curriculum Standards: Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Solve real-world and mathematical problems involving the four operations with rational numbers.

               Lesson 21-6: Problem Solving

                  Interactive Learning

                     21-6: Problem Solving: Launch
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     21-6: Problem Solving: Part 1
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                     21-6: Problem Solving: Part 2
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                     21-6: Problem Solving: Part 3
                       Curriculum Standards: Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

                     21-6: Problem Solving: Close and Check
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

                  Practice

                     21-6: Problem Solving: Homework G
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                     21-6: Problem Solving: Homework K
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                     21-6: Problem Solving: Mixed Review
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

               Topic 21 Review

                  Interactive Learning

                     Topic 21: 2- and 3-Dimensional Shapes: Vocabulary Review

                     Topic 21: 2- and 3-Dimensional Shapes: Pull It All Together

                     Topic 21: 2- and 3-Dimensional Shapes: Topic Close

                  Practice

                     Topic 21: 2- and 3-Dimensional Shapes: Review Homework
                       Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

               Topic 21: 2- and 3- Dimensional Shapes: Test
                 Curriculum Standards: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

            Topic 22: Surface Area and Volume

               Topic 22: Surface Area and Volume: Enrichment Project

               Lesson 22-1: Surface Areas of Right Prisms

                  Interactive Learning

                     22-1: Surface Areas of Right Prisms: Topic Opener

                     22-1: Surface Areas of Right Prisms: Launch
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                     22-1: Surface Areas of Right Prisms: Key Concept
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                     22-1: Surface Areas of Right Prisms: Part 1
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                     22-1: Surface Areas of Right Prisms: Part 2
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                     22-1: Surface Areas of Right Prisms: Part 3
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                     22-1: Surface Areas of Right Prisms: Close and Check
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                  Practice

                     22-1: Surface Areas of Right Prisms: Homework G
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                     22-1: Surface Areas of Right Prisms: Homework K
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                     22-1: Surface Areas of Right Prisms: Mixed Review
                       Curriculum Standards: Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts. Solve real-world and mathematical problems involving the four operations with rational numbers.

               Lesson 22-2: Volumes of Right Prisms

                  Interactive Learning

                     22-2: Volumes of Right Prisms: Launch
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                     22-2: Volumes of Right Prisms: Key Concept
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                     22-2: Volumes of Right Prisms: Part 1
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                     22-2: Volumes of Right Prisms: Part 2
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                     22-2: Volumes of Right Prisms: Part 3
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                     22-2: Volumes of Right Prisms: Close and Check
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                  Practice

                     22-2: Volumes of Right Prisms: Homework G
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                     22-2: Volumes of Right Prisms: Homework K
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                     22-2: Volumes of Right Prisms: Mixed Review
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Solve real-world and mathematical problems involving the four operations with rational numbers.

               Lesson 22-3: Surface Areas of Right Pyramids

                  Interactive Learning

                     22-3: Surface Areas of Right Pyramids: Launch
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                     22-3: Surface Areas of Right Pyramids: Key Concept
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                     22-3: Surface Areas of Right Pyramids: Part 1
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                     22-3: Surface Areas of Right Pyramids: Part 2
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                     22-3: Surface Areas of Right Pyramids: Part 3
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                     22-3: Surface Areas of Right Pyramids: Close and Check
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                  Practice

                     22-3: Surface Areas of Right Pyramids: Homework G
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                     22-3: Surface Areas of Right Pyramids: Homework K
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                     22-3: Surface Areas of Right Pyramids: Mixed Review
                       Curriculum Standards: Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. Solve real-world and mathematical problems involving the four operations with rational numbers.

               Lesson 22-4: Volumes of Right Pyramids

                  Interactive Learning

                     22-4: Volumes of Right Pyramids: Launch
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                     22-4: Volumes of Right Pyramids: Key Concept
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                     22-4: Volumes of Right Pyramids: Part 1
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                     22-4: Volumes of Right Pyramids: Part 2
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                     22-4: Volumes of Right Pyramids: Part 3
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                     22-4: Volumes of Right Pyramids: Close and Check
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                  Practice

                     22-4: Volumes of Right Pyramids: Homework G
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                     22-4: Volumes of Right Pyramids: Homework K
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                     22-4: Volumes of Right Pyramids: Mixed Review
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. Solve real-world and mathematical problems involving the four operations with rational numbers. Recognize and represent proportional relationships between quantities.

               Lesson 22-5: Problem Solving

                  Interactive Learning

                     22-5: Problem Solving: Launch
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                     22-5: Problem Solving: Part 1
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                     22-5: Problem Solving: Part 2
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                     22-5: Problem Solving: Close and Check
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                  Practice

                     22-5: Problem Solving: Homework G
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                     22-5: Problem Solving: Homework K
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

                     22-5: Problem Solving: Mixed Review
                       Curriculum Standards: Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

               Topic 22 Review

                  Interactive Learning

                     Topic 22: Surface Area and Volume: Vocabulary Review

                     Topic 22: Surface Area and Volume: Pull It All Together

                     Topic 22: Surface Area and Volume: Topic Close

                  Practice

                     Topic 22: Surface Area and Volume: Review Homework
                       Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

               Topic 22: Surface Area and Volume
                 Curriculum Standards: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

            Topic 23: Congruence

               Topic 23: Congruence: Enrichment Project

               Lesson 23-1: Translations

                  Interactive Learning

                     23-1: Translations: Topic Opener

                     23-1: Translations: Launch
                       Curriculum Standards: Verify experimentally the properties of rotations, reflections, and translations: Verify experimentally the properties of rotations, reflections, and translations: Lines are taken to lines, and line segments to line segments of the same length. Verify experimentally the properties of rotations, reflections, and translations: Angles are taken to angles of the same measure. Verify experimentally the properties of rotations, reflections, and translations: Parallel lines are taken to parallel lines.

                     23-1: Translations: Part 1
                       Curriculum Standards: Verify experimentally the properties of rotations, reflections, and translations:

                     23-1: Translations: Key Concept
                       Curriculum Standards: Verify experimentally the properties of rotations, reflections, and translations: Verify experimentally the properties of rotations, reflections, and translations: Lines are taken to lines, and line segments to line segments of the same length. Verify experimentally the properties of rotations, reflections, and translations: Angles are taken to angles of the same measure. Verify experimentally the properties of rotations, reflections, and translations: Parallel lines are taken to parallel lines.

                     23-1: Translations: Part 2
                       Curriculum Standards: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

                     23-1: Translations: Part 3
                       Curriculum Standards: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

                     23-1: Translations: Close and Check
                       Curriculum Standards: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

                  Practice

                     23-1: Translations: Homework G
                       Curriculum Standards: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Verify experimentally the properties of rotations, reflections, and translations:

                     23-1: Translations: Homework K
                       Curriculum Standards: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Verify experimentally the properties of rotations, reflections, and translations:

                     23-1: Translations: Mixed Review
                       Curriculum Standards: Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'. Solve linear equations in one variable. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts.

               Lesson 23-2: Reflections

                  Interactive Learning

                     23-2: Reflections: Launch
                       Curriculum Standards: Verify experimentally the properties of rotations, reflections, and translations: Verify experimentally the properties of rotations, reflections, and translations: Lines are taken to lines, and line segments to line segments of the same length. Verify experimentally the properties of rotations, reflections, and translations: Angles are taken to angles of the same measure. Verify experimentally the properties of rotations, reflections, and translations: Parallel lines are taken to parallel lines.

                     23-2: Reflections: Key Concept
                       Curriculum Standards: Verify experimentally the properties of rotations, reflections, and translations: Verify experimentally the properties of rotations, reflections, and translations: Lines are taken to lines, and line segments to line segments of the same length. Verify experimentally the properties of rotations, reflections, and translations: Angles are taken to angles of the same measure. Verify experimentally the properties of rotations, reflections, and translations: Parallel lines are taken to parallel lines.

                     23-2: Reflections: Part 1
                       Curriculum Standards: Verify experimentally the properties of rotations, reflections, and translations:

                     23-2: Reflections: Part 2
                       Curriculum Standards: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

                     23-2: Reflections: Part 3
                       Curriculum Standards: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

                     23-2: Reflections: Close and Check
                       Curriculum Standards: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

                  Practice

                     23-2: Reflections: Homework G
                       Curriculum Standards: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Verify experimentally the properties of rotations, reflections, and translations:

                     23-2: Reflections: Homework K
                       Curriculum Standards: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Verify experimentally the properties of rotations, reflections, and translations:

                     23-2: Reflections: Mixed Review
                       Curriculum Standards: Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

               Lesson 23-3: Rotations

                  Interactive Learning

                     23-3: Rotations: Launch
                       Curriculum Standards: Verify experimentally the properties of rotations, reflections, and translations: Verify experimentally the properties of rotations, reflections, and translations: Lines are taken to lines, and line segments to line segments of the same length. Verify experimentally the properties of rotations, reflections, and translations: Angles are taken to angles of the same measure. Verify experimentally the properties of rotations, reflections, and translations: Parallel lines are taken to parallel lines.

                     23-3: Rotations: Key Concept
                       Curriculum Standards: Verify experimentally the properties of rotations, reflections, and translations: Verify experimentally the properties of rotations, reflections, and translations: Lines are taken to lines, and line segments to line segments of the same length. Verify experimentally the properties of rotations, reflections, and translations: Angles are taken to angles of the same measure. Verify experimentally the properties of rotations, reflections, and translations: Parallel lines are taken to parallel lines.

                     23-3: Rotations: Part 1
                       Curriculum Standards: Verify experimentally the properties of rotations, reflections, and translations:

                     23-3: Rotations: Part 2
                       Curriculum Standards: Verify experimentally the properties of rotations, reflections, and translations: Verify experimentally the properties of rotations, reflections, and translations: Lines are taken to lines, and line segments to line segments of the same length. Verify experimentally the properties of rotations, reflections, and translations: Angles are taken to angles of the same measure. Verify experimentally the properties of rotations, reflections, and translations: Parallel lines are taken to parallel lines.

                     23-3: Rotations: Part 3
                       Curriculum Standards: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

                     23-3: Rotations: Close and Check
                       Curriculum Standards: Verify experimentally the properties of rotations, reflections, and translations: Verify experimentally the properties of rotations, reflections, and translations: Lines are taken to lines, and line segments to line segments of the same length. Verify experimentally the properties of rotations, reflections, and translations: Angles are taken to angles of the same measure. Verify experimentally the properties of rotations, reflections, and translations: Parallel lines are taken to parallel lines.

                  Practice

                     23-3: Rotations: Homework G
                       Curriculum Standards: Verify experimentally the properties of rotations, reflections, and translations: Verify experimentally the properties of rotations, reflections, and translations: Lines are taken to lines, and line segments to line segments of the same length. Verify experimentally the properties of rotations, reflections, and translations: Angles are taken to angles of the same measure. Verify experimentally the properties of rotations, reflections, and translations: Parallel lines are taken to parallel lines. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

                     23-3: Rotations: Homework K
                       Curriculum Standards: Verify experimentally the properties of rotations, reflections, and translations: Verify experimentally the properties of rotations, reflections, and translations: Lines are taken to lines, and line segments to line segments of the same length. Verify experimentally the properties of rotations, reflections, and translations: Angles are taken to angles of the same measure. Verify experimentally the properties of rotations, reflections, and translations: Parallel lines are taken to parallel lines. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

                     23-3: Rotations: Mixed Review
                       Curriculum Standards: Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

               Lesson 23-4: Congruent Figures

                  Interactive Learning

                     23-4: Congruent Figures: Launch
                       Curriculum Standards: Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

                     23-4: Congruent Figures: Key Concept
                       Curriculum Standards: Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

                     23-4: Congruent Figures: Part 1
                       Curriculum Standards: Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

                     23-4: Congruent Figures: Part 2
                       Curriculum Standards: Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

                     23-4: Congruent Figures: Part 3
                       Curriculum Standards: Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

                     23-4: Congruent Figures: Close and Check
                       Curriculum Standards: Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

                  Practice

                     23-4: Congruent Figures: Homework G
                       Curriculum Standards: Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

                     23-4: Congruent Figures: Homework K
                       Curriculum Standards: Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

                     23-4: Congruent Figures: Mixed Review
                       Curriculum Standards: Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

               Lesson 23-5: Problem Solving

                  Interactive Learning

                     23-5: Problem Solving: Launch
                       Curriculum Standards: Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

                     23-5: Problem Solving: Part 1
                       Curriculum Standards: Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

                     23-5: Problem Solving: Part 2
                       Curriculum Standards: Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

                     23-5: Problem Solving: Close and Check
                       Curriculum Standards: Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

                  Practice

                     23-5: Problem Solving: Homework G
                       Curriculum Standards: Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

                     23-5: Problem Solving: Homework K
                       Curriculum Standards: Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

                     23-5: Problem Solving: Mixed Review
                       Curriculum Standards: Solve linear equations in one variable. Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

               Topic 23 Review

                  Interactive Learning

                     Topic 23: Congruence: Vocabulary Review

                     Topic 23: Congruence: Pull It All Together

                     Topic 23: Congruence: Topic Close

                  Practice

                     Topic 23: Congruence: Review Homework
                       Curriculum Standards: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Verify experimentally the properties of rotations, reflections, and translations: Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

               Topic 23: Congruence: Test
                 Curriculum Standards: Verify experimentally the properties of rotations, reflections, and translations: Verify experimentally the properties of rotations, reflections, and translations: Lines are taken to lines, and line segments to line segments of the same length. Verify experimentally the properties of rotations, reflections, and translations: Angles are taken to angles of the same measure. Verify experimentally the properties of rotations, reflections, and translations: Parallel lines are taken to parallel lines. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

            Topic 24: Similarity

               Topic 24: Similarity: Enrichment Project

               Lesson 24-1: Dilations

                  Interactive Learning

                     24-1: Dilations: Topic Opener

                     24-1: Dilations: Launch
                       Curriculum Standards: Verify experimentally the properties of rotations, reflections, and translations:

                     24-1: Dilations: Key Concept
                       Curriculum Standards: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

                     24-1: Dilations: Part 1
                       Curriculum Standards: Verify experimentally the properties of rotations, reflections, and translations:

                     24-1: Dilations: Part 2
                       Curriculum Standards: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

                     24-1: Dilations: Part 3
                       Curriculum Standards: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

                     24-1: Dilations: Close and Check
                       Curriculum Standards: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

                  Practice

                     24-1: Dilations: Homework G
                       Curriculum Standards: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Verify experimentally the properties of rotations, reflections, and translations:

                     24-1: Dilations: Homework K
                       Curriculum Standards: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Verify experimentally the properties of rotations, reflections, and translations:

                     24-1: Dilations: Mixed Review
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Verify experimentally the properties of rotations, reflections, and translations: Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

               Lesson 24-2: Similar Figures

                  Interactive Learning

                     24-2: Similar Figures: Launch
                       Curriculum Standards: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two- dimensional figures, describe a sequence that exhibits the similarity between them.

                     24-2: Similar Figures: Key Concept
                       Curriculum Standards: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two- dimensional figures, describe a sequence that exhibits the similarity between them.

                     24-2: Similar Figures: Part 1
                       Curriculum Standards: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two- dimensional figures, describe a sequence that exhibits the similarity between them.

                     24-2: Similar Figures: Part 2
                       Curriculum Standards: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two- dimensional figures, describe a sequence that exhibits the similarity between them.

                     24-2: Similar Figures: Part 3
                       Curriculum Standards: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two- dimensional figures, describe a sequence that exhibits the similarity between them.

                     24-2: Similar Figures: Close and Check
                       Curriculum Standards: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two- dimensional figures, describe a sequence that exhibits the similarity between them.

                  Practice

                     24-2: Similar Figures: Homework G
                       Curriculum Standards: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two- dimensional figures, describe a sequence that exhibits the similarity between them.

                     24-2: Similar Figures: Homework K
                       Curriculum Standards: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two- dimensional figures, describe a sequence that exhibits the similarity between them.

                     24-2: Similar Figures: Mixed Review
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

               Lesson 24-3: Relating Similar Triangles and Slope

                  Interactive Learning

                     24-3: Relating Similar Triangles and Slope: Launch
                       Curriculum Standards: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two- dimensional figures, describe a sequence that exhibits the similarity between them.

                     24-3: Relating Similar Triangles and Slope: Part 1
                       Curriculum Standards: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

                     24-3: Relating Similar Triangles and Slope: Part 2
                       Curriculum Standards: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

                     24-3: Relating Similar Triangles and Slope: Key Concept
                       Curriculum Standards: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

                     24-3: Relating Similar Triangles and Slope: Close and Check
                       Curriculum Standards: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

                  Practice

                     24-3: Relating Similar Triangles and Slope: Homework G
                       Curriculum Standards: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

                     24-3: Relating Similar Triangles and Slope: Homework K
                       Curriculum Standards: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

                     24-3: Relating Similar Triangles and Slope: Mixed Review
                       Curriculum Standards: Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger. Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

               Lesson 24-4: Problem Solving

                  Interactive Learning

                     24-4: Problem Solving: Launch
                       Curriculum Standards: Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two- dimensional figures, describe a sequence that exhibits the similarity between them.

                     24-4: Problem Solving: Part 1
                       Curriculum Standards: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two- dimensional figures, describe a sequence that exhibits the similarity between them.

                     24-4: Problem Solving: Part 2
                       Curriculum Standards: Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two- dimensional figures, describe a sequence that exhibits the similarity between them.

                     24-4: Problem Solving: Part 3
                       Curriculum Standards: Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two- dimensional figures, describe a sequence that exhibits the similarity between them.

                     24-4: Problem Solving: Close and Check
                       Curriculum Standards: Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two- dimensional figures, describe a sequence that exhibits the similarity between them.

                  Practice

                     24-4: Problem Solving: Homework G
                       Curriculum Standards: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two- dimensional figures, describe a sequence that exhibits the similarity between them.

                     24-4: Problem Solving: Homework K
                       Curriculum Standards: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two- dimensional figures, describe a sequence that exhibits the similarity between them.

                     24-4: Problem Solving: Mixed Review
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). Verify experimentally the properties of rotations, reflections, and translations: Verify experimentally the properties of rotations, reflections, and translations: Lines are taken to lines, and line segments to line segments of the same length. Verify experimentally the properties of rotations, reflections, and translations: Angles are taken to angles of the same measure. Verify experimentally the properties of rotations, reflections, and translations: Parallel lines are taken to parallel lines. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

               Topic 24 Review

                  Interactive Learning

                     Topic 24: Similarity: Vocabulary Review

                     Topic 24: Similarity: Pull It All Together

                     Topic 24: Similarity: Topic Close

                  Practice

                     Topic 24: Similarity: Review Homework
                       Curriculum Standards: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two- dimensional figures, describe a sequence that exhibits the similarity between them.

               Topic 24: Similarity: Test
                 Curriculum Standards: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Verify experimentally the properties of rotations, reflections, and translations: Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two- dimensional figures, describe a sequence that exhibits the similarity between them.

            Topic 25: Reasoning in Geometry

               Topic 25: Reasoning in Geometry: Enrichment Project

               Lesson 25-1: Angles, Lines, and Transversals

                  Interactive Learning

                     25-1: Angles, Lines, and Transversals: Topic Opener

                     25-1: Angles, Lines, and Transversals: Launch
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-1: Angles, Lines, and Transversals: Key Concept
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-1: Angles, Lines, and Transversals: Part 1
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-1: Angles, Lines, and Transversals: Part 2
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-1: Angles, Lines, and Transversals: Part 3
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-1: Angles, Lines, and Transversals: Close and Check
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                  Practice

                     25-1: Angles, Lines, and Transversals: Homework G
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-1: Angles, Lines, and Transversals: Homework K
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-1: Angles, Lines, and Transversals: Mixed Review
                       Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. Solve real-world and mathematical problems involving the four operations with rational numbers. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

               Lesson 25-2: Reasoning and Parallel Lines

                  Interactive Learning

                     25-2: Reasoning and Parallel Lines: Launch
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-2: Reasoning and Parallel Lines: Key Concept
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-2: Reasoning and Parallel Lines: Part 1
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-2: Reasoning and Parallel Lines: Part 2
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-2: Reasoning and Parallel Lines: Part 3
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-2: Reasoning and Parallel Lines: Close and Check
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                  Practice

                     25-2: Reasoning and Parallel Lines: Homework G
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-2: Reasoning and Parallel Lines: Homework K
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-2: Reasoning and Parallel Lines: Mixed Review
                       Curriculum Standards: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

               Lesson 25-3: Interior Angles of Triangles

                  Interactive Learning

                     25-3: Interior Angles of Triangles: Launch
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-3: Interior Angles of Triangles: Key Concept
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-3: Interior Angles of Triangles: Part 1
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-3: Interior Angles of Triangles: Part 2
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-3: Interior Angles of Triangles: Part 3
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-3: Interior Angles of Triangles: Close and Check
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                  Practice

                     25-3: Interior Angles of Triangles: Homework G
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-3: Interior Angles of Triangles: Homework K
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-3: Interior Angles of Triangles: Mixed Review
                       Curriculum Standards: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. Solve linear equations in one variable. Apply properties of operations as strategies to add and subtract rational numbers. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

               Lesson 25-4: Exterior Angles of Triangles

                  Interactive Learning

                     25-4: Exterior Angles of Triangles: Launch
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-4: Exterior Angles of Triangles: Part 1
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-4: Exterior Angles of Triangles: Key Concept
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-4: Exterior Angles of Triangles: Part 2
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-4: Exterior Angles of Triangles: Part 3
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-4: Exterior Angles of Triangles: Close and Check
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                  Practice

                     25-4: Exterior Angles of Triangles: Homework G
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-4: Exterior Angles of Triangles: Homework K
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-4: Exterior Angles of Triangles: Mixed Review
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two- dimensional figures, describe a sequence that exhibits the similarity between them. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

               Lesson 25-5: Angle-Angle Triangle Similarity

                  Interactive Learning

                     25-5: Angle-Angle Triangle Similarity: Launch
                       Curriculum Standards: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two- dimensional figures, describe a sequence that exhibits the similarity between them.

                     25-5: Angle-Angle Triangle Similarity: Key Concept
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-5: Angle-Angle Triangle Similarity: Part 1
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-5: Angle-Angle Triangle Similarity: Part 2
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-5: Angle-Angle Triangle Similarity: Part 3
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-5: Angle-Angle Triangle Similarity: Close and Check
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                  Practice

                     25-5: Angle-Angle Triangle Similarity: Homework G
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-5: Angle-Angle Triangle Similarity: Homework K
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-5: Angle-Angle Triangle Similarity: Mixed Review
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. Verify experimentally the properties of rotations, reflections, and translations: Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

               Lesson 25-6: Problem Solving

                  Interactive Learning

                     25-6: Problem Solving: Launch
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-6: Problem Solving: Part 1
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-6: Problem Solving: Part 2
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-6: Problem Solving: Part 3
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-6: Problem Solving: Close and Check
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                  Practice

                     25-6: Problem Solving: Homework G
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-6: Problem Solving: Homework K
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

                     25-6: Problem Solving: Mixed Review
                       Curriculum Standards: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two- dimensional figures, describe a sequence that exhibits the similarity between them.

               Topic 25 Review

                  Interactive Learning

                     Topic 25: Reasoning in Geometry: Vocabulary Review

                     Topic 25: Reasoning in Geometry: Pull It All Together

                     Topic 25: Reasoning in Geometry: Topic Close

                  Practice

                     Topic 25: Reasoning in Geometry: Review Homework
                       Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

               Topic 25: Reasoning in Geometry: Test
                 Curriculum Standards: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

            Topic 26: Surface Area and Volume

               Topic 26: Surface Area and Volume: Enrichment Project

               Lesson 26-1: Surface Areas of Cylinders

                  Interactive Learning

                     26-1: Surface Areas of Cylinders: Topic Opener

                     26-1: Surface Area of Cylinders: Launch
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-1: Surface Areas of Cylinders: Part 1
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-1: Surface Areas of Cylinders: Key Concept
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-1: Surface Areas of Cylinders: Part 2
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-1: Surface Areas of Cylinders: Part 3
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-1: Surface Areas of Cylinders: Close and Check
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                  Practice

                     26-1: Surface Areas of Cylinders: Homework G
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-1: Surface Areas of Cylinders: Homework K
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-1: Surface Areas of Cylinders: Mixed Review
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two- dimensional figures, describe a sequence that exhibits the similarity between them. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

               Lesson 26-2: Volumes of Cylinders

                  Interactive Learning

                     26-2: Volumes of Cylinder: Launch
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-2: Volumes of Cylinders: Key Concept
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-2: Volumes of Cylinders: Part 1
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-2: Volumes of Cylinders: Part 2
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-2: Volumes of Cylinders: Part 3
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-2: Volumes of Cylinders: Close and Check
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                  Practice

                     26-2: Volumes of Cylinders: Homework G
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-2: Volumes of Cylinders: Homework K
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-2: Volumes of Cylinders: Mixed Review
                       Curriculum Standards: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Solve linear equations in one variable. Verify experimentally the properties of rotations, reflections, and translations: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., pi^2). For example, by truncating the decimal expansion of the square root of 2, show that the square root of 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

               Lesson 26-3: Surface Areas of Cones

                  Interactive Learning

                     26-3: Surface Areas of Cones: Launch
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-3: Surface Areas of Cones: Part 1
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-3: Surface Areas of Cones: Key Concept
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-3: Surface Areas of Cones: Part 2
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-3: Surface Areas of Cones: Part 3
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-3: Surface Areas of Cones: Close and Check
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                  Practice

                     26-3: Surface Areas of Cones: Homework G
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-3: Surface Areas of Cones: Homework K
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-3: Surface Areas of Cones: Mixed Review
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. Solve real-world and mathematical problems involving the four operations with rational numbers.

               Lesson 26-4: Volumes of Cones

                  Interactive Learning

                     26-4: Volumes of Cones: Launch
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-4: Volumes of Cones: Key Concept
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-4: Volumes of Cones: Part 1
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-4: Volumes of Cones: Part 2
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-4: Volumes of Cones: Part 3
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-4: Volumes of Cones: Close and Check
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                  Practice

                     26-4: Volumes of Cones: Homework G
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-4: Volumes of Cones: Homework K
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-4: Volumes of Cones: Mixed Review
                       Curriculum Standards: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. Solve real-world and mathematical problems involving the four operations with rational numbers. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

               Lesson 26-5: Surface Areas of Spheres

                  Interactive Learning

                     26-5: Surface Areas of Spheres: Launch
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-5: Surface Areas of Spheres: Key Concept
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-5: Surface Areas of Spheres: Part 1
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-5: Surface Areas of Spheres: Part 2
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-5: Surface Areas of Spheres: Part 3
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-5: Surface Areas of Spheres: Close and Check
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                  Practice

                     26-5: Surface Areas of Spheres: Homework G
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-5: Surface Areas of Spheres: Homework K
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-5: Surface Areas of Spheres: Mixed Review
                       Curriculum Standards: Solve linear equations in one variable. Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. Recognize and represent proportional relationships between quantities.

               Lesson 26-6: Volumes of Spheres

                  Interactive Learning

                     26-6: Volumes of Spheres: Launch
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-6: Volumes of Spheres: Key Concept
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-6: Volumes of Spheres: Part 1
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-6: Volumes of Spheres: Part 2
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-6: Volumes of Spheres: Part 3
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-6: Volumes of Spheres: Close and Check
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                  Practice

                     26-6: Volumes of Spheres: Homework G
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-6: Volumes of Spheres: Homework K
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-6: Volumes of Spheres: Mixed Review
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

               Lesson 26-7: Problem Solving

                  Interactive Learning

                     26-7: Problem Solving: Launch
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-7: Problem Solving: Part 1
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-7: Problem Solving: Part 2
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-7: Problem Solving: Close and Check
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                  Practice

                     26-7: Problem Solving: Homework G
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-7: Problem Solving: Homework K
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

                     26-7: Problem Solving: Mixed Review
                       Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Verify experimentally the properties of rotations, reflections, and translations: Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

               Topic 26 Review

                  Interactive Learning

                     Topic 26: Surface Area and Volume: Vocabulary Review

                     Topic 26: Surface Area and Volume: Pull It All Together

                     Topic 26: Surface Area and Volume: Topic Close

                  Practice

                     Topic 26: Surface Area and Volume: Review Homework
                       Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

               Topic 26: Surface Area and Volume: Test
                 Curriculum Standards: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

            Unit IV: Creating, Comparing, and Analyzing Geometric Figures: Test
              Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Verify experimentally the properties of rotations, reflections, and translations: Verify experimentally the properties of rotations, reflections, and translations: Lines are taken to lines, and line segments to line segments of the same length. Verify experimentally the properties of rotations, reflections, and translations: Angles are taken to angles of the same measure. Verify experimentally the properties of rotations, reflections, and translations: Parallel lines are taken to parallel lines. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two- dimensional figures, describe a sequence that exhibits the similarity between them. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

         Progress Monitoring

            Diagnostic Assessments

               Beginning of Year Diagnostic Test

            Unit Assessments

               Unit I: Rational Numbers and Exponents: Test
                 Curriculum Standards: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27. Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that the square root of 2 is irrational. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts. Apply properties of operations as strategies to multiply and divide rational numbers. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. Solve real-world and mathematical problems involving the four operations with rational numbers. Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., pi^2). For example, by truncating the decimal expansion of the square root of 2, show that the square root of 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

               Unit II: Proportionality and Linear Relationships: Test
                 Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. Solve real-world and mathematical problems involving the four operations with rational numbers. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

               Mid-Year Test
                 Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Solve real-world and mathematical problems involving the four operations with rational numbers. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., pi^2). For example, by truncating the decimal expansion of the square root of 2, show that the square root of 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

               Unit III: Introduction to Sampling and Inference: Test
                 Curriculum Standards: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies? Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., rolling double sixes), identify the outcomes in the sample space which compose the event. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

               Unit IV: Creating, Comparing, and Analyzing Geometric Figures: Test
                 Curriculum Standards: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Verify experimentally the properties of rotations, reflections, and translations: Verify experimentally the properties of rotations, reflections, and translations: Lines are taken to lines, and line segments to line segments of the same length. Verify experimentally the properties of rotations, reflections, and translations: Angles are taken to angles of the same measure. Verify experimentally the properties of rotations, reflections, and translations: Parallel lines are taken to parallel lines. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two- dimensional figures, describe a sequence that exhibits the similarity between them. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

               End-of-Year Test
                 Curriculum Standards: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that 'increase by 5' is the same as 'multiply by 1.05'. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two- dimensional figures, describe a sequence that exhibits the similarity between them. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real- world contexts. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. Solve real-world and mathematical problems involving the four operations with rational numbers. Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., pi^2). For example, by truncating the decimal expansion of the square root of 2, show that the square root of 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., rolling double sixes), identify the outcomes in the sample space which compose the event. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

            Readiness Assessments

               Lesson i12-1: Mixed Numbers and Improper Fractions: Part 1

               Lesson i12-1: Mixed Numbers and Improper Fractions: Part 2

               Lesson i12-1: Mixed Numbers and Improper Fractions: Part 3

               Lesson i12-1: Mixed Numbers and Improper Fractions: Lesson Check

               i12-1 Journal

               i12-1 Practice

               Lesson i22-5: Comparing and Ordering Rational Numbers: Part 1

               Lesson i22-5: Comparing and Ordering Rational Numbers: Part 2

               Lesson i22-5: Comparing and Ordering Rational Numbers: Part 3

               Lesson i22-5: Comparing and Ordering Rational Numbers: Lesson Check

               i22-5 Journal

               i22-5 Practice

               Lesson i22-4: Rational Numbers on the Number Line: Part 1

               Lesson i22-4: Rational Numbers on the Number Line: Part 2

               Lesson i22-4: Rational Numbers on the Number Line: Part 3

               Lesson i22-4: Rational Numbers on the Number Line: Lesson Check

               i22-4 Journal

               i22-4 Practice

               Lesson i12-2: Adding Mixed Numbers: Part 1

               Lesson i12-2: Adding Mixed Numbers: Part 2

               Lesson i12-2: Adding Mixed Numbers: Part 3

               Lesson i12-2: Adding Mixed Numbers: Lesson Check

               i12-2 Journal

               i12-2 Practice

               Lesson i11-5: Dividing Fractions: Part 1

               Lesson i11-5: Dividing Fractions: Part 2

               Lesson i11-5: Dividing Fractions: Part 3

               Lesson i11-5: Dividing Fractions: Lesson Check

               i11-5 Journal

               i11-5 Practice

               Lesson i12-3: Subtracting Mixed Numbers: Part 1

               Lesson i12-3: Subtracting Mixed Numbers: Part 2

               Lesson i12-3: Subtracting Mixed Numbers: Part 3

               Lesson i12-3: Subtracting Mixed Numbers: Lesson Check

               i12-3 Journal

               i12-3 Practice

               Lesson i10-4: Subtracting with Unlike Denominators: Part 1

               Lesson i10-4: Subtracting with Unlike Denominators: Part 2

               Lesson i10-4: Subtracting with Unlike Denominators: Part 3

               Lesson i10-4: Subtracting with Unlike Denominators: Lesson Check

               i10-4 Journal

               i10-4 Practice

               Lesson i10-3: Adding Fractions with Unlike Denominators: Part 1

               Lesson i10-3: Adding Fractions with Unlike Denominators: Part 2

               Lesson i10-3: Adding Fractions with Unlike Denominators: Part 3

               Lesson i10-3: Adding Fractions with Unlike Denominators: Lesson Check

               i10-3 Journal

               i10-3 Practice

               Lesson i9-4: Fractions and Division: Part 1

               Lesson i9-4: Fractions and Division: Part 2

               Lesson i9-4: Fractions and Division: Part 3

               Lesson i9-4: Fractions and Division: Lesson Check

               i9-4 Journal

               i9-4 Practice

               Lesson i8-5: Dividing Decimals: Part 1

               Lesson i8-5: Dividing Decimals: Part 2

               Lesson i8-5: Dividing Decimals: Part 3

               Lesson i8-5: Dividing Decimals: Lesson Check

               i8-5 Practice

               i8-5 Journal

               Lesson i8-2: Multiplying Decimals: Part 1

               Lesson i8-2: Multiplying Decimals: Part 2

               Lesson i8-2: Multiplying Decimals: Part 3

               Lesson i8-2: Multiplying Decimals: Lesson Check

               i8-2 Journal

               i8-2 Practice

               Lesson i21-1: Understanding Integers: Part 1

               Lesson i21-1: Understanding Integers: Part 2

               Lesson i21-1: Understanding Integers: Part 3

               Lesson i21-1: Understanding Integers: Lesson Check

               i21-1 Journal

               i21-1 Practice

               Unit I: Rational Numbers and Exponents: Readiness Assessment

               Lesson i2-1: Addition and Multiplication Properties: Part 1

               Lesson i2-1: Addition and Multiplication Properties: Part 2

               Lesson i2-1: Addition and Multiplication Properties: Part 3

               Lesson i2-1: Addition and Multiplication Properties: Lesson Check

               i2-1 Journal

               i2-1 Practice

               Lesson i2-2: Distributive Property: Part 1

               Lesson i2-2: Distributive Property: Part 2

               Lesson i2-2: Distributive Property: Part 3

               Lesson i2-2: Distributive Property: Lesson Check

               i2-2 Journal

               i2-2 Practice

               Lesson i4-2: Estimating Quotients with 1-Digit Divisors: Part 1

               Lesson i4-2: Estimating Quotients with 1-Digit Divisors: Part 2

               Lesson i4-2: Estimating Quotients with 1-Digit Divisors: Part 3

               Lesson i4-2: Estimating Quotients with 1-Digit Divisors: Lesson Check

               i4-2 Journal

               i4-2 Practice

               Lesson i8-5: Dividing Decimals: Part 1

               Lesson i8-5: Dividing Decimals: Part 2

               Lesson i8-5: Dividing Decimals: Part 3

               Lesson i8-5: Dividing Decimals: Lesson Check

               i8-5 Journal

               i8-5 Practice

               Lesson i11-2: Multiplying Fractions: Part 1

               Lesson i11-2: Multiplying Fractions: Part 2

               Lesson i11-2: Multiplying Fractions: Part 3

               Lesson i11-2: Multiplying Fractions: Lesson Check

               i11-2 Journal

               i11-2 Practice

               Lesson i13-1: Ratios: Part 1

               Lesson i13-1: Ratios: Part 2

               Lesson i13-1: Ratios: Part 3

               Lesson i13-1: Ratios: Lesson Check

               i13-1 Journal

               i13-1 Practice
                 Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

               Lesson i13-2: Equivalent Ratios: Part 1

               Lesson i13-2: Equivalent Ratios: Part 2

               Lesson i13-2: Equivalent Ratios: Part 3

               Lesson i13-2: Equivalent Ratios: Lesson Check

               i13-2 Journal

               i13-2 Practice

               Lesson i14-1: Unit Rates: Part 1

               Lesson i14-1: Unit Rates: Part 2

               Lesson i14-1: Unit Rates: Part 3

               Lesson i14-1: Unit Rates: Lesson Check

               i14-1 Journal

               i14-1 Practice
                 Curriculum Standards: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

               Lesson i14-2: Converting Customary Measurements: Part 1

               Lesson i14-2: Converting Customary Measurements: Part 2

               Lesson i14-2: Converting Customary Measurements: Part 3

               Lesson i14-2: Converting Customary Measurements: Lesson Check

               i14-2 Journal

               i14-2 Practice

               Lesson i14-3: Converting Metric Measurements: Part 1

               Lesson i14-3: Converting Metric Measurements: Part 2

               Lesson i14-3: Converting Metric Measurements: Part 3

               Lesson i14-3: Converting Metric Measurements: Lesson Check

               i14-3 Journal

               i14-3 Practice

               Lesson i15-1: Graphing Ratios: Part 1

               Lesson i15-1: Graphing Ratios: Part 2

               Lesson i15-1: Graphing Ratios: Part 3

               Lesson i15-1: Graphing Ratios: Lesson Check

               i15-1 Journal

               i15-1 Practice

               Lesson i16-1: Understanding Percent: Part 1

               Lesson i16-1: Understanding Percent: Part 2

               Lesson i16-1: Understanding Percent: Part 3

               Lesson i16-1: Understanding Percent: Lesson Check

               i16-1 Journal

               i16-1 Practice

               Lesson i17-1: Finding a Percent of a Number: Part 1

               Lesson i17-1: Finding a Percent of a Number: Part 2

               Lesson i17-1: Finding a Percent of a Number: Part 3

               Lesson i17-1: Finding a Percent of a Number: Lesson Check

               i17-1 Journal

               i17-1 Practice

               Lesson i23-1: Order of Operations: Part 1

               Lesson i23-1: Order of Operations: Part 2

               Lesson i23-1: Order of Operations: Part 3

               Lesson i23-1: Order of Operations: Lesson Check

               i23-1 Journal

               i23-1 Practice

               Lesson i23-2: Variables and Expressions: Part 1

               Lesson i23-2: Variables and Expressions: Part 2

               Lesson i23-2: Variables and Expressions: Part 3

               Lesson i23-2: Variables and Expressions: Lesson Check

               i23-2 Journal

               i23-2 Practice

               Lesson i24-2: Equivalent Expressions: Part 1

               Lesson i24-2: Equivalent Expressions: Part 2

               Lesson i24-2: Equivalent Expressions: Part 3

               Lesson i24-2: Equivalent Expressions: Lesson Check

               i24-2 Journal

               i24-2 Practice

               Lesson i24-3: Simplifying Expressions: Part 1

               Lesson i24-3: Simplifying Expressions: Part 2

               Lesson i24-3: Simplifying Expressions: Part 3

               Lesson i24-3: Simplifying Expressions: Lesson Check

               i24-3 Journal

               i24-3 Practice

               Lesson i25-1: Writing Equations: Part 1

               Lesson i25-1: Writing Equations: Part 2

               Lesson i25-1: Writing Equations: Part 3

               Lesson i25-1: Writing Equations: Lesson Check

               i25-1 Journal

               i25-1 Practice

               Lesson i25-2: Principles of Solving Equations: Part 1

               Lesson i25-2: Principles of Solving Equations: Part 2

               Lesson i25-2: Principles of Solving Equations: Part 3

               Lesson i25-2: Principles of Solving Equations: Lesson Check

               i25-2 Journal

               i25-2 Practice

               Lesson i25-3: Solving Addition and Subtraction Equations: Part 1

               Lesson i25-3: Solving Addition and Subtraction Equations: Part 2

               Lesson i25-3: Solving Addition and Subtraction Equations: Part 3

               Lesson i25-3: Solving Addition and Subtraction Equations: Lesson Check

               i25-3 Journal

               i25-3 Practice

               Lesson i25-5: Solving Rational-Number Equations, Part 1: Part 1

               Lesson i25-5: Solving Rational-Number Equations, Part 1: Part 2

               Lesson i25-5: Solving Rational-Number Equations, Part 1: Part 3

               Lesson i25-5: Solving Rational-Number Equations, Part 1: Lesson Check

               i25-5 Journal

               i25-5 Practice

               Lesson i25-6: Solving Rational-Number Equations, Part 2: Part 1

               Lesson i25-6: Solving Rational-Number Equations, Part 2: Part 2

               Lesson i25-6: Solving Rational-Number Equations, Part 2: Part 3

               Lesson i25-6: Solving Rational-Number Equations, Part 2: Lesson Check

               i25-6 Journal

               i25-6 Practice

               Unit II: Proportionality and Linear Relationships: Readiness Assessment

               Lesson i11-1: Multiplying a Whole Number and a Fraction: Part 1

               Lesson i11-1: Multiplying a Whole Number and a Fraction: Part 2

               Lesson i11-1: Multiplying a Whole Number and a Fraction: Part 3

               i11-1 Journal

               i11-1 Practice

               Lesson i13-1: Ratios: Part 1

               Lesson i13-1: Ratios: Part 2

               Lesson i13-1: Ratios: Part 3

               Lesson i13-1: Ratios: Lesson Check

               i13-1 Journal

               i13-1 Practice

               Lesson i16-1: Understanding Percent: Part 1

               Lesson i16-1: Understanding Percent: Part 2

               Lesson i16-1: Understanding Percent: Part 3

               Lesson i16-1: Understanding Percent: Lesson Check

               i16-1 Journal

               i16-1 Practice

               Lesson i16-2: Estimating Percent: Part 1

               Lesson i16-2: Estimating Percent: Part 2

               Lesson i16-2: Estimating Percent: Part 3

               Lesson i16-2: Estimating Percent: Lesson Check

               i16-2 Journal

               i16-2 Practice

               Lesson i17-1: Finding a Percent of a Number: Part 1

               Lesson i17-1: Finding a Percent of a Number: Part 2

               Lesson i17-1: Finding a Percent of a Number: Part 3

               Lesson i17-1: Finding a Percent of a Number: Lesson Check

               i17-1 Journal

               i17-1 Practice

               Lesson i17-2: Finding a Percent: Part 1

               Lesson i17-2: Finding a Percent: Part 2

               Lesson i17-2: Finding a Percent: Part 3

               Lesson i17-2: Finding a Percent: Lesson Check

               i17-2 Journal

               i17-2 Practice

               Lesson i17-3: Finding the Whole Given a Percent: Part 1

               Lesson i17-3: Finding the Whole Given a Percent: Part 2

               Lesson i17-3: Finding the Whole Given a Percent: Part 3

               Lesson i17-3: Finding the Whole Given a Percent: Lesson Check

               i17-3 Journal

               i17-3 Practice

               Lesson i8-2: Multiplying Decimals: Part 1

               Lesson i8-2: Multiplying Decimals: Part 2

               Lesson i8-2: Multiplying Decimals: Part 3

               Lesson i8-2: Multiplying Decimals: Lesson Check

               i18-2 Journal

               i8-2 Practice

               Lesson i9-1: Equivalent Fractions: Part 1

               Lesson i9-1: Equivalent Fractions: Part 2

               Lesson i9-1: Equivalent Fractions: Part 3

               Lesson i9-1: Equivalent Fractions: Lesson Check

               i9-1 Journal

               i9-1 Practice

               Lesson i9-2: Fractions in Simplest Form: Part 1

               Lesson i9-2: Fractions in Simplest Form: Part 2

               Lesson i9-2: Fractions in Simplest Form: Part 3

               Lesson i9-2: Fractions in Simplest Form: Lesson Check

               i9-2 Journal

               i9-2 Practice

               Lesson i9-3: Comparing and Ordering Fractions: Part 1

               Lesson i9-3: Comparing and Ordering Fractions: Part 2

               Lesson i9-3: Comparing and Ordering Fractions: Part 3

               Lesson i9-3: Comparing and Ordering Fractions: Lesson Check

               i9-3 Journal

               i9-3 Practice

               Lesson i9-5: Fractions and Decimals: Part 1

               Lesson i9-5: Fractions and Decimals: Part 2

               Lesson i9-5: Fractions and Decimals: Part 3

               Lesson i9-5: Fractions and Decimals: Lesson Check

               i9-5 Journal

               i9-5 Practice

               Lesson i11-1: Multiplying a Whole Number and a Fraction: Lesson Check

               Unit III: Introduction to Sampling and Inference: Readiness Assessment

               Lesson i19-1: Classifying Triangles: Part 1

               Lesson i19-1: Classifying Triangles: Part 2

               Lesson i19-1: Classifying Triangles: Part 3

               Lesson i19-1: Classifying Triangles: Lesson Check

               i19-1 Journal

               i19-1 Practice

               Lesson i19-2: Classifying Quadrilaterals: Part 1

               Lesson i19-2: Classifying Quadrilaterals: Part 2

               Lesson i19-2: Classifying Quadrilaterals: Part 3

               Lesson i19-2: Classifying Quadrilaterals: Lesson Check

               i19-2 Journal

               i19-2 Practice

               Lesson i20-2: Area of Rectangles and Squares: Part 1

               Lesson i20-2: Area of Rectangles and Squares: Part 2

               Lesson i20-2: Area of Rectangles and Squares: Part 3

               Lesson i20-2: Area of Rectangles and Squares: Lesson Check

               i20-2 Journal

               i20-2 Practice

               Lesson i20-3: Area of Parallelograms and Triangles: Part 1

               Lesson i20-3: Area of Parallelograms and Triangles: Part 2

               Lesson i20-3: Area of Parallelograms and Triangles: Part 3

               Lesson i20-3: Area of Parallelograms and Triangles: Lesson Check

               i20-3 Journal

               i20-3 Practice

               Lesson i20-4: Nets and Surface Area: Part 1

               Lesson i20-4: Nets and Surface Area: Part 2

               Lesson i20-4: Nets and Surface Area: Lesson Check

               i20-4 Journal

               i20-4 Practice

               Lesson i20-5: Volume of Prisms: Part 1

               Lesson i20-5: Volume of Prisms: Part 2

               Lesson i20-5: Volume of Prisms: Part 3

               Lesson i20-5: Volume of Prisms: Lesson Check

               i20-5 Journal

               i20-5 Practice

               Lesson i23-4: Evaluating Expressions: Whole Numbers: Part 1

               Lesson i23-4: Evaluating Expressions: Whole Numbers: Part 2

               Lesson i23-4: Evaluating Expressions: Whole Numbers: Part 3

               Lesson i23-4: Evaluating Expressions: Whole Numbers: Lesson Check

               i23-4 Journal

               i23-4 Practice

               Lesson i24-1: Evaluating Expressions: Rational Numbers: Part 1

               Lesson i24-1: Evaluating Expressions: Rational Numbers: Part 2

               Lesson i24-1: Evaluating Expressions: Rational Numbers: Part 3

               Lesson i24-1: Evaluating Expressions: Rational Numbers: Lesson Check

               i24-1 Journal

               i24-1 Practice

               Lesson i25-2: Principles of Solving Equations: Part 1

               Lesson i25-2: Principles of Solving Equations: Part 2

               Lesson i25-2: Principles of Solving Equations: Part 3

               Lesson i25-2: Principles of Solving Equations: Lesson Check

               i25-2 Journal

               i25-2 Practice

               Lesson i8-2: Multiplying Decimals: Part 1

               Lesson i8-2: Multiplying Decimals: Part 2

               Lesson i8-2: Multiplying Decimals: Part 3

               Lesson i8-2: Multiplying Decimals: Lesson Check

               i8-2 Journal

               i8-2 Practice

               Unit IV: Creating, Comparing, and Analyzing Geometric Figures: Readiness Assessment

         Intervention Lessons

            Cluster 1: Place Value

               Lesson i1-1: Place Value

                  Interactive Learning

                     i1-1: Place Value: Part 1

                     i1-1: Place Value: Part 2

                     i1-1: Place Value: Part 3

                     i1-1: Place Value: Lesson Check

                  Journal

                     i1-1: Place Value: Journal

                  Practice

                     i1-1: Place Value: Practice

               Lesson i1-2: Comparing and Ordering Whole Numbers

                  Interactive Learning

                     i1-2: Comparing and Ordering Whole Numbers: Part 1

                     i1-2: Comparing and Ordering Whole Numbers: Part 2

                     i1-2: Comparing and Ordering Whole Numbers: Part 3

                     i1-2: Comparing and Ordering Whole Numbers: Lesson Check

                  Journal

                     i1-2: Comparing and Ordering Whole Numbers: Journal

                  Practice

                     i1-2: Comparing and Ordering Whole Numbers: Practice

            Cluster 2: Multiplication Number Sense

               Lesson i2-1: Addition and Multiplication Properties

                  Interactive Learning

                     Lesson i2-1: Addition and Multiplication Properties: Part 1

                     Lesson i2-1: Addition and Multiplication Properties: Part 2

                     Lesson i2-1: Addition and Multiplication Properties: Part 3

                     Lesson i2-1: Addition and Multiplication Properties: Lesson Check

                  Journal

                     i2-1: Addition and Multiplication Properties: Journal

                  Practice

                     i2-1: Addition and Multiplication Properties: Practice

               Lesson i2-2: Distributive Property

                  Interactive Learning

                     Lesson i2-2: Distributive Property: Part 1

                     Lesson i2-2: Distributive Property: Part 2

                     Lesson i2-2: Distributive Property: Part 3

                     Lesson i2-2: Distributive Property: Lesson Check

                  Journal

                     i2-2: Distributive Property: Journal

                  Practice

                     i2-2: Distributive Property: Practice

               Lesson i2-3: Multiplying by Multiples of 10, 100, and 1,000

                  Interactive Learning

                     i2-3: Multiplying by Multiples of 10, 100, and 1,000: Part 1

                     i2-3: Multiplying by Multiples of 10, 100, and 1,000: Part 2

                     i2-3: Multiplying by Multiples of 10, 100, and 1,000: Part 3

                     i2-3: Multiplying by Multiples of 10, 100, and 1,000: Lesson Check

                  Journal

                     i2-3: Multiplying by Multiples of 10, 100, and 1,000: Journal

                  Practice

                     i2-3: Multiplying by Multiples of 10, 100, and 1,000: Practice

               Lesson i2-4: Using Mental Math to Multiply

                  Interactive Learning

                     i2-4: Using Mental Math to Multiply: Part 1

                     i2-4: Using Mental Math to Multiply: Part 2

                     i2-4: Using Mental Math to Multiply: Part 3

                     i2-4: Using Mental Math to Multiply: Lesson Check

                  Journal

                     i2-4: Using Mental Math to Multiply: Journal

                  Practice

                     i2-4: Using Mental Math to Multiply: Practice

               Lesson i2-5: Estimating Products

                  Interactive Learning

                     i2-5: Estimating Products: Part 1

                     i2-5: Estimating Products: Part 2

                     i2-5: Estimating Products: Part 3

                     i2-5: Estimating Products: Lesson Check

                  Journal

                     i2-5: Estimating Products: Journal

                  Practice

                     i2-5: Estimating Products: Practice

            Cluster 3: Multiplying Whole Numbers

               Lesson i3-1: Multiplying by 1-Digit Numbers: Expanded

                  Interactive Learning

                     i3-1: Multiplying by 1-Digit Numbers: Expanded: Part 1

                     i3-1: Multiplying by 1-Digit Numbers: Expanded: Part 2

                     i3-1: Multiplying by 1-Digit Numbers: Expanded: Part 3

                     i3-1: Multiplying by 1-Digit Numbers: Expanded: Lesson Check

                  Journal

                     i3-1: Multiplying by 1-Digit Numbers: Expanded: Journal

                  Practice

                     i3-1: Multiplying by 1-Digit Numbers: Expanded: Practice

               Lesson i3-2: Multiplying by 1-Digit Numbers

                  Interactive Learning

                     i3-2: Multiplying by 1-Digit Numbers: Part 1

                     i3-2: Multiplying by 1-Digit Numbers: Part 2

                     i3-2: Multiplying by 1-Digit Numbers: Part 3

                     i3-2: Multiplying by 1-Digit Numbers: Lesson Check

                  Journal

                     i3-2: Multiplying by 1-Digit Numbers: Journal

                  Practice

                     i3-2: Multiplying by 1-Digit Numbers: Practice

               Lesson i3-3: Using Patterns to Multiply and Estimate

                  Interactive Learning

                     i3-3: Using Patterns to Multiply and Estimate: Part 1

                     i3-3: Using Patterns to Multiply and Estimate: Part 2

                     i3-3: Using Patterns to Multiply and Estimate: Part 3

                     i3-3: Using Patterns to Multiply and Estimate: Lesson Check

                  Journal

                     i3-3: Using Patterns to Multiply and Estimate: Journal

                  Practice

                     i3-3: Using Patterns to Multiply and Estimate: Practice

               Lesson i3-4: Multiplying by 2-Digit Numbers: Expanded

                  Interactive Learning

                     i3-4: Multiplying by 2-Digit Numbers: Expanded: Part 1

                     i3-4: Multiplying by 2-Digit Numbers: Expanded: Part 2

                     i3-4: Multiplying by 2-Digit Numbers: Expanded: Part 3

                     i3-4: Multiplying by 2-Digit Numbers: Expanded: Lesson Check

                  Journal

                     i3-4: Multiplying by 2-Digit Numbers: Expanded: Journal

                  Practice

                     i3-4: Multiplying by 2-Digit Numbers: Expanded: Practice

               Lesson i3-5: Multiplying by 2-Digit Numbers

                  Interactive Learning

                     i3-5: Multiplying by 2-Digit Numbers: Part 1

                     i3-5: Multiplying by 2-Digit Numbers: Part 2

                     i3-5: Multiplying by 2-Digit Numbers: Part 3

                     i3-5: Multiplying by 2-Digit Numbers: Lesson Check

                  Journal

                     i3-5: Multiplying by 2-Digit Numbers: Journal

                  Practice

                     i3-5: Multiplying by 2-Digit Numbers: Practice

            Cluster 4: Dividing by 1-Digit Numbers

               Lesson i4-1: Dividing Multiples of 10 and 100

                  Interactive Learning

                     i4-1: Dividing Multiples of 10 and 100: Part 1

                     i4-2: Dividing Multiples of 10 and 100: Part 1

                     i4-1: Dividing Multiples of 10 and 100: Part 3

                     i4-1: Dividing Multiples of 10 and 100: Lesson Check

                  Journal

                     i4-1: Dividing Multiples of 10 and 100: Journal

                  Practice

                     i4-1: Dividing Multiples of 10 and 100: Practice

               Lesson i4-2: Estimating Quotients with 1-Digit Divisors

                  Interactive Learning

                     Lesson i4-2: Estimating Quotients with 1-Digit Divisors: Part 1

                     Lesson i4-2: Estimating Quotients with 1-Digit Divisors: Part 2

                     Lesson i4-2: Estimating Quotients with 1-Digit Divisors: Part 3

                     Lesson i4-2: Estimating Quotients with 1-Digit Divisors: Lesson Check

                  Journal

                     i4-2: Estimating Quotients with 1-Digit Divisors: Journal

                  Practice

                     i4-2: Estimating Quotients with 1-Digit Divisors: Practice

               Lesson i4-3: Dividing: 1-Digit Divisors, 2-Digit Dividends

                  Interactive Learning

                     i4-3: Dividing: 1-Digit Divisors, 2-Digit Dividends: Part 1

                     i4-3: Dividing: 1-Digit Divisors, 2-Digit Dividends: Part 2

                     i4-3: Dividing: 1-Digit Divisors, 2-Digit Dividends: Part 3

                     i4-3 Lesson Check

                  Journal

                     i4-3: Dividing: 1-Digit Divisors, 2-Digit Dividends: Journal

                  Practice

                     i4-3: Dividing: 1-Digit Divisors, 2-Digit Dividends: Practice

               Lesson i4-4: Dividing: 1-Digit Divisors, 3-Digit Dividends

                  Interactive Learning

                     i4-4: Dividing: 1-Digit Divisors, 3-Digit Dividends: Part 1

                     i4-4: Dividing: 1-Digit Divisors, 3-Digit Dividends: Part 2

                     i4-4: Dividing: 1-Digit Divisors, 3-Digit Dividends: Part 3

                     i4-4: Dividing: 1-Digit Divisors, 3-Digit Dividends: Lesson Check

                  Journal

                     i4-4: Dividing: 1-Digit Divisors, 3-Digit Dividends: Journal

                  Practice

                     i4-4: Dividing: 1-Digit Divisors, 3-Digit Dividends: Practice

               Lesson i4-5: Dividing: 1-Digit Divisors, 4-Digit Dividends

                  Interactive Learning

                     i4-5: Dividing: 1-Digit Divisors, 4-Digit Dividends: Part 1

                     i4-5: Dividing: 1-Digit Divisors, 4-Digit Dividends: Part 2

                     i4-5: Dividing: 1-Digit Divisors, 4-Digit Dividends: Part 3

                     i4-5: Dividing: 1-Digit Divisors, 4-Digit Dividends: Lesson Check

                  Journal

                     i4-5: Dividing: 1-Digit Divisors, 4-Digit Dividends: Journal

                  Practice

                     i4-5: Dividing: 1-Digit Divisors, 4-Digit Dividends: Practice

               Lesson i4-6: Divisibility Rules

                  Interactive Learning

                     i4-6: Divisibility Rules: Part 1

                     i4-6: Divisibility Rules: Part 2

                     i4-6: Divisibility Rules: Part 3

                     i4-6: Divisibility Rules: Lesson Check

                  Journal

                     i4-6: Divisibility Rules: Journal

                  Practice

                     i4-6: Divisibility Rules: Practice

            Cluster 5: Dividing by 2-Digit Numbers

               Lesson i5-1: Using Patterns to Divide

                  Interactive Learning

                     i5-1: Using Patterns to Divide: Part 1

                     i5-1: Using Patterns to Divide: Part 2

                     i5-1: Using Patterns to Divide: Part 3

                     i5-1: Using Patterns to Divide: Lesson Check

                  Journal

                     i5-1: Using Patterns to Divide: Journal

                  Practice

                     i5-1: Using Patterns to Divide: Practice

               Lesson i5-2: Estimating Quotients with 2-Digit Divisors

                  Interactive Learning

                     i5-2: Part 1

                     i5-2: Estimating Quotients with 2-Digit Divisors: Part 2

                     i5-2: Estimating Quotients with 2-Digit Divisors: Part 3

                     i5-2: Estimating Quotients with 2-Digit Divisors: Lesson Check

                  Journal

                     i5-2: Estimating Quotients with 2-Digit Divisors: Journal

                  Practice

                     i5-2: Estimating Quotients with 2-Digit Divisors: Practice

               Lesson i5-3: Dividing: 2-Digit Divisors, 1-Digit Quotients

                  Interactive Learning

                     i5-3: Dividing: 2-Digit Divisors, 1-Digit Quotients: Part 1

                     i5-3: Dividing: 2-Digit Divisors, 1-Digit Quotients: Part 2

                     i5-3 Part 3: Dividing: 2-Digit Divisors, 1-Digit Quotients: Part 3

                     i5-3: Dividing: 2-Digit Divisors, 1-Digit Quotients: Lesson Check

                  Journal

                     i5-3: Dividing: 2-Digit Divisors, 1-Digit Quotients: Journal

                  Practice

                     i5-3: Dividing: 2-Digit Divisors, 1-Digit Quotients: Practice

               Lesson i5-4: Dividing: 2-Digit Divisors, 2-Digit Quotients

                  Interactive Learning

                     i5-4: Dividing: 2-Digit Divisors, 2-Digit Quotients: Part 1

                     i5-4: Dividing: 2-Digit Divisors, 2-Digit Quotients Part 2

                     i5-4: Dividing: 2-Digit Divisors, 2-Digit Quotients: Part 3

                     i5-4: Dividing: 2-Digit Divisors, 2-Digit Quotients: Lesson Check

                  Journal

                     i5-4: Dividing: 2-Digit Divisors, 2-Digit Quotients: Journal

                  Practice

                     i5-4: Dividing: 2-Digit Divisors, 2-Digit Quotients: Practice

            Cluster 6: Decimal Number Sense

               Lesson i6-1: Understanding Decimals

                  Interactive Learning

                     i6-1: Understanding Decimals: Part 1

                     i6-1: Understanding Decimals: Part 2

                     i6-1: Understanding Decimals: Part 3

                     i6-1: Understanding Decimals: Lesson Check

                  Journal

                     i6-1: Understanding Decimals: Journal

                  Practice

                     i6-1: Understanding Decimals: Practice

               Lesson i6-2: Comparing and Ordering Decimals

                  Interactive Learning

                     i6-2: Comparing and Ordering Decimals: Part 1

                     i6-2: Comparing and Ordering Decimals: Part 2

                     i6-2: Comparing and Ordering Decimals: Lesson Check

                     i6-2: Comparing and Ordering Decimals: Part 3

                  Journal

                     i6-2: Comparing and Ordering Decimals: Journal

                  Practice

                     i6-2: Comparing and Ordering Decimals: Practice

               Lesson i6-3: Rounding Decimals

                  Interactive Learning

                     i6-3: Rounding Decimals: Part 1

                     i6-3: Rounding Decimals: Part 2

                     i6-3: Rounding Decimals: Part 3

                     i6-3: Rounding Decimals: Lesson Check

                  Journal

                     i6-3: Rounding Decimals: Journal

                  Practice

                     i6-3: Rounding Decimals: Practice

            Cluster 7: Adding and Subtracting Decimals

               Lesson i7-2: Adding and Subtracting Decimals

                  Interactive Learning

                     i7-2: Adding and Subtracting Decimals: Part 1

                     i7-2: Adding and Subtracting Decimals: Part 2

                     i7-2: Adding and Subtracting Decimals: Part 3

                     i7-2: Adding and Subtracting Decimals: Lesson Check

                  Journal

                     i7-2: Adding and Subtracting Decimals: Journal

                  Practice

                     i7-2: Adding and Subtracting Decimals: Practice

               Lesson i7-1: Estimating Sums and Differences of Decimals

                  Interactive Learning

                     i7-1 Estimating Sums and Differences of Decimals: Part 1

                     i7-1: Estimating Sums and Differences of Decimals: Part 2

                     i7-1: Estimating Sums and Differences of Decimals: Part 3

                     i7-1: Estimating Sums and Differences of Decimals: Lesson Check

                  Journal

                     i7-1: Estimating Sums and Differences of Decimals: Journal

                  Practice

                     i7-1: Estimating Sums and Differences of Decimals: Practice

            Cluster 8: Multiplying and Dividing Decimals

               Lesson i8-1: Patterns in Multiplying and Dividing Decimals

                  Interactive Learning

                     i8-1: Patterns in Multiplying and Dividing Decimals: Part 1

                     i8-1: Patterns in Multiplying and Dividing Decimals: Part 2

                     i8-1: Patterns in Multiplying and Dividing Decimals: Part 3

                     i8-1: Patterns in Multiplying and Dividing Decimals: Lesson Check

                  Journal

                     i8-1: Patterns in Multiplying and Dividing Decimals: Journal

                  Practice

                     i8-1: Patterns in Multiplying and Dividing Decimals: Practice

               Lesson i8-2: Multiplying Decimals

                  Interactive Learning

                     Lesson i8-2: Multiplying Decimals: Part 1

                     Lesson i8-2: Multiplying Decimals: Part 2

                     Lesson i8-2: Multiplying Decimals: Part 3

                     Lesson i8-2: Multiplying Decimals: Lesson Check

                  Journal

                     i8-2: Multiplying Decimals: Journal

                  Practice

                     i8-2: Multiplying Decimals: Practice

               Lesson i8-3: Dividing Decimals by Whole Numbers

                  Interactive Learning

                     i8-3: Dividing Decimals by Whole Numbers: Part 1

                     i8-3: Dividing Decimals by Whole Numbers: Part 2

                     i8-3: Dividing Decimals by Whole Numbers: Part 3

                     i8-3: Dividing Decimals by Whole Numbers: Lesson Check

                  Journal

                     i8-3: Dividing Decimals by Whole Numbers: Journal

                  Practice

                     i8-3: Dividing Decimals by Whole Numbers: Practice

               Lesson i8-4: Estimating Decimal Products and Quotients

                  Interactive Learning

                     i8-4: Estimating Decimal Products and Quotients: Part 1

                     i8-4: Estimating Decimal Products and Quotients: Part 2

                     i8-4: Estimating Decimal Products and Quotients: Part 3

                     i8-4: Estimating Decimal Products and Quotients: Lesson Check

                  Journal

                     i8-4: Estimating Decimal Products and Quotients: Journal

                  Practice

                     i8-4: Estimating Decimal Products and Quotients: Practice

               Lesson i8-5: Dividing Decimals

                  Interactive Learning

                     Lesson i8-5: Dividing Decimals: Part 1

                     Lesson i8-5: Dividing Decimals: Part 2

                     Lesson i8-5: Dividing Decimals: Part 3

                     Lesson i8-5: Dividing Decimals: Lesson Check

                  Journal

                     i8-5: Dividing Decimals: Journal

                  Practice

                     i8-5: Dividing Decimals: Practice

            Cluster 9: Fraction Number Sense

               Lesson i9-1: Equivalent Fractions

                  Interactive Learning

                     Lesson i9-1: Equivalent Fractions: Part 1

                     Lesson i9-1: Equivalent Fractions: Part 2

                     Lesson i9-1: Equivalent Fractions: Part 3

                     Lesson i9-1: Equivalent Fractions: Lesson Check

                  Journal

                     i9-1: Equivalent Fractions: Journal

                  Practice

                     i9-1: Equivalent Fractions: Practice

               Lesson i9-2: Fractions in Simplest Form

                  Interactive Learning

                     Lesson i9-2: Fractions in Simplest Form: Part 1

                     Lesson i9-2: Fractions in Simplest Form: Part 2

                     Lesson i9-2: Fractions in Simplest Form: Part 3

                     Lesson i9-2: Fractions in Simplest Form: Lesson Check

                  Journal

                     i9-2: Fractions in Simplest Form: Journal

                  Practice

                     i9-2: Fractions in Simplest Form: Practice

               Lesson i9-3: Comparing and Ordering Fractions

                  Interactive Learning

                     Lesson i9-3: Comparing and Ordering Fractions: Part 1

                     Lesson i9-3: Comparing and Ordering Fractions: Part 2

                     Lesson i9-3: Comparing and Ordering Fractions: Part 3

                     Lesson i9-3: Comparing and Ordering Fractions: Lesson Check

                  Journal

                     i9-3: Comparing and Ordering Fractions: Journal

                  Practice

                     i9-3: Comparing and Ordering Fractions: Practice

               Lesson i9-4: Fractions and Division

                  Interactive Learning

                     Lesson i9-4: Fractions and Division: Part 1

                     Lesson i9-4: Fractions and Division: Part 2

                     Lesson i9-4: Fractions and Division: Part 3

                     Lesson i9-4: Fractions and Division: Lesson Check

                  Journal

                     i9-4: Fractions and Division: Journal

                  Practice

                     i9-4: Fractions and Division: Practice

               Lesson i9-5: Fractions and Decimals

                  Interactive Learning

                     Lesson i9-5: Fractions and Decimals: Part 1

                     Lesson i9-5: Fractions and Decimals: Part 2

                     Lesson i9-5: Fractions and Decimals: Part 3

                     Lesson i9-5: Fractions and Decimals: Lesson Check

                  Journal

                     i9-5 Journal

                  Practice

                     i9-5: Fractions and Decimals: Practice

            Cluster 10: Adding and Subtracting Fractions

               Lesson i10-1: Adding Fractions with Like Denominators

                  Interactive Learning

                     i10-1: Adding Fractions with Like Denominators: Part 1

                     i10-1: Adding Fractions with Like Denominators: Part 2

                     i10-1: Adding Fractions with Like Denominators: Part 3

                     i10-1: Adding Fractions with Like Denominators: Lesson Check

                  Journal

                     i10-1: Adding Fractions with Like Denominators: Journal

                  Practice

                     i10-1: Adding Fractions with Like Denominators: Practice

               Lesson i10-2: Subtracting Fractions with Like Denominators

                  Interactive Learning

                     i10-2: Subtracting Fractions with Like Denominators: Part 1

                     i10-2: Subtracting Fractions with Like Denominators: Part 2

                     i10-2: Subtracting Fractions with Like Denominators: Part 3

                     i10-2: Subtracting Fractions with Like Denominators: Lesson Check

                  Journal

                     i10-2: Subtracting Fractions with Like Denominators: Journal

                  Practice

                     i10-2: Subtracting Fractions with Like Denominators: Practice

               Lesson i10-3: Adding Fractions with Unlike Denominators

                  Interactive Learning

                     Lesson i10-3: Adding Fractions with Unlike Denominators: Part 1

                     Lesson i10-3: Adding Fractions with Unlike Denominators: Part 2

                     Lesson i10-3: Adding Fractions with Unlike Denominators: Part 3

                     Lesson i10-3: Adding Fractions with Unlike Denominators: Lesson Check

                  Journal

                     i10-3: Adding Fractions with Unlike Denominators: Journal

                  Practice

                     i10-3: Adding Fractions with Unlike Denominators: Practice

               Lesson i10-4: Subtracting with Unlike Denominators

                  Interactive Learning

                     Lesson i10-4: Subtracting with Unlike Denominators: Part 1

                     Lesson i10-4: Subtracting with Unlike Denominators: Part 2

                     Lesson i10-4: Subtracting with Unlike Denominators: Part 3

                     Lesson i10-4: Subtracting with Unlike Denominators: Lesson Check

                  Journal

                     i10-4: Subtracting with Unlike Denominators: Journal

                  Practice

                     i10-4: Subtracting with Unlike Denominators: Practice

            Cluster 11: Multiplying and Dividing Fractions

               Lesson i11-1: Multiplying a Whole Number and a Fraction

                  Interactive Learning

                     Lesson i11-1: Multiplying a Whole Number and a Fraction: Part 1

                     Lesson i11-1: Multiplying a Whole Number and a Fraction: Part 2

                     Lesson i11-1: Multiplying a Whole Number and a Fraction: Part 3

                     Lesson i11-1: Multiplying a Whole Number and a Fraction: Lesson Check

                  Journal

                     i11-1: Multiplying a Whole Number and a Fraction: Journal

                  Practice

                     i11-1: Multiplying a Whole Number and a Fraction: Practice

               Lesson i11-2: Multiplying Fractions

                  Interactive Learning

                     Lesson i11-2: Multiplying Fractions: Part 1

                     Lesson i11-2: Multiplying Fractions: Part 2

                     Lesson i11-2: Multiplying Fractions: Part 3

                     Lesson i11-2: Multiplying Fractions: Lesson Check

                  Journal

                     i11-2: Multiplying Fractions: Journal

                  Practice

                     i11-2: Multiplying Fractions: Practice

               Lesson i11-3: Dividing a Unit Fraction by a Whole Number

                  Interactive Learning

                     i11-3: Dividing a Unit Fraction by a Whole Number: Part 1

                     i11-3: Dividing a Unit Fraction by a Whole Number: Part 2

                     i11-3: Dividing a Unit Fraction by a Whole Number: Part 3

                     i11-3: Dividing a Unit Fraction by a Whole Number: Lesson Check

                  Journal

                     i11-3: Dividing a Unit Fraction by a Whole Number: Journal

                  Practice

                     i11-3: Dividing a Unit Fraction by a Whole Number: Practice

               Lesson i11-4: Dividing a Whole Number by a Unit Fraction

                  Interactive Learning

                     i11-4: Dividing a Whole Number by a Unit Fraction: Part 1

                     i11-4: Dividing a Whole Number by a Unit Fraction: Part 2

                     i11-4: Dividing a Whole Number by a Unit Fraction: Part 3

                     i11-4: Dividing a Whole Number by a Unit Fraction: Lesson Check

                  Journal

                     i11-4: Dividing a Whole Number by a Unit Fraction: Journal

                  Practice

                     i11-4: Dividing a Whole Number by a Unit Fraction: Practice

               Lesson i11-5: Dividing Fractions

                  Interactive Learning

                     Lesson i11-5: Dividing Fractions: Part 1

                     Lesson i11-5: Dividing Fractions: Part 2

                     Lesson i11-5: Dividing Fractions: Part 3

                     Lesson i11-5: Dividing Fractions: Lesson Check

                  Journal

                     i11-5: Dividing Fractions: Journal

                  Practice

                     i11-5: Dividing Fractions: Practice

            Cluster 12: Mixed Numbers

               Lesson i12-1: Mixed Numbers and Improper Fractions

                  Interactive Learning

                     Lesson i12-1: Mixed Numbers and Improper Fractions: Part 1

                     Lesson i12-1: Mixed Numbers and Improper Fractions: Part 2

                     Lesson i12-1: Mixed Numbers and Improper Fractions: Part 3

                     Lesson i12-1: Mixed Numbers and Improper Fractions: Lesson Check

                  Journal

                     i12-1: Mixed Numbers and Improper Fractions: Journal

                  Practice

                     i12-1: Mixed Numbers and Improper Fractions: Practice

               Lesson i12-2: Adding Mixed Numbers

                  Interactive Learning

                     Lesson i12-2: Adding Mixed Numbers: Part 1

                     Lesson i12-2: Adding Mixed Numbers: Part 2

                     Lesson i12-2: Adding Mixed Numbers: Part 3

                     Lesson i12-2: Adding Mixed Numbers: Lesson Check

                  Journal

                     i12-2: Adding Mixed Numbers: Journal

                  Practice

                     i12-2: Adding Mixed Numbers: Practice

               Lesson i12-3: Subtracting Mixed Numbers

                  Interactive Learning

                     Lesson i12-3: Subtracting Mixed Numbers: Part 1

                     Lesson i12-3: Subtracting Mixed Numbers: Part 2

                     Lesson i12-3: Subtracting Mixed Numbers: Part 3

                     Lesson i12-3: Subtracting Mixed Numbers: Lesson Check

                  Journal

                     i12-3: Subtracting Mixed Numbers: Journal

                  Practice

                     i12-3: Subtracting Mixed Numbers: Practice

               Lesson i12-4: Multiplying Mixed Numbers

                  Interactive Learning

                     i12-4: Multiplying Mixed Numbers: Part 1

                     i12-4: Multiplying Mixed Numbers: Part 2

                     i12-4: Multiplying Mixed Numbers: Part 3

                     i12-4: Multiplying Mixed Numbers: Lesson Check

                  Journal

                     i12-4: Multiplying Mixed Numbers: Journal

                  Practice

                     i12-4: Multiplying Mixed Numbers: Practice

               Lesson i12-5: Dividing Mixed Numbers

                  Interactive Learning

                     i12-5: Dividing Mixed Numbers: Part 1

                     i12-5: Dividing Mixed Numbers: Part 2

                     i12-5: Dividing Mixed Numbers: Part 3

                     i12-5: Dividing Mixed Numbers: Lesson Check

                  Journal

                     i12-5: Dividing Mixed Numbers: Journal

                  Practice

                     i12-5: Dividing Mixed Numbers Practice

            Cluster 13: Ratios

               Lesson i13-1: Ratios

                  Interactive Learning

                     Lesson i13-1: Ratios: Part 1

                     Lesson i13-1: Ratios: Part 2

                     Lesson i13-1: Ratios: Part 3

                     Lesson i13-1: Ratios: Lesson Check

                  Journal

                     i13-1: Ratios: Journal

                  Practice

                     i13-1: Ratios: Practice

               Lesson i13-2: Equivalent Ratios

                  Interactive Learning

                     Lesson i13-2: Equivalent Ratios: Part 1

                     Lesson i13-2: Equivalent Ratios: Part 2

                     Lesson i13-2: Equivalent Ratios: Part 3

                     Lesson i13-2: Equivalent Ratios: Lesson Check

                  Journal

                     i13-2: Equivalent Ratios: Journal

                  Practice

                     i13-2: Equivalent Ratios: Practice

            Cluster 14: Rates and Measurements

               Lesson i14-1: Unit Rates

                  Interactive Learning

                     Lesson i14-1: Unit Rates: Part 1

                     Lesson i14-1: Unit Rates: Part 2

                     Lesson i14-1: Unit Rates: Part 3

                     Lesson i14-1: Unit Rates: Lesson Check

                  Journal

                     i14-1: Unit Rates: Journal

                  Practice

                     i14-1: Unit Rates: Practice

               Lesson i14-2: Converting Customary Measurements

                  Interactive Learning

                     Lesson i14-2: Converting Customary Measurements: Part 1

                     Lesson i14-2: Converting Customary Measurements: Part 2

                     Lesson i14-2: Converting Customary Measurements: Part 3

                     Lesson i14-2: Converting Customary Measurements: Lesson Check

                  Journal

                     i14-2: Converting Customary Measurements: Journal

                  Practice

                     i14-2: Converting Customary Measurements: Practice

               Lesson i14-3: Converting Metric Measurements

                  Interactive Learning

                     Lesson i14-3: Converting Metric Measurements: Part 1

                     Lesson i14-3: Converting Metric Measurements: Part 2

                     Lesson i14-3: Converting Metric Measurements: Part 3

                     Lesson i14-3: Converting Metric Measurements: Lesson Check

                  Journal

                     i14-3: Converting Metric Measurements: Journal

                  Practice

                     i14-3: Converting Metric Measurements: Practice

            Cluster 15: Proportional Relationships

               Lesson i15-1: Graphing Ratios

                  Interactive Learning

                     Lesson i15-1: Graphing Ratios: Part 1

                     Lesson i15-1: Graphing Ratios: Part 2

                     Lesson i15-1: Graphing Ratios: Part 3

                     Lesson i15-1: Graphing Ratios: Lesson Check

                  Journal

                     i15-1: Graphing Ratios: Journal

                  Practice

                     i15-1: Graphing Ratios: Practice

               Lesson i15-2: Recognizing Proportional Relationships

                  Interactive Learning

                     i15-2: Recognizing Proportional Relationships: Part 1

                     i15-2: Recognizing Proportional Relationships: Part 2

                     i15-2: Recognizing Proportional Relationships: Part 3

                     i15-2: Recognizing Proportional Relationships: Lesson Check

                  Journal

                     i15-2: Recognizing Proportional Relationships: Journal

                  Practice

                     i15-2: Recognizing Proportional Relationships: Practice

               Lesson i15-3: Constant of Proportionality

                  Interactive Learning

                     i15-3: Constant of Proportionality: Part 1

                     i15-3: Constant of Proportionality: Part 2

                     i15-3: Constant of Proportionality: Part 3

                     i15-3: Constant of Proportionality: Lesson Check

                  Journal

                     i15-3: Constant of Proportionality: Journal

                  Practice

                     i15-3: Constant of Proportionality: Practice

            Cluster 16: Number Sense with Percents

               Lesson i16-1: Understanding Percent

                  Interactive Learning

                     Lesson i16-1: Understanding Percent: Part 1

                     Lesson i16-1: Understanding Percent: Part 3

                     Lesson i16-1: Understanding Percent: Lesson Check

                     Lesson i16-1: Understanding Percent: Part 2

                  Journal

                     i16-1: Understanding Percent: Journal

                  Practice

                     i16-1: Understanding Percent: Practice

               Lesson i16-2: Estimating Percent

                  Interactive Learning

                     Lesson i16-2: Estimating Percent: Part 1

                     Lesson i16-2: Estimating Percent: Part 2

                     Lesson i16-2: Estimating Percent: Part 3

                     Lesson i16-2: Estimating Percent: Lesson Check

                  Journal

                     i16-2: Estimating Percent: Journal

                  Practice

                     i16-2: Estimating Percent: Practice

            Cluster 17: Computations with Percents

               Lesson i17-1: Finding a Percent of a Number

                  Interactive Learning

                     Lesson i17-1: Finding a Percent of a Number: Part 2

                     Lesson i17-1: Finding a Percent of a Number: Part 3

                     Lesson i17-1: Finding a Percent of a Number: Lesson Check

                     Lesson i17-1: Finding a Percent of a Number: Part 1

                  Journal

                     i17-1: Finding a Percent of a Number: Journal

                  Practice

                     i17-1: Finding a Percent of a Number: Practice

               Lesson i17-2: Finding a Percent

                  Interactive Learning

                     Lesson i17-2: Finding a Percent: Part 1

                     Lesson i17-2: Finding a Percent: Part 2

                     Lesson i17-2: Finding a Percent: Part 3

                     Lesson i17-2: Finding a Percent: Lesson Check

                  Journal

                     i17-2: Finding a Percent: Journal

                  Practice

                     i17-2: Finding a Percent: Practice

               Lesson i17-3: Finding the Whole Given a Percent

                  Interactive Learning

                     Lesson i17-3: Finding the Whole Given a Percent: Part 1

                     Lesson i17-3: Finding the Whole Given a Percent: Part 2

                     Lesson i17-3: Finding the Whole Given a Percent: Part 3

                     Lesson i17-3: Finding the Whole Given a Percent: Lesson Check

                  Journal

                     i17-3: Finding the Whole Given a Percent: Journal

                  Practice

                     i17-3: Finding the Whole Given a Percent: Practice

               Lesson i17-4: Sales Tax, Tips, and Simple Interest

                  Interactive Learning

                     i17-4: Sales Tax, Tips, and Simple Interest: Part 1

                     i17-4: Sales Tax, Tips, and Simple Interest: Part 2

                     i17-4: Sales Tax, Tips, and Simple Interest: Part 3

                     i17-4: Sales Tax, Tips, and Simple Interest: Lesson Check

                  Journal

                     i17-4: Sales Tax, Tips, and Simple Interest: Journal

                  Practice

                     i17-4: Sales Tax, Tips, and Simple Interest: Practice

               Lesson i17-5: Markdowns

                  Interactive Learning

                     i17-5: Markdowns: Part 1

                     i17-5: Markdowns: Part 2

                     i17-5: Markdowns: Part 3

                     i17-5: Markdowns: Lesson Check

                  Journal

                     i17-5: Markdowns: Journal

                  Practice

                     i17-5: Markdowns: Practice

            Cluster 18: Exponents

               Lesson i18-1: Exponents

                  Interactive Learning

                     i18-1: Exponents: Part 1

                     i18-1: Exponents: Part 2

                     i18-1: Exponents: Part 3

                     i18-1: Exponents: Lesson Check

                  Journal

                     i18-1: Exponents: Journal

                  Practice

                     i18-1: Exponents: Practice

               Lesson i18-2: Multiplying Decimals by Powers of Ten

                  Interactive Learning

                     i18-2: Multiplying Decimals by Powers of Ten: Part 1

                     i18-2: Multiplying Decimals by Powers of Ten: Part 2

                     i18-2: Multiplying Decimals by Powers of Ten: Part 3

                     i18-2: Multiplying Decimals by Powers of Ten: Lesson Check

                  Journal

                     i18-2: Multiplying Decimals by Powers of Ten: Journal

                  Practice

                     i18-2: Multiplying Decimals by Powers of Ten: Practice

            Cluster 19: Geometry

               Lesson i19-1: Classifying Triangles

                  Interactive Learning

                     Lesson i19-1: Classifying Triangles: Part 1

                     Lesson i19-1: Classifying Triangles: Part 2

                     Lesson i19-1: Classifying Triangles: Part 3

                     Lesson i19-1: Classifying Triangles: Lesson Check

                  Journal

                     i19-1: Classifying Triangles: Journal

                  Practice

                     i19-1: Classifying Triangles: Practice

               Lesson i19-2: Classifying Quadrilaterals

                  Interactive Learning

                     Lesson i19-2: Classifying Quadrilaterals: Part 1

                     Lesson i19-2: Classifying Quadrilaterals: Part 2

                     Lesson i19-2: Classifying Quadrilaterals: Part 3

                     Lesson i19-2: Classifying Quadrilaterals: Lesson Check

                  Journal

                     i19-2: Classifying Quadrilaterals: Journal

                  Practice

                     i19-2: Classifying Quadrilaterals: Practice

            Cluster 20: Measuring 2- and 3-Dimensional Objects

               Lesson i20-1: Perimeter

                  Interactive Learning

                     i20-1: Perimeter: Part 1

                     i20-1: Perimeter: Part 2

                     i20-1: Perimeter: Part 3

                     i20-1: Perimeter: Lesson Check

                  Journal

                     i20-1: Perimeter: Journal

                  Practice

                     i20-1: Perimeter: Practice

               Lesson i20-2: Area of Rectangles and Squares

                  Interactive Learning

                     Lesson i20-2: Area of Rectangles and Squares: Part 1

                     Lesson i20-2: Area of Rectangles and Squares: Part 2

                     Lesson i20-2: Area of Rectangles and Squares: Part 3

                     Lesson i20-2: Area of Rectangles and Squares: Lesson Check

                  Journal

                     i20-2: Area of Rectangles and Squares: Journal

                  Practice

                     i20-2: Area of Rectangles and Squares: Practice

               Lesson i20-3: Area of Parallelograms and Triangles

                  Interactive Learning

                     Lesson i20-3: Area of Parallelograms and Triangles: Part 1

                     Lesson i20-3: Area of Parallelograms and Triangles: Part 2

                     Lesson i20-3: Area of Parallelograms and Triangles: Part 3

                     Lesson i20-3: Area of Parallelograms and Triangles: Lesson Check

                  Journal

                     i20-3: Area of Parallelograms and Triangles: Journal

                  Practice

                     i20-3: Area of Parallelograms and Triangles: Practice

               Lesson i20-4: Nets and Surface Area

                  Interactive Learning

                     Lesson i20-4: Nets and Surface Area: Part 1

                     Lesson i20-4: Nets and Surface Area: Part 2

                     Lesson i20-4: Nets and Surface Area: Lesson Check

                  Journal

                     i20-4: Nets and Surface Area: Journal

                  Practice

                     i20-4: Nets and Surface Area: Practice

               Lesson i20-5: Volume of Prisms

                  Interactive Learning

                     Lesson i20-5: Volume of Prisms: Part 1

                     Lesson i20-5: Volume of Prisms: Part 2

                     Lesson i20-5: Volume of Prisms: Part 3

                     Lesson i20-5: Volume of Prisms: Lesson Check

                  Journal

                     i20-5: Volume of Prisms: Journal

                  Practice

                     i20-5: Volume of Prisms: Practice

            Cluster 21: Integers

               Lesson i21-1: Understanding Integers

                  Interactive Learning

                     Lesson i21-1: Understanding Integers: Part 1

                     Lesson i21-1: Understanding Integers: Part 2

                     Lesson i21-1: Understanding Integers: Part 3

                     Lesson i21-1: Understanding Integers: Lesson Check

                  Journal

                     i21-1: Understanding Integers: Journal

                  Practice

                     i21-1: Understanding Integers: Practice

               Lesson i21-2: Comparing and Ordering Integers

                  Interactive Learning

                     i21-2: Comparing and Ordering Integers: Part 2

                     i21-2: Comparing and Ordering Integers: Part 3

                     i21-2: Comparing and Ordering Integers: Lesson Check

                     i21-2: Comparing and Ordering Integers: Part 1

                  Journal

                     i21-2: Comparing and Ordering Integers: Journal

                  Practice

                     i21-2: Comparing and Ordering Integers: Practice

               Lesson i21-3: Adding Integers

                  Interactive Learning

                     i21-3: Adding Integers: Part 1

                     i21-3: Adding Integers: Part 2

                     i21-3: Adding Integers: Part 3

                     i21-3: Adding Integers: Lesson Check

                  Journal

                     i21-3: Adding Integers: Journal

                  Practice

                     i21-3: Adding Integers: Practice

               Lesson i21-4: Subtracting Integers

                  Interactive Learning

                     i21-4: Subtracting Integers: Part 1

                     i21-4: Subtracting Integers: Part 2

                     i21-4: Subtracting Integers: Part 3

                     i21-4: Subtracting Integers: Lesson Check

                  Journal

                     i21-4: Subtracting Integers: Journal

                  Practice

                     i21-4: Subtracting Integers: Practice

               Lesson i21-5: Multiplying Integers

                  Interactive Learning

                     i21-5: Multiplying Integers: Part 1

                     i21-5: Multiplying Integers: Part 2

                     i21-5: Multiplying Integers: Part 3

                     i21-5: Multiplying Integers: Lesson Check

                  Journal

                     i21-5: Multiplying Integers: Journal

                  Practice

                     i21-5: Multiplying Integers: Practice

               Lesson i21-6: Dividing Integers

                  Interactive Learning

                     i21-6: Dividing Integers: Part 1

                     i21-6: Dividing Integers: Part 2

                     i21-6: Dividing Integers: Part 3

                     i21-6: Dividing Integers: Lesson Check

                  Journal

                     i21-6: Dividing Integers: Journal

                  Practice

                     i21-6: Dividing Integers: Practice

            Cluster 22: Graphing and Rational Numbers

               Lesson i22-1: Graphing in the First Quadrant

                  Interactive Learning

                     i22-1: Graphing in the First Quadrant: Part 1

                     i22-1: Graphing in the First Quadrant: Part 2

                     i22-1: Graphing in the First Quadrant: Part 3

                     i22-1: Graphing in the First Quadrant: Lesson Check

                  Journal

                     i22-1: Graphing in the First Quadrant: Journal

                  Practice

                     i22-1: Graphing in the First Quadrant: Practice

               Lesson i22-2: Graphing in the Coordinate Plane

                  Interactive Learning

                     i22-2: Graphing in the Coordinate Plane: Part 2

                     i22-2: Graphing in the Coordinate Plane: Part 3

                     i22-2: Graphing in the Coordinate Plane: Lesson Check

                     i22-2: Graphing in the Coordinate Plane: Part 1

                  Journal

                     i22-2: Graphing in the Coordinate Plane: Journal

                  Practice

                     i22-2: Graphing in the Coordinate Plane: Practice

               Lesson i22-3: Distance When There's a Common Coordinate

                  Interactive Learning

                     i22-3: Distance When There's a Common Coordinate: Part 1

                     i22-3: Distance When There's a Common Coordinate: Part 2

                     i22-3: Distance When There's a Common Coordinate: Part 3

                     i22-3: Distance When There's a Common Coordinate: Lesson Check

                  Journal

                     i22-3: Distance When There's a Common Coordinate: Journal

                  Practice

                     i22-3: Distance When There's a Common Coordinate: Practice

               Lesson i22-4: Rational Numbers on the Number Line

                  Interactive Learning

                     Lesson i22-4: Rational Numbers on the Number Line: Part 1

                     Lesson i22-4: Rational Numbers on the Number Line: Part 2

                     Lesson i22-4: Rational Numbers on the Number Line: Part 3

                     Lesson i22-4: Rational Numbers on the Number Line: Lesson Check

                  Journal

                     i22-4: Rational Numbers on the Number Line: Journal

                  Practice

                     i22-4: Rational Numbers on the Number Line: Practice

               Lesson i22-5: Comparing and Ordering Rational Numbers

                  Interactive Learning

                     Lesson i22-5: Comparing and Ordering Rational Numbers: Part 1

                     Lesson i22-5: Comparing and Ordering Rational Numbers: Part 2

                     Lesson i22-5: Comparing and Ordering Rational Numbers: Part 3

                     Lesson i22-5: Comparing and Ordering Rational Numbers: Lesson Check

                  Journal

                     i22-5: Comparing and Ordering Rational Numbers: Journal

                  Practice

                     i22-5: Comparing and Ordering Rational Numbers: Practice

            Cluster 23: Numerical and Algebraic Expressions

               Lesson i23-1: Order of Operations

                  Interactive Learning

                     Lesson i23-1: Order of Operations: Part 1

                     Lesson i23-1: Order of Operations: Part 2

                     Lesson i23-1: Order of Operations: Part 3

                     Lesson i23-1: Order of Operations: Lesson Check

                  Journal

                     i23-1: Order of Operations: Journal

                  Practice

                     i23-1: Order of Operations: Practice

               Lesson i23-2: Variables and Expressions

                  Interactive Learning

                     Lesson i23-2: Variables and Expressions: Part 1

                     Lesson i23-2: Variables and Expressions: Part 2

                     Lesson i23-2: Variables and Expressions: Lesson Check

                     Lesson i23-2: Variables and Expressions: Part 3

                  Journal

                     i23-2: Variables and Expressions: Journal

                  Practice

                     i23-2: Variables and Expressions: Practice

               Lesson i23-3: Patterns and Expressions

                  Interactive Learning

                     i23-3: Patterns and Expressions: Part 1

                     i23-3: Patterns and Expressions: Part 2

                     i23-3: Patterns and Expressions: Part 3

                     i23-3: Patterns and Expressions: Lesson Check

                  Journal

                     i23-3: Patterns and Expressions: Journal

                  Practice

                     i23-3: Patterns and Expressions: Practice

               Lesson i23-4: Evaluating Expressions: Whole Numbers

                  Interactive Learning

                     Lesson i23-4: Evaluating Expressions: Whole Numbers: Part 1

                     Lesson i23-4: Evaluating Expressions: Whole Numbers: Part 2

                     Lesson i23-4: Evaluating Expressions: Whole Numbers: Part 3

                     Lesson i23-4: Evaluating Expressions: Whole Numbers: Lesson Check

                  Journal

                     i23-4: Evaluating Expressions: Whole Numbers: Journal

                  Practice

                     i23-4: Evaluating Expressions: Whole Numbers: Practice

            Cluster 24: More Algebraic Expressions

               Lesson i24-1: Evaluating Expressions: Rational Numbers

                  Interactive Learning

                     Lesson i24-1: Evaluating Expressions: Rational Numbers: Part 1

                     Lesson i24-1: Evaluating Expressions: Rational Numbers: Part 2

                     Lesson i24-1: Evaluating Expressions: Rational Numbers: Part 3

                     Lesson i24-1: Evaluating Expressions: Rational Numbers: Lesson Check

                  Journal

                     i24-1: Evaluating Expressions: Rational Numbers: Journal

                  Practice

                     i24-1: Evaluating Expressions: Rational Numbers: Practice

               Lesson i24-2: Equivalent Expressions

                  Interactive Learning

                     Lesson i24-2: Equivalent Expressions: Part 1

                     Lesson i24-2: Equivalent Expressions: Part 2

                     Lesson i24-2: Equivalent Expressions: Part 3

                     Lesson i24-2: Equivalent Expressions: Lesson Check

                  Journal

                     i24-2: Equivalent Expressions: Journal

                  Practice

                     i24-2: Equivalent Expressions: Practice

               Lesson i24-3: Simplifying Expressions

                  Interactive Learning

                     Lesson i24-3: Simplifying Expressions: Part 1

                     Lesson i24-3: Simplifying Expressions: Part 2

                     Lesson i24-3: Simplifying Expressions: Part 3

                     Lesson i24-3: Simplifying Expressions: Lesson Check

                  Journal

                     i24-3: Simplifying Expressions: Journal

                  Practice

                     i24-3: Simplifying Expressions: Practice

            Cluster 25: Equations

               Lesson i25-1: Writing Equations

                  Interactive Learning

                     Lesson i25-1: Writing Equations: Part 1

                     Lesson i25-1: Writing Equations: Part 2

                     Lesson i25-1: Writing Equations: Part 3

                     Lesson i25-1: Writing Equations: Lesson Check

                  Journal

                     i25-1: Writing Equations: Journal

                  Practice

                     i25-1: Writing Equations: Practice

               Lesson i25-2: Principles of Solving Equations

                  Interactive Learning

                     Lesson i25-2: Principles of Solving Equations: Part 1

                     Lesson i25-2: Principles of Solving Equations: Part 2

                     Lesson i25-2: Principles of Solving Equations: Part 3

                     Lesson i25-2: Principles of Solving Equations: Lesson Check

                  Journal

                     i25-2: Principles of Solving Equations: Journal

                  Practice

                     i25-2: Principles of Solving Equations: Practice

               Lesson i25-3: Solving Addition and Subtraction Equations

                  Interactive Learning

                     Lesson i25-3: Solving Addition and Subtraction Equations: Part 1

                     Lesson i25-3: Solving Addition and Subtraction Equations: Part 2

                     Lesson i25-3: Solving Addition and Subtraction Equations: Part 3

                     Lesson i25-3: Solving Addition and Subtraction Equations: Lesson Check

                  Journal

                     i25-3: Solving Addition and Subtraction Equations: Journal

                  Practice

                     i25-3: Solving Addition and Subtraction Equations: Practice

               Lesson i25-4: Solving Multiplication and Division Equations

                  Interactive Learning

                     i25-4: Solving Multiplication and Division Equations: Part 1

                     i25-4: Solving Multiplication and Division Equations: Part 2

                     i25-4: Solving Multiplication and Division Equations; Part 3

                     i25-4: Solving Multiplication and Division Equations: Lesson Check

                  Journal

                     i25-4: Solving Multiplication and Division Equations: Journal

                  Practice

                     i25-4: Solving Multiplication and Division Equations: Practice

               Lesson i25-5: Solving Rational-Number Equations, Part 1

                  Interactive Learning

                     Lesson i25-5: Solving Rational-Number Equations, Part 1: Part 1

                     Lesson i25-5: Solving Rational-Number Equations, Part 1: Part 2

                     Lesson i25-5: Solving Rational-Number Equations, Part 1: Part 3

                     Lesson i25-5: Solving Rational-Number Equations, Part 1: Lesson Check

                  Journal

                     i25-5: Solving Rational-Number Equations, Part 1: Journal

                  Practice

                     i25-5: Solving Rational-Number Equations, Part 1: Practice

               Lesson i25-6: Solving Rational-Number Equations, Part 2

                  Interactive Learning

                     Lesson i25-6: Solving Rational-Number Equations, Part 2: Part 1

                     Lesson i25-6: Solving Rational-Number Equations, Part 2: Part 2

                     Lesson i25-6: Solving Rational-Number Equations, Part 2: Part 3

                     Lesson i25-6: Solving Rational-Number Equations, Part 2: Lesson Check

                  Journal

                     i25-6: Solving Rational-Number Equations, Part 2: Journal

                  Practice

                     i25-6: Solving Rational-Number Equations, Part 2: Practice

               Lesson i25-7: Solving Two-Step Equations

                  Interactive Learning

                     i25-7: Solving Two-Step Equations: Part 1

                     i25-7: Solving Two-Step Equations: Part 2

                     i25-7: Solving Two-Step Equations: Part 3

                     i25-7: Solving Two-Step Equations: Lesson Check

                  Journal

                     i25-7: Solving Two-Step Equations: Journal

                  Practice

                     i25-7: Solving Two-Step Equations: Practice

         3/4-Year Practice Performance Tasks

            Grade 7 3-4 Year Practice Performance Task 1

            Grade 7 3-4 Year Practice Performance Task 2

            Grade 8 3-4 Year Practice Performance Task 1

            Grade 8 3-4 Year Practice Performance Task 2

         Grade 7 Next Generation Assessment Practice Test

         Grade 8 Next Generation Assessment Practice Test

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            Topic 9: Percents: Review Homework with Answer Key
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            Topic 10: Equivalent Expressions: Review Homework with Answer Key
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            11-1: Solving Simple Equations: Teacher Guide
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            11-4: Solving Equations Using the Distributive Property: Teacher Guide
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            Topic 11: Equations: Review Homework with Answer Key
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            12-2: Solving Equations with Variables on Both Sides: Teacher Guide
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            12-4: Solutions – One, None, or Infinitely Many: Teacher Guide
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            Topic 12: Linear Equations in One Variable: Review Homework with Answer Key
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            13-1: Solving Inequalities Using Addition or Subtraction: Teacher Guide
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            Topic 19 Review: Angles: Homework with Answer Key
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            Topic 20 Review: Circles: Homework with Answer Key
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            Topic 21 Review: 2- and 3- Dimensional Shapes: Homework with Answer Key
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            22-1: Surface Areas of Right Prisms: Teacher Guide
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            Topic 22 Review: Surface Area and Volume: Homework with Answer Key
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            25-1: Angles, Lines, and Transversals: Teacher Guide
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