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Curriculum Standards:


Divide rational numbers. - 7.NC.1.9
Divide integers. - 7.NC.1.8
Multiply rational numbers. - 7.NC.1.7
Compare an algebraic solution process for equations and an algebraic solution process for inequalities. - NC.7.EE.4.b.2
Multiply integers. - 7.NC.1.6
Graph the solution set of the inequality and interpret in context. - NC.7.EE.4.b.3
Mathematical Modeling: Probability - 7.DP.7MM
Add and subtract rational numbers. - 7.NC.1.5
Subtract integers. - 7.NC.1.4
Represent real-world or mathematical situations using equations and inequalities involving variables and rational numbers. - 7.A.3.3
Fluently solve multi-step inequalities with the variable on one side, including those generated by word problems. - NC.7.EE.4.b.1
Add integers. - 7.NC.1.3
Represent, write, solve, and graph problems leading to linear inequalities with one variable in the form x + p > q and x + p < q, where p, and q are nonnegative rational numbers. - 7.A.3.2
Recognize rational numbers and write them in decimal form. - 7.NC.1.2
Write and solve problems leading to linear equations with one variable in the form px + q = r and p(x + q) = r where p, q, and r are rational numbers. - 7.A.3.1
Relate integers, their opposites, and their absolute values. - 7.NC.1.1
Solve equations resulting from proportional relationships in various contexts. - 7.2.4.2
Represent relationships in various contexts with equations involving variables and positive and negative rational numbers. Use the properties of equality to solve for the value of a variable. Interpret the solution in the original context. - 7.2.4.1
Reporting the number of observations. - M.7.20a
Test for equivalent ratios to decide whether quantities are in a proportional relationship. - 7.P.2.3
Use the constant of proportionality in an equation to represent a proportional relationship. - 7.P.2.4
Use ratio concepts and reasoning to solve multi-step problems. - 7.P.2.1
Find unit rates with ratios of fractions and use them to solve problems. - 7.P.2.2
Calculate the measure of variability of a data set and understand that it describes how the values of the data set vary with a single number. - NC.7.SP.3.a
Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. - M.7.20c
Use a graph to determine whether two quantities are proportional. - 7.P.2.5
Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. - M.7.20b
Informally assess the difference between two data sets by examining the overlap and separation between the graphical representations of two data sets. - NC.7.SP.3.b
Determine whether a relationship is proportional and use representations to solve problems. - 7.P.2.6
The student will compare and contrast quadrilaterals based on their properties. - 7.6a
Use division and previous understandings of fractions and decimals. - NC.7.NS.2.c
Apply properties of operations as strategies, including the standard algorithms, to multiply and divide rational numbers and describe the product and quotient in real-world contexts. - NC.7.NS.2.b
Understand that a rational number is any number that can be written as a quotient of integers with a non-zero divisor. - NC.7.NS.2.a
Use proportions and ratios to solve problems involving scale drawings and conversions of measurement units. - 7.3.2.3
Generate multiple random samples (or simulated samples) of the same size to gauge the variation in estimates or predictions, and use this data to draw inferences about a population with an unknown characteristic of interest. - NC.7.SP.2
Use angle properties to write and solve equations for an unknown angle. - 7.GM.B.5
Recognize the role of variability when comparing two populations. - NC.7.SP.3
Use measures of center and measures of variability for numerical data from random samples to draw comparative inferences about two populations. - NC.7.SP.4
Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. - NC.7.SP.5
Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation. - 7.RP.A.2c
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. - MAFS.7.EE.2.3
Collect data to calculate the experimental probability of a chance event, observing its long-run relative frequency. Use this experimental probability to predict the approximate relative frequency. - NC.7.SP.6
Identify and/or compute the constant of proportionality (unit rate). - 7.RP.A.2b
Determine when two quantities are in a proportional relationship. - 7.RP.A.2a
Develop a probability model and use it to find probabilities of simple events. - NC.7.SP.7
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. - MAFS.7.EE.2.4
Determine probabilities of compound events using organized lists, tables, tree diagrams, and simulation. - NC.7.SP.8
Describe the likelihood that an event will occur. - 7.DP.7.1
Recognize that the graph of any proportional relationship will pass through the origin. - 7.RP.A.2d
Simulate a compound event to approximate its probability. - 7.DP.7.7
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. - M.7.10
Find the probability of a compound event. - 7.DP.7.6
Finding the whole, given a part and the percent. - NC.6.RP.4.c
Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. - NC.6.RP.4.b
Understanding and finding a percent of a quantity as a ratio per 100. - NC.6.RP.4.a
Determine the experimental probability of an event. - 7.DP.7.3
Determine the theoretical probability of an event. - 7.DP.7.2
Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. - MAFS.K12.MP.3.1
Find all possible outcomes of a compound event. - 7.DP.7.5
Use probability models to find probabilities of events. - 7.DP.7.4
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. (e.g., 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.) - M.7.18
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. - M.7.17
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. - M.7.16
The student will solve practical problems involving operations with rational numbers. - 7.2
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. - M.7.15
The student will solve single-step and multistep practical problems, using proportional reasoning. - 7.3
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. - M.7.14
Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. - M.7.13
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. - M.7.12
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. - M.7.11
Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. - M.7.19
Use proportional reasoning to assess the reasonableness of solutions. - 7.A.2.4
Use proportional reasoning to solve real-world and mathematical problems involving ratios. - 7.A.2.3
Solve multi-step problems involving proportional relationships involving distance-time, percent increase or decrease, discounts, tips, unit pricing, similar figures, and other real-world and mathematical situations. - 7.A.2.2
Represent proportional relationships with tables, verbal descriptions, symbols, and graphs; translate from one representation to another. Determine and compare the unit rate (constant of proportionality, slope, or rate of change) given any of these representations. - 7.A.2.1
Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. - M.6.3c
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. (e.g., 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.) - M.7.21
Use proportions to solve percent problems. - 7.P.3.2
Represent and solve percent problems using equations. - 7.P.3.3
Understand, find, and analyze percents of numbers. - 7.P.3.1
Apply percent reasoning to solve simple interest problems. - 7.P.3.6
Solve problems involving percent change and percent error. - 7.P.3.4
Solve problems involving percent markup and markdown. - 7.P.3.5
Apply properties of operations to simplify and to factor linear algebraic expressions with rational coefficients. - 7.EEI.A.1
The student will investigate and describe the difference between the experimental probability and theoretical probability of an event. - 7.8b
Understand how to use equivalent expressions to clarify quantities in a problem. - 7.EEI.A.2
The student will determine the theoretical and experimental probabilities of an event. - 7.8a
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. (e.g., 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.) - M.7.24
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 ½ indicates an event that is neither unlikely nor likely and a probability near 1 indicates a likely event. - M.7.23
Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. (e.g., 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.) - M.7.22
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. - MAFS.7.G.2.5
Volume and surface area of pyramids, prisms, or three-dimensional objects composed of cubes, pyramids, and right prisms. - NC.7.G.6.b
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. - MAFS.7.G.2.6
Area and perimeter of two-dimensional objects composed of triangles, quadrilaterals, and polygons. - NC.7.G.6.a
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. - MAFS.7.EE.1.1
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.” - MAFS.7.EE.1.2
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. - MAFS.7.G.2.4
Solve problems involving scale drawings of real objects and geometric figures, including computing actual lengths and areas from a scale drawing and reproducing the drawing at a different scale. - 7.GM.A.1
Design simple experiments and collect data. Determine mean, median and range for quantitative data and from data represented in a display. Use these quantities to draw conclusions about the data, compare different data sets, and make predictions. - 7.4.1.1
Describe two-dimensional cross sections of pyramids, prisms, cones and cylinders. - 7.GM.A.3
Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize-to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. - MAFS.K12.MP.2.1
Find the area of triangles, quadrilaterals and other polygons composed of triangles and rectangles. - 7.GM.B.6a
Find the volume and surface area of prisms, pyramids and cylinders. - 7.GM.B.6b
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). - M.7.2a
Compute unit rates associated with ratios of fractions to solve real-world and mathematical problems. - NC.7.RP.1
Look for and express regularity in repeated reasoning. - 7.MP.8
Compute unit rates, including those that involve complex fractions, with like or different units. - 7.RP.A.1
Recognize and represent proportional relationships between quantities. - NC.7.RP.2
Make sense of problems and persevere in solving them. - MP.1
Use scale factors and unit rates in proportional relationships to solve ratio and percent problems. - NC.7.RP.3
Reason abstractly and quantitatively. - MP.2
Solve problems involving ratios, rates, percentages and proportional relationships. - 7.RP.A.3
Attend to precision. - 7.MP.6
Look for and make use of structure. - 7.MP.7
Model with mathematics. - 7.MP.4
Use appropriate tools strategically. - 7.MP.5
Understand that every quotient of integers (with non-zero divisor) is a rational number. - 7.NS.A.2c
Given two congruent figures, describe a sequence that exhibits the congruence between them. - NC.8.G.2.c
Look for and make use of structure. - MP.7
Look for and express regularity in repeated reasoning. - MP.8
Convert a rational number to a decimal. - 7.NS.A.2d
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. - NC.8.G.2.b
Understand that all rational numbers can be written as fractions or decimal numbers that terminate or repeat. - 7.NS.A.2e
Interpret products and quotients of rational numbers by describing real-world contexts. - 7.NS.A.2f
Construct viable arguments and critique the reasoning of others. - MP.3
Model with mathematics. - MP.4
Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation. Focus special attention on the points (0, 0) and (1, r) where r is the unit rate. - M.7.2d
Represent proportional relationships by equations. (e.g., 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.) - M.7.2c
Use appropriate tools strategically. - MP.5
Attend to precision. - MP.6
Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams and verbal descriptions of proportional relationships. - M.7.2b
Determine what the cross section looks like when a 3D figure is sliced. - 7.G.8.7
Solve inequalities using multiplication or division. - 7.AF.5.5
Understand that generalizations from a sample are valid only if the sample is representative of the population. - 7.DSP.A.1b
Understand that random sampling is used to produce representative samples and support valid inferences. - 7.DSP.A.1c
Write and solve two-step inequalities. - 7.AF.5.6
Solve problems involving the area of a circle. - 7.G.8.6
Use the Distributive Property to solve equations. - 7.AF.5.3
Solve problems involving radius, diameter, and circumference of circles. - 7.G.8.5
Recognizing that generalizations about a population from a sample are valid only if the sample is representative of that population. - NC.7.SP.1.a
Explain the meaning of (0, 0) and why it is included. - NC.7.RP.2.d.2
Solve problems involving angle relationships. - 7.G.8.4
Solve inequalities using addition or subtraction. - 7.AF.5.4
Understand that a sample is a subset of a population. - 7.DSP.A.1a
Understand that the y-coordinate of the ordered pair (1, r) corresponds to the unit rate and explain its meaning. - NC.7.RP.2.d.3
Using random sampling to produce representative samples to support valid inferences. - NC.7.SP.1.b
Explain the meaning of any point (x, y). - NC.7.RP.2.d.1
Multiply and divide rational numbers. - 7.NS.A.2a
Use the area of the base of a three-dimensional figure to find its volume. - 7.G.8.9
Solve inequalities that require multiple steps. - 7.AF.5.7
Verify experimentally the properties of rotations, reflections, and translations that create congruent figures. - NC.8.G.2.a
Determine that a number and its reciprocal have a product of 1 (multiplicative inverse). - 7.NS.A.2b
Find the area and surface area of 2-dimensional composite shapes and 3-dimensional prisms. - 7.G.8.8
Describe a possible sequence of transformations between two similar figures. - 8.GM.A.4a
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. - M.8.17
Use transformations to define congruence. - NC.8.G.2
Solve percent problems. - 6.RP.A.3c
Represent a problem with a two-step equation. - 7.AF.5.1
Solve problems with rational numbers. - 7.NC.1.10
Solve a problem with a two-step equation. - 7.AF.5.2
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. - MAFS.7.NS.1.2d
Apply properties of operations as strategies to multiply and divide rational numbers. - MAFS.7.NS.1.2c
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. - MAFS.7.G.1.2
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. - MAFS.7.NS.1.2b
Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. - MAFS.7.G.1.3
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. - MAFS.7.NS.1.2a
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. - MAFS.7.G.1.1
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. - MAFS.7.SP.3.6
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. - MAFS.7.SP.3.7
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. - MAFS.7.SP.3.5
Draw triangles when given information about their side lengths and angle measures. - 7.G.8.3
Draw figures with given conditions. - 7.G.8.2
Use the key in a scale drawing to find missing measures. - 7.G.8.1
Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. - MAFS.K12.MP.5.1
Find probabilities of compound events using organized lists, tables, tree diagrams and simulations. - 7.DSP.C.8
Mathematical Modeling: Generate Equivalent Expressions - 7.AF.4MM
Recognize and generate equivalent representations of positive and negative rational numbers, including equivalent fractions. - 7.1.1.5
Understand that division of two integers will always result in a rational number. Use this information to interpret the decimal result of a division problem when using a calculator. - 7.1.1.2
Creating a scale drawing. - NC.7.G.1.c
Use variables to represent quantities to solve real-world or mathematical problems. - NC.7.EE.4
Using a scale factor to compute actual lengths and areas from a scale drawing. - NC.7.G.1.b
Know that every rational number can be written as the ratio of two integers or as a terminating or repeating decimal. Recognize that π is not rational, but that it can be approximated by rational numbers such as 22/7 and 3.14. - 7.1.1.1
Understand that equivalent expressions can reveal real-world and mathematical relationships. Interpret the meaning of the parts of each expression in context. - NC.7.EE.2
Building an understanding that angle measures remain the same and side lengths are proportional. - NC.7.G.1.a
Solve multi-step real-world and mathematical problems posed with rational numbers in algebraic expressions. - NC.7.EE.3
Locate positive and negative rational numbers on the number line, understand the concept of opposites, and plot pairs of positive and negative rational numbers on a coordinate grid. - 7.1.1.3
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. - M.7.4c
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. (i.e., To add “p + q” on the number line, start at “0” and move to “p” then move |q| 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. - M.7.4b
Apply properties of operations as strategies to add and subtract rational numbers. - MAFS.7.NS.1.1d
Describe situations in which opposite quantities combine to make 0. (e.g., A hydrogen atom has 0 charge because its two constituents are oppositely charged.) - M.7.4a
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. - MAFS.7.NS.1.1c
Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). - 6.NS.C.8
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. - MAFS.7.NS.1.1b
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. - MAFS.7.NS.1.1a
Mathematical Modeling: Solve Problems Involving Geometry - 7.G.8MM
Apply understanding of order of operations and grouping symbols when using calculators and other technologies. - 7.A.4.2
Use properties of operations (limited to associative, commutative, and distributive) to generate equivalent numerical and algebraic expressions containing rational numbers, grouping symbols and whole number exponents. - 7.A.4.1
Mathematical Modeling: Use Sampling to Draw Inferences about Populations - 7.DP.6MM
Apply properties of operations as strategies to add and subtract rational numbers. - M.7.4d
Add expressions that represent real-world problems. - 7.AF.4.6
Subtract expressions using properties of operations. - 7.AF.4.7
Expand expressions using the Distributive Property. - 7.AF.4.4
Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers. - 6.N.4.4
Use common factors and the Distributive Property to factor expressions. - 7.AF.4.5
Add, subtract, and expand linear expressions with rational coefficients. - NC.7.EE.1.a
Factor linear expression with an integer GCF. - NC.7.EE.1.b
Use an equivalent expression to find new information. - 7.AF.4.8
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. - MAFS.7.RP.1.3
Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. - MAFS.8.G.1.3
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. - MAFS.7.RP.1.1
For an event described in everyday language, identify the outcomes in the sample space which compose the event, when the sample space is represented using organized lists, tables, and tree diagrams. - NC.7.SP.8.b
Describe a possible sequence of rigid transformations between two congruent figures. - 8.GM.A.2a
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. - NC.7.SP.8.a
Recognize and represent proportional relationships between quantities. - MAFS.7.RP.1.2
Write equivalent expressions for given expressions. - 7.AF.4.2
Design and use a simulation to generate frequencies for compound events. - NC.7.SP.8.c
Convert a fraction to a decimal using long division. - NC.7.NS.2.c.1
Use properties of operations to simplify expressions. - 7.AF.4.3
Understand that the decimal form of a rational number terminates in 0s or eventually repeats. - NC.7.NS.2.c.2
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. - MAFS.8.G.1.2
Write and evaluate algebraic expressions. - 7.AF.4.1
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. - M.7.5d
Apply properties of operations as strategies to multiply and divide rational numbers. - M.7.5c
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. - M.7.5b
Understand the characteristics of angles and side lengths that create a unique triangle, more than one triangle or no triangle. Build triangles from three measures of angles and/or sides. - NC.7.G.2
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. - M.7.5a
Understand area and circumference of a circle. - NC.7.G.4
Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve equations for an unknown angle in a figure. - NC.7.G.5
Make inferences about a population from a sample data set. - 7.DP.6.2
Determine if a sample is representative of a population. - 7.DP.6.1
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. - MAFS.7.SP.2.3
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. - MAFS.7.SP.2.4
Use random numbers generated by a calculator or a spreadsheet or taken from a table to simulate situations involving randomness, make a histogram to display the results, and compare the results to known probabilities. - 7.4.3.1
Calculate probability as a fraction of sample space or as a fraction of area. Express probabilities as percents, decimals and fractions. - 7.4.3.2
Use proportional reasoning to draw conclusions about and predict relative frequencies of outcomes based on probabilities. - 7.4.3.3
Compare populations using the mean, median, mode, range, interquartile range, and mean absolute deviation. - 7.DP.6.4
Draw comparative inferences about two populations using median and interquartile range (IQR). - 7.DP.6.3
Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. - MAFS.K12.MP.4.1
Estimate solutions to multiplication and division of integers in order to assess the reasonableness of results. - 7.N.2.1
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? - MAFS.7.EE.2.4a
Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. - MAFS.7.RP.1.2b
Illustrate multiplication and division of integers using a variety of representations. - 7.N.2.2
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. - MAFS.7.RP.1.2a
Design and use a simulation to generate frequencies for compound events. - 7.DSP.C.8b
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. - MAFS.7.RP.1.2d
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. - MAFS.7.RP.1.2c
Represent the sample space of a compound event. - 7.DSP.C.8a
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. - MAFS.7.EE.2.4b
Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. - 6.1.1.4
Understand that percent represents parts out of 100 and ratios to 100. - 6.1.1.3
Construct inequalities to solve problems by reasoning about the quantities. - NC.7.EE.4.b
Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. - NC.7.SP.7.a
Compare theoretical and experimental probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. - NC.7.SP.7.c
Construct equations to solve problems by reasoning about the quantities. - NC.7.EE.4.a
Develop a probability model (which may not be uniform) by repeatedly performing a chance process and observing frequencies in the data generated. - NC.7.SP.7.b
The student will solve one- and two-step linear inequalities in one variable, including practical problems, involving addition, subtraction, multiplication, and division, and graph the solution on a number line. - 7.13
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. - MAFS.7.SP.1.1
The student will solve two-step linear equations in one variable, including practical problems that require the solution of a two-step linear equation in one variable. - 7.12
Understand that two-dimensional figures are congruent if a series of rigid transformations can be performed to map the preimage to the image. - 8.GM.A.2
Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. - 7.DSP.C.7b
Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. - 7.DSP.C.7a
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. - MAFS.7.SP.1.2
The student will evaluate algebraic expressions for given replacement values of the variables. - 7.11
Explain that a percent represents parts “out of 100” and ratios “to 100.” - 6.N.1.3
Use data from multiple samples to draw inferences about a population and investigate variability in estimates of the characteristic of interest. - 7.DSP.A.2
Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x² + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. - MAFS.K12.MP.7.1
Solve problems involving the four arithmetic operations with rational numbers. - 7.NS.A.3
Explain the relationship between the absolute value of a rational number and the distance of that number from zero on a number line. Use the symbol for absolute value. - 7.N.2.6
Solve real-world and mathematical problems involving addition, subtraction, multiplication and division of rational numbers; use efficient and generalizable procedures including but not limited to standard algorithms. - 7.N.2.3
Solve real-world and mathematical problems involving the four operations with rational numbers. - MAFS.7.NS.1.3
The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. - 6.2a
Recognize and represent proportional relationships between quantities. - M.7.2
Use proportional relationships to solve multistep ratio and percent problems (e.g., simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, and/or percent error). - M.7.3
Understand that the graph of a proportional relationship is a line through the origin whose slope is the unit rate (constant of proportionality). Know how to use graphing technology to examine what happens to a line when the unit rate is changed. - 7.2.1.2
Understand that a relationship between two variables, 𝑥 and 𝑥𝑦, is proportional if it can be expressed in the form 𝑥𝑦𝑦/𝑥𝑦𝑦𝑥 = k or 𝑥𝑦𝑦𝑥𝑦 = k𝑥𝑦𝑦𝑥𝑦𝑥. Distinguish proportional relationships from other relationships, including inversely proportional relationships (xy = k or y = k/x). - 7.2.1.1
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. - MAFS.7.SP.3.7a
Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. (e.g., If a person walks ½ mile in each ¼ hour, compute the unit rate as the complex fraction ½ /¼ miles per hour, equivalently 2 miles per hour.) - M.7.1
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? - MAFS.7.SP.3.7b
Solve real-world and mathematical problems involving the four operations with rational numbers. Instructional Note: Computations with rational numbers extend the rules for manipulating fractions to complex fractions. - M.7.6
Apply properties of operations as strategies to add, subtract, factor and expand linear expressions with rational coefficients. - M.7.7
Solve real-world and mathematical problems involving numerical expressions with rational numbers using the four operations. - NC.7.NS.3
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers, using the properties of operations, and describing real-world contexts using sums and differences. - NC.7.NS.1
Apply properties of operations to calculate with positive and negative numbers in any form. - NC.7.EE.3.a
Convert between different forms of a number and equivalent forms of the expression as appropriate. - NC.7.EE.3.b
Use reasoning with proportions to display and interpret data in circle graphs (pie charts) and histograms. Choose the appropriate data display and know how to create the display using a spreadsheet or other graphing technology. - 7.D.1.2
Understand that the range describes the spread of the entire data set. - NC.7.SP.3.a.2
Understand the mean absolute deviation of a data set is a measure of variability that describes the average distance that points within a data set are from the mean of the data set. - NC.7.SP.3.a.1
Understand that the interquartile range describes the spread of the middle 50% of the data. - NC.7.SP.3.a.3
Represent addition and subtraction on a horizontal or vertical number line. - 7.NS.A.1b
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. - MAFS.7.SP.3.8a
Describe situations and show that a number and its opposite have a sum of 0 (additive inverses). - 7.NS.A.1c
Understand subtraction of rational numbers as adding the additive inverse. - 7.NS.A.1d
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. - MAFS.7.SP.3.8b
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? - MAFS.7.SP.3.8c
Determine the distance between two rational numbers on the number line is the absolute value of their difference. - 7.NS.A.1e
Interpret sums and differences of rational numbers. - 7.NS.A.1f
Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. - MAFS.K12.MP.6.1
Analyze different data distributions using statistical measures. - 7.DSP.B.3
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. (e.g., a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”) - M.7.8
The student will identify and describe absolute value of rational numbers. - 7.1e
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. (e.g., 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.) - M.7.9
Compare the numerical measures of center, measures of frequency and measures of variability from two random samples to draw inferences about the population. - 7.DSP.B.4
Add and subtract rational numbers. - 7.NS.A.1a
Use proportional reasoning to solve problems involving ratios in various contexts. - 7.1.2.5
Reason abstractly and quantitatively. - 7.MP.2
Solve problems in various contexts involving calculations with positive and negative rational numbers and positive integer exponents, including computing simple and compound interest. - 7.1.2.4
Construct viable arguments and critique the reasoning of others. - 7.MP.3
Mathematical Modeling: Solve Problems Using Equations and Inequalities - 7.AF.5MM
Demonstrate an understanding of the relationship between the absolute value of a rational number and distance on a number line. Use the symbol for absolute value. - 7.1.2.6
Make sense of problems and persevere in solving them. - 7.MP.1
Add, subtract, multiply and divide positive and negative rational numbers that are integers, fractions and terminating decimals; use efficient and generalizable procedures, including standard algorithms; raise positive rational numbers to whole-number exponents. - 7.1.2.1
Understand that calculators and other computing technologies often truncate or round numbers. - 7.1.2.3
Use real-world contexts and the inverse relationship between addition and subtraction to explain why the procedures of arithmetic with negative rational numbers make sense. - 7.1.2.2
Construct special quadrilaterals given specific parameters. - 7.GM.A.2b
Determine if provided constraints will create a unique triangle through construction. - 7.GM.A.2a
Solve multi-step problems involving proportional relationships in numerous contexts. - 7.2.2.2
Represent proportional relationships with tables, verbal descriptions, symbols, equations and graphs; translate from one representation to another. Determine the unit rate (constant of proportionality or slope) given any of these representations. - 7.2.2.1
Mathematical Modeling: Analyze and Solve Percent Problems - 7.P.3MM
Represent real-world or mathematical situations using equations and inequalities involving variables and positive and negative rational numbers. - 7.2.2.4
Recognize that the graph of a proportional relationship is a line through the origin and the coordinate (1, r), where both r and the slope are the unit rate (constant of proportionality, k). - 7.A.1.2
Use knowledge of proportions to assess the reasonableness of solutions. - 7.2.2.3
Describe that the relationship between two variables, x and y, is proportional if it can be expressed in the form y/x = k or y = kx; distinguish proportional relationships from other relationships, including inversely proportional relationships ( xy = k or y = k/x ). - 7.A.1.1
Calculate probability as a fraction of sample space or as a fraction of area. Express probabilities as percents, decimals and fractions. - 7.D.2.2
Determine the theoretical probability of an event using the ratio between the size of the event and the size of the sample space; represent probabilities as percents, fractions and decimals between 0 and 1. - 7.D.2.1
Use proportional reasoning to draw conclusions about and predict relative frequencies of outcomes based on probabilities. - 7.D.2.3
Write percents that are greater than 100 or less than 1. - 6.P.6.3
Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. - MAFS.K12.MP.1.1
Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. - MAFS.6.RP.1.3c
Assess the reasonableness of answers using mental computation and estimation strategies. - 7.EEI.B.3b
Describe the properties of similarity, compare geometric figures for similarity, and determine scale factors resulting from dilations. - 7.GM.4.1
Convert between equivalent forms of the same number. - 7.EEI.B.3a
Apply proportions, ratios, and scale factors to solve problems involving scale drawings and determine side lengths and areas of similar triangles and rectangles. - 7.GM.4.2
Know and apply the formulas for circumference and area of circles to solve problems. - 7.GM.A.4b
Analyze the relationships among the circumference, the radius, the diameter, the area and Pi in a circle. - 7.GM.A.4a
Interpret the solution in context. - NC.7.EE.4.a.3
Use properties of algebra to generate equivalent numerical and algebraic expressions containing rational numbers, grouping symbols and whole number exponents. Properties of algebra include associative, commutative and distributive laws. - 7.2.3.1
Perform experiments that model theoretical probability. - 7.DSP.C.6b
Predict outcomes using theoretical probability. - 7.DSP.C.6a
Recognize and generate equivalent representations of rational numbers, including equivalent fractions. - 7.N.1.3
Fluently solve multistep equations with the variable on one side, including those generated by word problems. - NC.7.EE.4.a.1
Know that every rational number can be written as the ratio of two integers or as a terminating or repeating decimal. - 7.N.1.1
Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. - NC.7.EE.4.a.2
Apply understanding of order of operations and grouping symbols when using calculators and other technologies. - 7.2.3.3
Compare theoretical and experimental probabilities. - 7.DSP.C.6c
Evaluate algebraic expressions containing rational numbers and whole number exponents at specified values of their variables. - 7.2.3.2
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. (e.g., 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.) - M.7.10b
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. (e.g., The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? An arithmetic solution similar to “54 – 6 – 6 divided by 2” may be compared with the reasoning involved in solving the equation 2w – 12 = 54. An arithmetic solution similar to “54/2 – 6” may be compared with the reasoning involved in solving the equation 2(w – 6) = 54.) - M.7.10a
Compare two different proportional relationships using tables, graphs, equations, and verbal descriptions. - NC.7.RP.2.a.3
Represent proportional relationships using tables and graphs. - NC.7.RP.2.a.1
Recognize whether ratios are in a proportional relationship using tables and graphs. - NC.7.RP.2.a.2
Demonstrate an understanding of the proportional relationship between the diameter and circumference of a circle and that the unit rate (constant of proportionality) is π. Calculate the circumference and area of circles and sectors of circles to solve problems in various contexts. - 7.3.1.1
Write, solve and/or graph inequalities of the form px + q > r or px + q < r, where p, q and r are rational numbers. - 7.EEI.B.4c
Write and/or solve two-step equations of the form px + q = r and p(x + q) = r, where p, q and r are rational numbers, and interpret the meaning of the solution in the context of the problem. - 7.EEI.B.4b
Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. - 7.EEI.B.4a
Apply the formulas for area and circumference of a circle to solve problems. - NC.7.G.4.b
Understand the relationships between the radius, diameter, circumference, and area. - NC.7.G.4.a
Determine probabilities of simple events. - 7.DSP.C.5a
Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. - 7.DSP.C.5b
Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x² + x + 1), and (x – 1)(x³ + x² + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. - MAFS.K12.MP.8.1
Understand that a proportion is a relationship of equality between ratios. - NC.7.RP.2.a
Identify the unit rate (constant of proportionality) within two quantities in a proportional relationship using tables, graphs, equations, and verbal descriptions. - NC.7.RP.2.b
Use a sequence of translations, reflections, and rotations to show that figures are congruent. - 8.G.6.5
Create equations and graphs to represent proportional relationships. - NC.7.RP.2.c
Calculate the circumference and area of circles to solve problems in various contexts, in terms of ! and using approximations for π. - 7.GM.3.2
Demonstrate an understanding of the proportional relationship between the diameter and circumference of a circle and that the unit rate (constant of proportionality) is π and can be approximated by rational numbers such as 22/7 and 3.14. - 7.GM.3.1




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