Source:     IMS Online Validator
Profile:    1.2.0
Identifier: realize-6283a113-2dc2-3139-afbc-32efce858155
Timestamp:  Thursday, February 23, 2017 01:51 PM EST
Status:     VALID!
Conformant: true

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Curriculum Standards:

Represent the product of 2 two-digit numbers using arrays, area models, or equations, including perfect squares through 15 by 15. - NO_4.4C
Determine products of a number and 10 or 100 using properties of operations and place value understandings. - NO_4.4B
Add and subtract whole numbers and decimals to the hundredths place using the standard algorithm. - NO_4.4A
Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold wholenumber products as volumes, e.g., to represent the associative property of multiplication. - 5.MD.C.5a
Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. - 5.MD.C.5c
Apply the formulas V = l x w x h and V = b x h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. - 5.MD.C.5b
Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1?100 with a common factor as a multiple of a sum of two whole numbers with no common factor. - 6.NS.B.4
Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. - 6.NS.B.3
Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 x (1/4), recording the conclusion by the equation 5/4 = 5 x (1/4). - 4.NF.B.4a
Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. - 4.NF.B.4b
Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. - 4.NF.B.4c
Round to the nearest 10, 100, or 1,000 or use compatible numbers to estimate solutions involving whole numbers. - NO_4.4G
Use strategies and algorithms, including the standard algorithm, to divide up to a four-digit dividend by a one-digit divisor. - NO_4.4F
Use strategies and algorithms, including the standard algorithm, to multiply up to a four-digit number by a one-digit number and to multiply a two-digit number by a two-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties. - NO_4.4D
Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) x 4 = 1/3. - 5.NF.B.7a
Apply knowledge of right angles to identify acute, right, and obtuse triangles. - GM_4.6C
Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb. of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? - 5.NF.B.7c
Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ 1/5 , and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 x (1/5) = 4. - 5.NF.B.7b
Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. - 5.NBT.B.7
Fluently multiply multi-digit whole numbers using the standard algorithm. - 5.NBT.B.5
Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. - 5.NBT.B.6
Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. - 5.NBT.A.1
Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. - 5.NBT.A.2
Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. - 4.G.A.1
Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. (Two dimensional shapes should include special triangles, e.g., equilateral, isosceles, scalene, and special quadrilaterals, e.g., rhombus, square, rectangle, parallelogram, trapezoid.) - 4.G.A.2
Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100 , and add 3/10 + 4/100 = 34/100. - 4.NF.C.5
Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100 ; describe a length as 0.62 meters; locate 0.62 on a number line diagram. - 4.NF.C.6
Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. - 5.NF.B.6
Solve problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate. - GM_4.8C
Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. - 5.NF.B.3
Classify two-dimensional figures in a hierarchy of sets and subsets using graphic organizers based on their attributes and properties. - GM_5.5A
Identify relative sizes of measurement units within the customary and metric systems. - GM_4.8A
Represent the value of the digit in decimals through the thousandths using expanded notation and numerals. - NO_5.2A
Convert measurements within the same measurement system, customary or metric, from a smaller unit into a larger unit or a larger unit into a smaller unit when given other equivalent measures represented in a table. - GM_4.8B
Compare and order two decimals to thousandths and represent comparisons using the symbols >, <, or =. - NO_5.2B
Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. - 4.OA.A.3
Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule U1Add 3Ue and the starting number 0, and given the rule U1Add 6Ue and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. - 5.OA.B.3
Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using the number line or another visual model. - 4.NF.C.7
Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. - 4.OA.A.1
Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. - 4.OA.A.2
Represent problems using an input-output table and numerical expressions to generate a number pattern that follows a given rule representing the relationship of the values in the resulting sequence and their position in the sequence. - AR_4.5B
Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. - 5.G.B.3
Interpret the value of each place-value position as 10 times the position to the right and as one-tenth of the value of the place to its left. - NO_4.2A
Solve problems related to perimeter and area of rectangles where dimensions are whole numbers. - AR_4.5D
Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y - 6.EE.A.2a
Determine the volume of a rectangular prism with whole number side lengths in problems related to the number of layers times the number of unit cubes in the area of the base. - GM_5.6B
Apply the properties of operations to generate equivalent expressions. - 6.EE.A.3
Recognize a cube with side length of one unit as a unit cube having one cubic unit of volume and the volume of a three-dimensional figure as the number of unit cubes (n cubic units) needed to fill it with no gaps or overlaps if possible. - GM_5.6A
Classify two-dimensional figures in a hierarchy based on properties. - 5.G.B.4
Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. - 5.NF.B.5a
Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n x a) /(n x b) to the effect of multiplying a/b by 1. - 5.NF.B.5b
Use place value understanding to round decimals to any place. - 5.NBT.A.4
Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems. - MP_4.1C
Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate. - MP_4.1D
Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . - 5.NF.A.1
Represent fractions and decimals to the tenths or hundredths as distances from zero on a number line. - NO_4.3G
Represent and solve addition and subtraction of fractions with equal denominators using objects and pictorial models that build to the number line and properties of operations. - NO_4.3E
Compare two fractions with different numerators and different denominators and represent the comparison using the symbols >, =, or < . - NO_4.3D
Determine if two given fractions are equivalent using a variety of methods. - NO_4.3C
Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. - 5.NF.A.2
Solve problems by calculating conversions within a measurement system, customary or metric. - GM_5.7A
Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. - 5.NF.B.4b
Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100+ 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100_ + 2 x (1/1000). - 5.NBT.A.3a
Interpret the product (a/b) x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷ b. For example, use a visual fraction model to show (2/3) x 4 = 8/3 , and create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd.) - 5.NF.B.4a
Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. - 5.NBT.A.3b
Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. - 5.MD.C.4
Recognize the difference between additive and multiplicative numerical patterns given in a table or graph. - AR_5.4D
Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. - 5.G.A.2
Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). - 5.G.A.1
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. - 6.RP.A.1
Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. - 6.RP.A.2
Describe the key attributes of the coordinate plane, including perpendicular number lines (axes) where the intersection (origin) of the two lines coincides with zero on each number line and the given point (0, 0); the x-coordinate, the first number in an ordered pair, indicates movement parallel to the x-axis starting at the origin; and the y-coordinate, the second number, indicates movement parallel to the y-axis starting at the origin. - GM_5.8A
Simplify numerical expressions that do not involve exponents, including up to two levels of grouping. - AR_5.4F
Describe the meaning of parentheses and brackets in a numeric expression. - AR_5.4E
Represent and solve problems related to perimeter and/or area and related to volume. - AR_5.4H
Use concrete objects and pictorial models to develop the formulas for the volume of a rectangular prism, including the special form for a cube (V = l x w x h, V = s x s x s, and V = Bh). - AR_5.4G
Describe the process for graphing ordered pairs of numbers in the first quadrant of the coordinate plane. - GM_5.8B
Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? - 6.RP.A.3b
Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. - 6.RP.A.3a
Use strategies and algorithms, including the standard algorithm, to multiply a two-digit number by a one-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties. - NO_3.4G
Explain why a fraction a/b is equivalent to a fraction (n - a) / (n - b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. - 4.NF.A.1
Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, <, and justify the conclusions, e.g., by using a visual fraction model. - 4.NF.A.2
Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution. - MP_5.1B
Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ... - 4.MD.A.1
Apply mathematics to problems arising in everyday life, society, and the workplace. - MP_5.1A
Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. Explain informally why the numbers will continue to alternate in this way. - 4.OA.C.5
Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. Represent and interpret data. - 4.MD.A.3
Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. - 4.MD.A.2
Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8 ). Use operations on fractions for this grade to solve problems involving information presented in line plots. - 5.MD.B.2
Create and use representations to organize, record, and communicate mathematical ideas. - MP_5.1E
Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate. - MP_5.1D
Represent multiplication of decimals with products to the hundredths using objects and pictorial models, including area models. - NO_5.3D
Solve for products of decimals to the hundredths, including situations involving money, using strategies based on place-value understandings, properties of operations, and the relationship to the multiplication of whole numbers. - NO_5.3E
Represent quotients of decimals to the hundredths, up to four-digit dividends and two-digit whole number divisors, using objects and pictorial models, including area models. - NO_5.3F
Solve for quotients of decimals to the hundredths, up to four-digit dividends and two-digit whole number divisors, using strategies and algorithms, including the standard algorithm. - NO_5.3G
Represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects and pictorial models and properties of operations. - NO_5.3H
Represent and solve multiplication of a whole number and a fraction that refers to the same whole using objects and pictorial models, including area models. - NO_5.3I
Represent division of a unit fraction by a whole number and the division of a whole number by a unit fraction such as 1/3 ? 7 and 7 ? 1/3 using objects and pictorial models, including area models. - NO_5.3J
A cube with side length 1 unit, called a U1unit cube,Ue is said to have U1one cubic unitUe of volume, and can be used to measure volume. - 5.MD.C.3a
Add and subtract positive rational numbers fluently. - NO_5.3K
A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. - 5.MD.C.3b
Estimate to determine solutions to mathematical and real-world problems involving addition, subtraction, multiplication, or division. - NO_5.3A
Multiply with fluency a three-digit number by a two-digit number using the standard algorithm. - NO_5.3B
Solve with proficiency for quotients of up to a four-digit dividend by a two-digit divisor using strategies and the standard algorithm. - NO_5.3C
Fluently add and subtract multi-digit whole numbers using the standard algorithm. - 4.NBT.B.4
Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. - 4.NBT.B.5
Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. - 4.NBT.B.6
The student applies mathematical process standards to develop and use strategies and methods for whole number computations and decimal sums and differences in order to solve problems with efficiency and accuracy. - NO_4.4
Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 = 70 x 10 by applying concepts of place value and division. - 4.NBT.A.1
Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. - 4.NF.B.3c
Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using ., 5, and , symbols to record the results of comparisons. - 4.NBT.A.2
Resuelven problemas verbales sobre sumas y restas de fracciones relacionados a un mismo entero y con el mismo denominador, por ejemplo, utilizando modelos visuales de fracciones y ecuaciones para representar el problema. - 4.NF.B.3d
Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. - 6.G.A.4
Use place value understanding to round multi-digit whole numbers to any place. - 4.NBT.A.3
Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. - 4.NF.B.3a
Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8. 2-1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. - 4.NF.B.3b
Identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. - GM_4.6A
Describe the mathematical relationships found in the base-10 place value system through the hundred thousands place. - NO_3.2B
Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. - 5.MD.A.1
Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. - 4.OA.B.4
Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. - 5.OA.A.1
Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation U1add 8 and 7, then multiply by 2Ue as 2 x (8 +7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. - 5.OA.A.2
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. - 4.MD.B.4
Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution. - MP_3.1B


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Title: enVisionMATH Common Core Realize Edition Grade  5

Description: enVisionMATH Common Core Realize Edition Grade 5


         Tools
         
            Grade 5: Accessible Student Edition

            Grade 05: ACTIVe-book

            Grade 5: Game Center

            Grade 5: Glossary

            Math Tools

         Grade 5: Mathematical Practices
         
            Mathematical Practice 1

            Mathematical Practice 2

            Mathematical Practice 3

            Mathematical Practice 4

            Mathematical Practice 5

            Mathematical Practice 6

            Mathematical Practice 7

            Mathematical Practice 8

         Grade 5: Online Placement Test
           Curriculum Standards: Round to the nearest 10, 100, or 1,000 or use compatible numbers to estimate solutions involving whole numbers. Round to the nearest 10, 100, or 1,000 or use compatible numbers to estimate solutions involving whole numbers. Solve problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate. Solve problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 x (1/4), recording the conclusion by the equation 5/4 = 5 x (1/4). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 x (1/4), recording the conclusion by the equation 5/4 = 5 x (1/4). Aplicar y ampliar los conocimientos previos sobre la multiplicación para multiplicar una fracción por un número entero no negativo. Entender que una fracción a/b es un múltiplo de 1/b. Por ejemplo, utilizar un modelo visual de fracciones para representar 5/4 como el producto 5 × (1/4), anotando la conclusión mediante la ecuación 5/4 = 5 × (1/4). Entienden que una fracción a/b es un múltiplo de 1/b. Por ejemplo, utilizan un modelo visual de fracciones para representar 5/4 como el producto 5 × (1/4), anotando la conclusión mediante la ecuación 5/4 = 5 × (1/4). Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Utilizar las cuatro operaciones para resolver problemas verbales sobre distancias, intervalos de tiempo, volúmenes líquidos, masas de objetos y dinero, incluyendo problemas con fracciones simples o números decimales, y problemas que requieren expresar las medidas dadas en una unidad más grande en términos de una unidad más pequeña. Representar cantidades medidas utilizando diagramas tales como rectas numéricas con escalas de medición. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Utilizan las cuatro operaciones para resolver problemas verbales sobre distancias, intervalos de tiempo, volúmenes líquidos, masas de objetos y dinero, incluyendo problemas con fracciones simples o decimales, y problemas que requieren expresar las medidas dadas en una unidad más grande en términos de una unidad más pequeña. Representan cantidades medidas utilizando diagramas tales como rectas numéricas con escalas de medición. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply knowledge of right angles to identify acute, right, and obtuse triangles. Apply knowledge of right angles to identify acute, right, and obtuse triangles. Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ... Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ... Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), Saber los tamaños relativos de las unidades de medición dentro de un sistema de unidades, incluyendo km, m, cm; kg, g; lb, oz.; L, mL; h, min, s. Dentro de un mismo sistema de medición, expresar las medidas en una unidad más grande en términos de una unidad más pequeña. Anotar las medidas equivalentes en una tabla de dos columnas. Por ejemplo, saber que 1 pie es 12 veces más largo que 1 pulg. Expresar la longitud de una culebra de 4 pies como 48 pulgs. Generar una tabla de conversión para pies y pulgadas con una lista de pares de números (1, 12), (2, 24), (3, 36), ... Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), Reconocen los tamaños relativos de las unidades de medición dentro de un sistema de unidades, incluyendo km, m, cm; kg, g; lb, oz.; L, mL; h, min, s. Dentro de un mismo sistema de medición, expresan las medidas en una unidad más grande en términos de una unidad más pequeña. Anotan las medidas equivalentes en una tabla de dos columnas. Por ejemplo, saben que 1 pie es 12 veces más largo que 1 pulgada. Expresan la longitud de una culebra de 4 pies como 48 pulgadas. Generan una tabla de conversión para pies y pulgadas con una lista de pares de números (1, 12), (2, 24), (3, 36), … Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), Identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. Entienden que un múltiplo de a/b es un múltiplo de 1/b, y utilizan este entendimiento para multiplicar una fracción por un número entero. Resuelven problemas verbales relacionados a la multiplicación de una fracción por un número entero, por ejemplo, utilizan modelos visuales de fracciones y ecuaciones para representar el problema. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. Hacer un diagrama de puntos para representar un conjunto de datos de medidas en fracciones de una unidad (1/2, 1/4, 1/8). Resolver problemas sobre sumas y restas de fracciones utilizando la información presentada en los diagramas de puntos. Por ejemplo, utilizando un diagrama de puntos, hallar e interpretar la diferencia de longitud entre los ejemplares más largos y más cortos de una colección de insectos. Hacen un diagrama de puntos para representar un conjunto de datos de medidas en fracciones de una unidad (1/2, 1/4, 1/8). Resuelven problemas sobre sumas y restas de fracciones utilizando la información presentada en los diagramas de puntos. Por ejemplo, al utilizar un diagrama de puntos, hallan e interpretan la diferencia de longitud entre los ejemplares más largos y más cortos en una colección de insectos. Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Hallar todos los pares de factores de un número entero no negativo con rango de 1 a 100. Reconocer que un número entero no negativo es un múltiplo de cada uno de sus factores. Determinar si cierto número entero no negativo con rango de 1 a 100 es un múltiplo de cierto número de un dígito. Determinar si cierto número entero no negativo con rango de 1 a 100 es primo o compuesto. Hallan todos los pares de factores de números enteros dentro del rango 1–100. Reconocen que un número entero es un múltiplo de cada uno de sus factores. Determinan si cierto número entero dentro del rango 1–100 es un múltiplo de cierto número de un solo dígito. Determinan si un número entero dentro del rango 1–100 es primo o compuesto. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Multiplicar un número entero no negativo de hasta cuatro dígitos por un número entero no negativo de un dígito, y multiplicar dos números de dos dígitos utilizando estrategias basadas en el valor de posición y las propiedades de las operaciones. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y/o modelos de área. Multiplican un número entero de hasta cuatro dígitos por un número entero de un dígito, y multiplican dos números de dos dígitos, utilizando estrategias basadas en el valor de posición y las propiedades de operaciones. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares, y/o modelos de area. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar cocientes y residuos de números enteros no negativos a partir de divisiones con dividendos de hasta cuatro dígitos y divisores de un dígito, utilizando las estrategias basadas en el valor de posición y/o la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y/o modelos de área. Hallan cocientes y residuos de números enteros, a partir de divisiones con dividendos de hasta cuatro dígitos y divisores de un dígito, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares, y/o modelos de área. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Entender una fracción a/b cuando a > 1 como una suma de fracciones 1/b. Entender la suma y la resta de fracciones como la unión y separación de partes que se refieren a un mismo entero. Entienden la suma y la resta de fracciones como la unión y la separación de partes que se refieren a un mismo entero. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. Interpretar una ecuación de multiplicación como una comparación, por ej., interpretar 35 = 5 × 7 como un enunciado de que 35 es 5 veces 7 y 7 veces 5. Representar enunciados verbales de comparaciones multiplicativas como ecuaciones de multiplicación. Interpretan una ecuación de multiplicación como una comparación, por ejemplo, 35 = 5x7 como un enunciados de que 35 es 5 veces 7, y 7 veces 5. Representan enunciados verbales de comparaciones multiplicativas como ecuaciones de multiplicación. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using ., 5, and , symbols to record the results of comparisons. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using ., 5, and , symbols to record the results of comparisons. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Leer y escribir números enteros no negativos con múltiples dígitos usando números de base diez, números en palabras y formas desarrolladas. Comparar dos números de múltiples dígitos en base al significado de los dígitos en cada lugar, utilizando los símbolos >, = y < para anotar los resultados de las comparaciones. Leen y escriben números enteros con dígitos múltiples usando numerales en base diez, los nombres de los números, y sus formas desarrolladas. Comparan dos números de dígitos múltiples basándose en el valor de los dígitos en cada lugar, utilizando los símbolos >, = y < para anotar los resultados de las comparaciones. Use strategies and algorithms, including the standard algorithm, to multiply up to a four-digit number by a one-digit number and to multiply a two-digit number by a two-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties. Use strategies and algorithms, including the standard algorithm, to multiply up to a four-digit number by a one-digit number and to multiply a two-digit number by a two-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.1 Multiplicar o dividir para resolver problemas verbales con comparaciones multiplicativas, por ej., representar el problema utilizando dibujos y ecuaciones con un símbolo para el número desconocido; distinguir la comparación multiplicativa de la comparación de suma. Multiplican o dividen para resolver problemas verbales que incluyen comparaciones multiplicativas, por ejemplo, para representar el problema usando dibujos y ecuaciones con un símbolo para el número desconocido, distinguen una comparación multiplicativa de una comparación de suma. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Resuelven problemas verbales de pasos múltiples con números enteros, cuya respuestas son números enteros, usando las cuatro operaciones, incluyendo problemas en los que los residuos deben ser interpretados. Representan estos problemas usando ecuaciones con una letra que representa la cantidad desconocida. Evalúan si las respuestas son razonables usando cálculos mentales y estrategias de estimación incluyendo el redondeo. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 = 70 x 10 by applying concepts of place value and division. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 = 70 x 10 by applying concepts of place value and division. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. Reconocer que en un número entero no negativo de múltiples dígitos, un dígito en determinado lugar representa diez veces lo que representa en el lugar a su derecha. Por ejemplo, reconocer que 700 ÷ 70 = 10 aplicando conceptos de valor de posición y de división. Reconocen que en un número entero de dígitos múltiples, un dígito en determinado lugar representa diez veces lo que representa en el lugar a su derecha. Por ejemplo, reconocen que 700 ÷ 70 = 10 al aplicar conceptos de valor de posición y de división. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. (Two dimensional shapes should include special triangles, e.g., equilateral, isosceles, scalene, and special quadrilaterals, e.g., rhombus, square, rectangle, parallelogram, trapezoid.) Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. Dibujar puntos, rectas, segmentos de rectas, semirrectas, ángulos (rectos, agudos, obtusos) y rectas perpendiculares y paralelas. Identificar estos elementos en las figuras bidimensionales. Dibujan puntos, rectas, segmentos de rectas, semirrectas, ángulos (rectos, agudos, obtusos), y rectas perpendiculares y paralelas. Identifican estos elementos en las figuras bidimensionales. Clasifican las figuras bidimensionales basándose en la presencia o ausencia de rectas paralelas o perpendiculares, o en la presencia o ausencia de ángulos de un tamaño especificado. Reconocen que los triángulos rectos forman una categoría en sí, e identifican triángulos rectos. (Las figuras bidimensionales deben incluir los triángulos especiales, por ejemplo, los triángulos equiláteros, isósceles y escalenos, y los cuadriláteros especiales, por ejemplo, los rombos, cuadrados, rectángulos, paralelogramos y trapecios.) Resuelven problemas verbales sobre sumas y restas de fracciones relacionados a un mismo entero y con el mismo denominador, por ejemplo, utilizando modelos visuales de fracciones y ecuaciones para representar el problema. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. Explain why a fraction a/b is equivalent to a fraction (n - a) / (n - b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Explain why a fraction a / b is equivalent to a fraction (n - a) / (n - b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Explicar por qué la fracción a/b es equivalente a la fracción (n × a)/(n × b) utilizando modelos visuales de fracciones, observando que el número y el tamaño de las partes difiere aunque las dos fracciones en sí son del mismo tamaño. Utilizar este principio para reconocer y generar fracciones equivalentes. Explican por qué la fracción a/b es equivalente a la fracción (n × a)/(n × b) al utilizar modelos visuales de fracciones, poniendo atención a como el número y el tamaño de las partes difiere aún cuando ambas fracciones son del mismo tamaño. Utilizan este principio para reconocer y generar fracciones equivalentes Represent problems using an input-output table and numerical expressions to generate a number pattern that follows a given rule representing the relationship of the values in the resulting sequence and their position in the sequence. Represent problems using an input-output table and numerical expressions to generate a number pattern that follows a given rule representing the relationship of the values in the resulting sequence and their position in the sequence. Identify relative sizes of measurement units within the customary and metric systems. Identify relative sizes of measurement units within the customary and metric systems. Use strategies and algorithms, including the standard algorithm, to divide up to a four-digit dividend by a one-digit divisor. Use strategies and algorithms, including the standard algorithm, to divide up to a four-digit dividend by a one-digit divisor. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. Explain informally why the numbers will continue to alternate in this way. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. Explain informally why the numbers will continue to alternate in this way. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. Generar un patrón de números o figuras que siga una regla dada. Identificar características aparentes de la regla que no estaban explícitas en la regla misma. Por ejemplo, dada la regla “Sumar 3” y el número 1 para comenzar, generar términos en la sucesión resultante y observar que los términos parecen alternarse entre números impares y pares. Explicar informalmente por qué los números seguirán alternándose de esta manera. Generan un patrón de números o figuras que sigue una regla dada. Identifican las características aparentes del patrón que no eran explícitas en la regla misma. Por ejemplo, dada la regla “Añadir 3” y con el número 1 para comenzar, generan términos en la secuencia resultante y observan que los términos parecen alternarse entre números impares y pares. Explican informalmente porqué los números continuarán alternándose de esta manera. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding  and explain why a rounded solution is appropriate. Resolver problemas verbales de varios pasos con números enteros no negativos y cuyas respuestas son números enteros no negativos utilizando las cuatro operaciones, incluyendo aquellos problemas en los que los residuos deben ser interpretados. Representar estos problemas utilizando ecuaciones con una letra para representar la cantidad desconocida. Evaluar lo razonable de las respuestas utilizando el cálculo mental y las estrategias de estimación, incluyendo el redondeo. Use place value understanding to round multi-digit whole numbers to any place. Utilizan la comprensión del valor de posición para redondear números enteros con dígitos múltiples a cualquier lugar. 

         Topic 01: Place Value
         
            Line Up and Compare

            Topic 01: Online Topic Readiness
              Curriculum Standards: Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100 ; describe a length as 0.62 meters; locate 0.62 on a number line diagram. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100 ; describe a length as 0.62 meters; locate 0.62 on a number line diagram. Use decimal notation for fractions with denominators 10 or 100. Utilizar la notación decimal para las fracciones con denominadores de 10 ó 100. Por ejemplo, reescribir 0.62 como 62/100; describir una longitud como 0.62 metros; localizar 0.62 en una recta numérica. Utilizan la notación decimal para las fracciones con denominadores de 10 ó 100. Por ejemplo, al escribir 0.62 como 62/100; al describir una longitud como 0.62 metros; al localizar 0.62 en una recta numérica. Describe the mathematical relationships found in the base-10 place value system through the hundred thousands place. Describe the mathematical relationships found in the base-10 place value system through the hundred thousands place. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using ., 5, and , symbols to record the results of comparisons. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using ., 5, and , symbols to record the results of comparisons. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Leer y escribir números enteros no negativos con múltiples dígitos usando números de base diez, números en palabras y formas desarrolladas. Comparar dos números de múltiples dígitos en base al significado de los dígitos en cada lugar, utilizando los símbolos >, = y < para anotar los resultados de las comparaciones. Leen y escriben números enteros con dígitos múltiples usando numerales en base diez, los nombres de los números, y sus formas desarrolladas. Comparan dos números de dígitos múltiples basándose en el valor de los dígitos en cada lugar, utilizando los símbolos >, = y < para anotar los resultados de las comparaciones. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 = 70 x 10 by applying concepts of place value and division. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 = 70 x 10 by applying concepts of place value and division. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. Reconocer que en un número entero no negativo de múltiples dígitos, un dígito en determinado lugar representa diez veces lo que representa en el lugar a su derecha. Por ejemplo, reconocer que 700 ÷ 70 = 10 aplicando conceptos de valor de posición y de división. Reconocen que en un número entero de dígitos múltiples, un dígito en determinado lugar representa diez veces lo que representa en el lugar a su derecha. Por ejemplo, reconocen que 700 ÷ 70 = 10 al aplicar conceptos de valor de posición y de división. 

            01-01: Place Value Relationships
            
               Develop the Concept: Visual
               
                  Place Value Relationships: Visual Learning
                    Curriculum Standards: Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Reconocer que en un número de varios dígitos, cualquier dígito en determinado lugar representa 10 veces lo que representa el mismo dígito en el lugar a su derecha y 1/10 de lo que representa en el lugar a su izquierda. Reconocen que en un número de varios dígitos, cualquier dígito en determinado lugar representa 10 veces lo que representa el mismo dígito en el lugar a su derecha y 1/10 de lo que representa en el lugar a su izquierda. 

               Assess & Differentiate
               
                  01-01: Digital Quick Check
                    Curriculum Standards: Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Reconocer que en un número de varios dígitos, cualquier dígito en determinado lugar representa 10 veces lo que representa el mismo dígito en el lugar a su derecha y 1/10 de lo que representa en el lugar a su izquierda. Reconocen que en un número de varios dígitos, cualquier dígito en determinado lugar representa 10 veces lo que representa el mismo dígito en el lugar a su derecha y 1/10 de lo que representa en el lugar a su izquierda. 

            01-02: Tenths and Hundredths
            
               Develop the Concept: Visual
               
                  Tenths and Hundredths: Visual Learning
                    Curriculum Standards: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100+ 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100_ + 2 x (1/1000). Read, write, and compare decimals to thousandths. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100+ 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100_ + 2 x (1/1000). Read, write, and compare decimals to thousandths. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100+ 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100_ + 2 x (1/1000). Leer, escribir y comparar números decimales hasta las milésimas. Leer, escribir y comparar números decimales hasta las milésimas usando números de base diez, números en palabras y la forma desarrollada; por ejemplo, 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1,000). Leen y escriben decimales hasta las milésimas usando números de base diez, los nombres de los números y su forma desarrollada; por ejemplo, 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). 

               Assess & Differentiate
               
                  01-02: Digital Quick Check
                    Curriculum Standards: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100+ 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100_ + 2 x (1/1000). Read, write, and compare decimals to thousandths. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100+ 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100_ + 2 x (1/1000). Read, write, and compare decimals to thousandths. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100+ 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100_ + 2 x (1/1000). Leer, escribir y comparar números decimales hasta las milésimas. Leer, escribir y comparar números decimales hasta las milésimas usando números de base diez, números en palabras y la forma desarrollada; por ejemplo, 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1,000). Leen y escriben decimales hasta las milésimas usando números de base diez, los nombres de los números y su forma desarrollada; por ejemplo, 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). 

            01-03: Thousandths
            
               Develop the Concept: Visual
               
                  Thousandths: Visual Learning
                    Curriculum Standards: Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Reconocer que en un número de varios dígitos, cualquier dígito en determinado lugar representa 10 veces lo que representa el mismo dígito en el lugar a su derecha y 1/10 de lo que representa en el lugar a su izquierda. Reconocen que en un número de varios dígitos, cualquier dígito en determinado lugar representa 10 veces lo que representa el mismo dígito en el lugar a su derecha y 1/10 de lo que representa en el lugar a su izquierda. 

               Assess & Differentiate
               
                  01-03: Digital Quick Check
                    Curriculum Standards: Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Reconocer que en un número de varios dígitos, cualquier dígito en determinado lugar representa 10 veces lo que representa el mismo dígito en el lugar a su derecha y 1/10 de lo que representa en el lugar a su izquierda. Reconocen que en un número de varios dígitos, cualquier dígito en determinado lugar representa 10 veces lo que representa el mismo dígito en el lugar a su derecha y 1/10 de lo que representa en el lugar a su izquierda. 

            01-04: Decimal Place Value
            
               Develop the Concept: Visual
               
                  Decimal Place Value: Visual Learning
                    Curriculum Standards: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100+ 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100_ + 2 x (1/1000). Read, write, and compare decimals to thousandths. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100+ 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100_ + 2 x (1/1000). Read, write, and compare decimals to thousandths. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100+ 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100_ + 2 x (1/1000). Leer, escribir y comparar números decimales hasta las milésimas. Leer, escribir y comparar números decimales hasta las milésimas usando números de base diez, números en palabras y la forma desarrollada; por ejemplo, 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1,000). Leen y escriben decimales hasta las milésimas usando números de base diez, los nombres de los números y su forma desarrollada; por ejemplo, 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). 

               Assess & Differentiate
               
                  01-04: Digital Quick Check
                    Curriculum Standards: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100+ 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100_ + 2 x (1/1000). Read, write, and compare decimals to thousandths. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100+ 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100_ + 2 x (1/1000). Read, write, and compare decimals to thousandths. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100+ 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100_ + 2 x (1/1000). Leer, escribir y comparar números decimales hasta las milésimas. Leer, escribir y comparar números decimales hasta las milésimas usando números de base diez, números en palabras y la forma desarrollada; por ejemplo, 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1,000). Leen y escriben decimales hasta las milésimas usando números de base diez, los nombres de los números y su forma desarrollada; por ejemplo, 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). 

            01-05: Comparing Decimals
            
               Develop the Concept: Visual
               
                  Comparing Decimals: Visual Learning
                    Curriculum Standards: Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Read, write, and compare decimals to thousandths. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Read, write, and compare decimals to thousandths. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Leer, escribir y comparar números decimales hasta las milésimas. Comparar dos números decimales hasta las milésimas en base al significado de los dígitos en cada lugar, utilizando los símbolos >, = y < para anotar los resultados de las comparaciones. Comparan dos decimales hasta las milésimas basándose en el valor de los dígitos en cada lugar, utilizando los símbolos >, = y < para anotar los resultados de las comparaciones. 

               Assess & Differentiate
               
                  01-05: Digital Quick Check
                    Curriculum Standards: Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Read, write, and compare decimals to thousandths. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Read, write, and compare decimals to thousandths. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Leer, escribir y comparar números decimales hasta las milésimas. Comparar dos números decimales hasta las milésimas en base al significado de los dígitos en cada lugar, utilizando los símbolos >, = y < para anotar los resultados de las comparaciones. Comparan dos decimales hasta las milésimas basándose en el valor de los dígitos en cada lugar, utilizando los símbolos >, = y < para anotar los resultados de las comparaciones. 

            01-06: Problem Solving: Look for a Pattern
            
               Develop the Concept: Visual
               
                  Problem Solving: Look for a Pattern: Visual Learning
                    Curriculum Standards: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100+ 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100_ + 2 x (1/1000). Read, write, and compare decimals to thousandths. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100+ 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100_ + 2 x (1/1000). Read, write, and compare decimals to thousandths. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100+ 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100_ + 2 x (1/1000). Leer, escribir y comparar números decimales hasta las milésimas. Leer, escribir y comparar números decimales hasta las milésimas usando números de base diez, números en palabras y la forma desarrollada; por ejemplo, 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1,000). Leen y escriben decimales hasta las milésimas usando números de base diez, los nombres de los números y su forma desarrollada; por ejemplo, 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). 

               Assess & Differentiate
               
                  01-06: Digital Quick Check
                    Curriculum Standards: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100+ 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100_ + 2 x (1/1000). Read, write, and compare decimals to thousandths. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100+ 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100_ + 2 x (1/1000). Read, write, and compare decimals to thousandths. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100+ 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100_ + 2 x (1/1000). Leer, escribir y comparar números decimales hasta las milésimas. Leer, escribir y comparar números decimales hasta las milésimas usando números de base diez, números en palabras y la forma desarrollada; por ejemplo, 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1,000). Leen y escriben decimales hasta las milésimas usando números de base diez, los nombres de los números y su forma desarrollada; por ejemplo, 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). 

            Topic 01: Online Topic Test
              Curriculum Standards: Represent the value of the digit in decimals through the thousandths using expanded notation and numerals. Represent the value of the digit in decimals through the thousandths using expanded notation and numerals. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Reconocer que en un número de varios dígitos, cualquier dígito en determinado lugar representa 10 veces lo que representa el mismo dígito en el lugar a su derecha y 1/10 de lo que representa en el lugar a su izquierda. Reconocen que en un número de varios dígitos, cualquier dígito en determinado lugar representa 10 veces lo que representa el mismo dígito en el lugar a su derecha y 1/10 de lo que representa en el lugar a su izquierda. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100+ 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100_ + 2 x (1/1000). Read, write, and compare decimals to thousandths. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100+ 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100_ + 2 x (1/1000). Read, write, and compare decimals to thousandths. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100+ 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100_ + 2 x (1/1000). Leer, escribir y comparar números decimales hasta las milésimas. Leer, escribir y comparar números decimales hasta las milésimas usando números de base diez, números en palabras y la forma desarrollada; por ejemplo, 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1,000). Leen y escriben decimales hasta las milésimas usando números de base diez, los nombres de los números y su forma desarrollada; por ejemplo, 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Describe the mathematical relationships found in the base-10 place value system through the hundred thousands place. Describe the mathematical relationships found in the base-10 place value system through the hundred thousands place. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Read, write, and compare decimals to thousandths. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Read, write, and compare decimals to thousandths. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Leer, escribir y comparar números decimales hasta las milésimas. Comparar dos números decimales hasta las milésimas en base al significado de los dígitos en cada lugar, utilizando los símbolos >, = y < para anotar los resultados de las comparaciones. Comparan dos decimales hasta las milésimas basándose en el valor de los dígitos en cada lugar, utilizando los símbolos >, = y < para anotar los resultados de las comparaciones. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 = 70 x 10 by applying concepts of place value and division. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 = 70 x 10 by applying concepts of place value and division. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. Reconocer que en un número entero no negativo de múltiples dígitos, un dígito en determinado lugar representa diez veces lo que representa en el lugar a su derecha. Por ejemplo, reconocer que 700 ÷ 70 = 10 aplicando conceptos de valor de posición y de división. Reconocen que en un número entero de dígitos múltiples, un dígito en determinado lugar representa diez veces lo que representa en el lugar a su derecha. Por ejemplo, reconocen que 700 ÷ 70 = 10 al aplicar conceptos de valor de posición y de división. Compare and order two decimals to thousandths and represent comparisons using the symbols >, <, or =. Compare and order two decimals to thousandths and represent comparisons using the symbols >, <, or =. 

            Alternate Test

            Digital Enhanced Topic Test

            Enhanced Topic Test

         Topic 02: Adding and Subtracting Decimals
         
            Decimal Olympiad

            Topic 02: Online Topic Readiness
              Curriculum Standards: Add and subtract whole numbers and decimals to the hundredths place using the standard algorithm. Add and subtract whole numbers and decimals to the hundredths place using the standard algorithm. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using the number line or another visual model. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using the number line or another visual model. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using the number line or another visual model. Comparar dos números decimales hasta las centésimas razonando sobre su tamaño. Reconocer que las comparaciones son válidas solamente cuando ambos números decimales se refieren al mismo entero. Anotar los resultados de las comparaciones con los símbolos >, = ó <, y justificar las conclusiones, por ej., utilizando un modelo visual. Comparan dos decimales hasta las centésimas al razonar sobre su tamaño. Reconocen que las comparaciones son válidas solamente cuando ambos decimales se refieren al mismo entero. Anotan los resultados de las comparaciones con los símbolos >, = ó <, y justifican las conclusiones, por ejemplo, utilizando una recta numérica u otro modelo visual. Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Utilizar la comprensión del valor de posición para redondear números decimales a cualquier lugar de redondeo. Utilizan el entendimiento del valor de posición para redondear decimales a cualquier lugar. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100 ; describe a length as 0.62 meters; locate 0.62 on a number line diagram. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100 ; describe a length as 0.62 meters; locate 0.62 on a number line diagram. Use decimal notation for fractions with denominators 10 or 100. Utilizar la notación decimal para las fracciones con denominadores de 10 ó 100. Por ejemplo, reescribir 0.62 como 62/100; describir una longitud como 0.62 metros; localizar 0.62 en una recta numérica. Utilizan la notación decimal para las fracciones con denominadores de 10 ó 100. Por ejemplo, al escribir 0.62 como 62/100; al describir una longitud como 0.62 metros; al localizar 0.62 en una recta numérica. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. Interpretar una ecuación de multiplicación como una comparación, por ej., interpretar 35 = 5 × 7 como un enunciado de que 35 es 5 veces 7 y 7 veces 5. Representar enunciados verbales de comparaciones multiplicativas como ecuaciones de multiplicación. Interpretan una ecuación de multiplicación como una comparación, por ejemplo, 35 = 5x7 como un enunciados de que 35 es 5 veces 7, y 7 veces 5. Representan enunciados verbales de comparaciones multiplicativas como ecuaciones de multiplicación. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Sumar y restar con fluidez los números enteros no negativos con múltiples dígitos utilizando el algoritmo convencional. Suman y restan con fluidez los números enteros con dígitos múltiples utilizando el algoritmo convencional. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Utilizan las cuatro operaciones para resolver problemas verbales sobre distancias, intervalos de tiempo, volúmenes líquidos, masas de objetos y dinero, incluyendo problemas con fracciones simples o decimales, y problemas que requieren expresar las medidas dadas en una unidad más grande en términos de una unidad más pequeña. Representan cantidades medidas utilizando diagramas tales como rectas numéricas con escalas de medición. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding  and explain why a rounded solution is appropriate. Resolver problemas verbales de varios pasos con números enteros no negativos y cuyas respuestas son números enteros no negativos utilizando las cuatro operaciones, incluyendo aquellos problemas en los que los residuos deben ser interpretados. Representar estos problemas utilizando ecuaciones con una letra para representar la cantidad desconocida. Evaluar lo razonable de las respuestas utilizando el cálculo mental y las estrategias de estimación, incluyendo el redondeo. Resuelven problemas verbales de pasos múltiples con números enteros, cuya respuestas son números enteros, usando las cuatro operaciones, incluyendo problemas en los que los residuos deben ser interpretados. Representan estos problemas usando ecuaciones con una letra que representa la cantidad desconocida. Evalúan si las respuestas son razonables usando cálculos mentales y estrategias de estimación incluyendo el redondeo. 

            02-01: Mental Math
            
               Develop the Concept: Visual
               
                  Mental Math: Visual Learning
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

               Assess & Differentiate
               
                  02-01: Digital Quick Check
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

            02-02: Rounding Decimals
            
               Develop the Concept: Visual
               
                  Rounding Whole Numbers and Decimals: Visual Learning
                    Curriculum Standards: Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Utilizar la comprensión del valor de posición para redondear números decimales a cualquier lugar de redondeo. Utilizan el entendimiento del valor de posición para redondear decimales a cualquier lugar. 

               Assess & Differentiate
               
                  02-02: Digital Quick Check
                    Curriculum Standards: Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Utilizar la comprensión del valor de posición para redondear números decimales a cualquier lugar de redondeo. Utilizan el entendimiento del valor de posición para redondear decimales a cualquier lugar. 

            02-03: Estimating Sums and Differences
            
               Develop the Concept: Visual
               
                  Estimating Sums and Differences: Visual Learning
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

               Assess & Differentiate
               
                  02-03: Digital Quick Check
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

            02-04: Modeling Addition and Subtraction of Decimals
            
               Develop the Concept: Visual
               
                  Modeling Addition and Subtraction of Decimals: Visual Learning
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

               Assess & Differentiate
               
                  02-04: Digital Quick Check
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

            02-05: Adding Decimals
            
               Develop the Concept: Visual
               
                  Adding Decimals: Visual Learning
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

               Assess & Differentiate
               
                  02-05: Digital Quick Check
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

            02-06: Subtracting Decimals
            
               Develop the Concept: Visual
               
                  Subtracting Decimals: Visual Learning
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

               Assess & Differentiate
               
                  02-06: Digital Quick Check
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

            02-07: Problem Solving: Multiple-Step Problems
            
               Develop the Concept: Visual
               
                  Problem Solving: Multiple-Step Problems: Visual Learning
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

               Assess & Differentiate
               
                  02-07: Digital Quick Check
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

            Topic 02: Online Topic Test
              Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Utilizar la comprensión del valor de posición para redondear números decimales a cualquier lugar de redondeo. Utilizan el entendimiento del valor de posición para redondear decimales a cualquier lugar. Add and subtract positive rational numbers fluently. Add and subtract positive rational numbers fluently. 

            Alternate Test

            Digital Enhanced Topic Test

            Enhanced Topic Test

         Topic 03: Multiplying Whole Numbers
         
            Estimate

            Topic 03: Online Topic Readiness
              Curriculum Standards: Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems. The student applies mathematical process standards to develop and use strategies and methods for whole number computations and decimal sums and differences in order to solve problems with efficiency and accuracy. Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems. The student applies mathematical process standards to develop and use strategies and methods for whole number computations and decimal sums and differences in order to solve problems with efficiency and accuracy. Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution. Use strategies and algorithms, including the standard algorithm, to multiply a two-digit number by a one-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties. Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution. Use strategies and algorithms, including the standard algorithm, to multiply a two-digit number by a one-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. Interpretar una ecuación de multiplicación como una comparación, por ej., interpretar 35 = 5 × 7 como un enunciado de que 35 es 5 veces 7 y 7 veces 5. Representar enunciados verbales de comparaciones multiplicativas como ecuaciones de multiplicación. Interpretan una ecuación de multiplicación como una comparación, por ejemplo, 35 = 5x7 como un enunciados de que 35 es 5 veces 7, y 7 veces 5. Representan enunciados verbales de comparaciones multiplicativas como ecuaciones de multiplicación. Interpret the value of each place-value position as 10 times the position to the right and as one-tenth of the value of the place to its left. Interpret the value of each place-value position as 10 times the position to the right and as one-tenth of the value of the place to its left. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Multiplicar un número entero no negativo de hasta cuatro dígitos por un número entero no negativo de un dígito, y multiplicar dos números de dos dígitos utilizando estrategias basadas en el valor de posición y las propiedades de las operaciones. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y/o modelos de área. Multiplican un número entero de hasta cuatro dígitos por un número entero de un dígito, y multiplican dos números de dos dígitos, utilizando estrategias basadas en el valor de posición y las propiedades de operaciones. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares, y/o modelos de area. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Resuelven problemas verbales de pasos múltiples con números enteros, cuya respuestas son números enteros, usando las cuatro operaciones, incluyendo problemas en los que los residuos deben ser interpretados. Representan estos problemas usando ecuaciones con una letra que representa la cantidad desconocida. Evalúan si las respuestas son razonables usando cálculos mentales y estrategias de estimación incluyendo el redondeo. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding  and explain why a rounded solution is appropriate. Resolver problemas verbales de varios pasos con números enteros no negativos y cuyas respuestas son números enteros no negativos utilizando las cuatro operaciones, incluyendo aquellos problemas en los que los residuos deben ser interpretados. Representar estos problemas utilizando ecuaciones con una letra para representar la cantidad desconocida. Evaluar lo razonable de las respuestas utilizando el cálculo mental y las estrategias de estimación, incluyendo el redondeo. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.1 Multiplicar o dividir para resolver problemas verbales con comparaciones multiplicativas, por ej., representar el problema utilizando dibujos y ecuaciones con un símbolo para el número desconocido; distinguir la comparación multiplicativa de la comparación de suma. Multiplican o dividen para resolver problemas verbales que incluyen comparaciones multiplicativas, por ejemplo, para representar el problema usando dibujos y ecuaciones con un símbolo para el número desconocido, distinguen una comparación multiplicativa de una comparación de suma. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 = 70 x 10 by applying concepts of place value and division. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 = 70 x 10 by applying concepts of place value and division. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. Reconocer que en un número entero no negativo de múltiples dígitos, un dígito en determinado lugar representa diez veces lo que representa en el lugar a su derecha. Por ejemplo, reconocer que 700 ÷ 70 = 10 aplicando conceptos de valor de posición y de división. Reconocen que en un número entero de dígitos múltiples, un dígito en determinado lugar representa diez veces lo que representa en el lugar a su derecha. Por ejemplo, reconocen que 700 ÷ 70 = 10 al aplicar conceptos de valor de posición y de división. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Sumar y restar con fluidez los números enteros no negativos con múltiples dígitos utilizando el algoritmo convencional. Suman y restan con fluidez los números enteros con dígitos múltiples utilizando el algoritmo convencional. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using ., 5, and , symbols to record the results of comparisons. Leen y escriben números enteros con dígitos múltiples usando numerales en base diez, los nombres de los números, y sus formas desarrolladas. Comparan dos números de dígitos múltiples basándose en el valor de los dígitos en cada lugar, utilizando los símbolos >, = y < para anotar los resultados de las comparaciones. Use place value understanding to round multi-digit whole numbers to any place. Utilizan la comprensión del valor de posición para redondear números enteros con dígitos múltiples a cualquier lugar. 

            03-01: Multiplication Properties
            
               Develop the Concept: Visual
               
                  Multiplication Properties: Visual Learning
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

               Assess & Differentiate
               
                  03-01: Digital Quick Check
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

            03-02: Multiplying by Powers of 10
            
               Develop the Concept: Visual
               
                  Using Mental Math to Multiply: Visual Learning

               Assess & Differentiate
               
                  03-02: Digital Quick Check

            03-03: Multiplying 2-Digit Numbers by Multiples of Ten
            
               Develop the Concept: Visual
               
                  Multiplying 2-Digit Numbers by Multiples of Ten: Visual Learning
                    Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiplicar números enteros no negativos de varios dígitos con fluidez, utilizando el algoritmo convencional. Multiplican números enteros de varios dígitos con fluidez, utilizando el algoritmo convencional. 

               Assess & Differentiate
               
                  03-03: Digital Quick Check
                    Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiplicar números enteros no negativos de varios dígitos con fluidez, utilizando el algoritmo convencional. Multiplican números enteros de varios dígitos con fluidez, utilizando el algoritmo convencional. 

            03-04: Multiplying 2-Digit by 2-Digit Numbers
            
               Develop the Concept: Visual
               
                  Multiplying 2-Digit by 2-Digit Numbers
                    Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiplicar números enteros no negativos de varios dígitos con fluidez, utilizando el algoritmo convencional. Multiplican números enteros de varios dígitos con fluidez, utilizando el algoritmo convencional. 

               Assess & Differentiate
               
                  03-04: Digital Quick Check
                    Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiplicar números enteros no negativos de varios dígitos con fluidez, utilizando el algoritmo convencional. Multiplican números enteros de varios dígitos con fluidez, utilizando el algoritmo convencional. 

            03-05: Multiplying Greater Numbers
            
               Develop the Concept: Visual
               
                  Multiplying Greater Numbers: Visual Learning
                    Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiplicar números enteros no negativos de varios dígitos con fluidez, utilizando el algoritmo convencional. Multiplican números enteros de varios dígitos con fluidez, utilizando el algoritmo convencional. 

               Assess & Differentiate
               
                  03-05: Digital Quick Check
                    Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiplicar números enteros no negativos de varios dígitos con fluidez, utilizando el algoritmo convencional. Multiplican números enteros de varios dígitos con fluidez, utilizando el algoritmo convencional. 

            03-06: Problem Solving: Draw a Picture and Write an Equation
            
               Develop the Concept: Visual
               
                  Problem Solving: Draw a Picture and Write an Equation: Visual Learning
                    Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiplicar números enteros no negativos de varios dígitos con fluidez, utilizando el algoritmo convencional. Multiplican números enteros de varios dígitos con fluidez, utilizando el algoritmo convencional. 

               Assess & Differentiate
               
                  03-06: Digital Quick Check
                    Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiplicar números enteros no negativos de varios dígitos con fluidez, utilizando el algoritmo convencional. Multiplican números enteros de varios dígitos con fluidez, utilizando el algoritmo convencional. 

            Topic 03: Online Topic Test
              Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiplicar números enteros no negativos de varios dígitos con fluidez, utilizando el algoritmo convencional. Multiplican números enteros de varios dígitos con fluidez, utilizando el algoritmo convencional. Determine products of a number and 10 or 100 using properties of operations and place value understandings. Determine products of a number and 10 or 100 using properties of operations and place value understandings. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. Multiply with fluency a three-digit number by a two-digit number using the standard algorithm. Multiply with fluency a three-digit number by a two-digit number using the standard algorithm. 

            Alternate Test

            Digital Enhanced Topic Test

            Enhanced Topic Test

         Topic 04: Dividing by 1-Digit Divisors
         
            Zeros in the Quotient

            Topic 04: Online Topic Readiness
              Curriculum Standards: Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.1 Multiplicar o dividir para resolver problemas verbales con comparaciones multiplicativas, por ej., representar el problema utilizando dibujos y ecuaciones con un símbolo para el número desconocido; distinguir la comparación multiplicativa de la comparación de suma. Multiplican o dividen para resolver problemas verbales que incluyen comparaciones multiplicativas, por ejemplo, para representar el problema usando dibujos y ecuaciones con un símbolo para el número desconocido, distinguen una comparación multiplicativa de una comparación de suma. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. Explain informally why the numbers will continue to alternate in this way. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. Explain informally why the numbers will continue to alternate in this way. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. Generar un patrón de números o figuras que siga una regla dada. Identificar características aparentes de la regla que no estaban explícitas en la regla misma. Por ejemplo, dada la regla “Sumar 3” y el número 1 para comenzar, generar términos en la sucesión resultante y observar que los términos parecen alternarse entre números impares y pares. Explicar informalmente por qué los números seguirán alternándose de esta manera. Generan un patrón de números o figuras que sigue una regla dada. Identifican las características aparentes del patrón que no eran explícitas en la regla misma. Por ejemplo, dada la regla “Añadir 3” y con el número 1 para comenzar, generan términos en la secuencia resultante y observan que los términos parecen alternarse entre números impares y pares. Explican informalmente porqué los números continuarán alternándose de esta manera. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar cocientes y residuos de números enteros no negativos a partir de divisiones con dividendos de hasta cuatro dígitos y divisores de un dígito, utilizando las estrategias basadas en el valor de posición y/o la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y/o modelos de área. Hallan cocientes y residuos de números enteros, a partir de divisiones con dividendos de hasta cuatro dígitos y divisores de un dígito, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares, y/o modelos de área. Resuelven problemas verbales de pasos múltiples con números enteros, cuya respuestas son números enteros, usando las cuatro operaciones, incluyendo problemas en los que los residuos deben ser interpretados. Representan estos problemas usando ecuaciones con una letra que representa la cantidad desconocida. Evalúan si las respuestas son razonables usando cálculos mentales y estrategias de estimación incluyendo el redondeo. 

            04-01: Dividing Multiples of 10 and 100
            
               Develop the Concept: Visual
               
                  Dividing Multiples of 10 and 100: Visual Learning
                    Curriculum Standards: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. 

               Assess & Differentiate
               
                  04-01: Digital Quick Check
                    Curriculum Standards: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. 

            04-02: Estimating Quotients
            
               Develop the Concept: Visual
               
                  Estimating Quotients: Visual Learning
                    Curriculum Standards: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. 

               Assess & Differentiate
               
                  04-02: Digital Quick Check
                    Curriculum Standards: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. 

            04-03: Problem Solving: Reasonableness
            
               Develop the Concept: Visual
               
                  Problem Solving: Reasonableness: Visual Learning
                    Curriculum Standards: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. 

               Assess & Differentiate
               
                  04-03: Digital Quick Check
                    Curriculum Standards: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. 

            04-04: Dividing by 1-Digit Divisors
            
               Develop the Concept: Visual
               
                  Dividing by 1-Digit Divisors: Visual Learning
                    Curriculum Standards: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. 

               Assess & Differentiate
               
                  04-04: Digital Quick Check
                    Curriculum Standards: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. 

            04-05: Zeros in the Quotient
            
               Develop the Concept: Visual
               
                  Zeros in the Quotient: Visual Learning
                    Curriculum Standards: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. 

               Assess & Differentiate
               
                  04-05: Digital Quick Check
                    Curriculum Standards: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. 

            04-06: More Dividing by 1-Digit Divisors
            
               Develop the Concept: Visual
               
                  More Dividing by 1-Digit Divisors: Visual Learning
                    Curriculum Standards: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. 

               Assess & Differentiate
               
                  04-06: Digital Quick Check
                    Curriculum Standards: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. 

            04-07: Problem Solving: Draw a Picture and Write an Equation
            
               Develop the Concept: Visual
               
                  Problem Solving: Draw a Picture and Write an Equation: Visual Learning
                    Curriculum Standards: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. 

               Assess & Differentiate
               
                  04-07: Digital Quick Check
                    Curriculum Standards: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. 

            Topic 04: Online Topic Test
              Curriculum Standards: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. 

            Alternate Test

            Digital Enhanced Topic Test

            Enhanced Topic Test

         Grade 5: Online Topics 01-04: Benchmark Test
           Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Reconocer que en un número de varios dígitos, cualquier dígito en determinado lugar representa 10 veces lo que representa el mismo dígito en el lugar a su derecha y 1/10 de lo que representa en el lugar a su izquierda. Reconocen que en un número de varios dígitos, cualquier dígito en determinado lugar representa 10 veces lo que representa el mismo dígito en el lugar a su derecha y 1/10 de lo que representa en el lugar a su izquierda. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiplicar números enteros no negativos de varios dígitos con fluidez, utilizando el algoritmo convencional. Multiplican números enteros de varios dígitos con fluidez, utilizando el algoritmo convencional. Determine products of a number and 10 or 100 using properties of operations and place value understandings. Determine products of a number and 10 or 100 using properties of operations and place value understandings. Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Utilizar la comprensión del valor de posición para redondear números decimales a cualquier lugar de redondeo. Utilizan el entendimiento del valor de posición para redondear decimales a cualquier lugar. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100+ 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100_ + 2 x (1/1000). Read, write, and compare decimals to thousandths. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100+ 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100_ + 2 x (1/1000). Read, write, and compare decimals to thousandths. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100+ 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100_ + 2 x (1/1000). Leer, escribir y comparar números decimales hasta las milésimas. Leer, escribir y comparar números decimales hasta las milésimas usando números de base diez, números en palabras y la forma desarrollada; por ejemplo, 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1,000). Leen y escriben decimales hasta las milésimas usando números de base diez, los nombres de los números y su forma desarrollada; por ejemplo, 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate. Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate. 

         Topic 05: Dividing by 2-Digit Divisors
         
            Dividing by 2-Digit Divisors

            Topic 05: Online Topic Readiness
              Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding  and explain why a rounded solution is appropriate. Resolver problemas verbales de varios pasos con números enteros no negativos y cuyas respuestas son números enteros no negativos utilizando las cuatro operaciones, incluyendo aquellos problemas en los que los residuos deben ser interpretados. Representar estos problemas utilizando ecuaciones con una letra para representar la cantidad desconocida. Evaluar lo razonable de las respuestas utilizando el cálculo mental y las estrategias de estimación, incluyendo el redondeo. Resuelven problemas verbales de pasos múltiples con números enteros, cuya respuestas son números enteros, usando las cuatro operaciones, incluyendo problemas en los que los residuos deben ser interpretados. Representan estos problemas usando ecuaciones con una letra que representa la cantidad desconocida. Evalúan si las respuestas son razonables usando cálculos mentales y estrategias de estimación incluyendo el redondeo. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using ., 5, and , symbols to record the results of comparisons. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using ., 5, and , symbols to record the results of comparisons. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Leer y escribir números enteros no negativos con múltiples dígitos usando números de base diez, números en palabras y formas desarrolladas. Comparar dos números de múltiples dígitos en base al significado de los dígitos en cada lugar, utilizando los símbolos >, = y < para anotar los resultados de las comparaciones. Leen y escriben números enteros con dígitos múltiples usando numerales en base diez, los nombres de los números, y sus formas desarrolladas. Comparan dos números de dígitos múltiples basándose en el valor de los dígitos en cada lugar, utilizando los símbolos >, = y < para anotar los resultados de las comparaciones. Use place value understanding to round multi-digit whole numbers to any place. Use place value understanding to round multi-digit whole numbers to any place. Use place value understanding to round multi-digit whole numbers to any place. Utilizar la comprensión del valor de posición para redondear números enteros no negativos con múltiples dígitos a cualquier lugar de redondeo. Utilizan la comprensión del valor de posición para redondear números enteros con dígitos múltiples a cualquier lugar. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Multiplicar un número entero no negativo de hasta cuatro dígitos por un número entero no negativo de un dígito, y multiplicar dos números de dos dígitos utilizando estrategias basadas en el valor de posición y las propiedades de las operaciones. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y/o modelos de área. Multiplican un número entero de hasta cuatro dígitos por un número entero de un dígito, y multiplican dos números de dos dígitos, utilizando estrategias basadas en el valor de posición y las propiedades de operaciones. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares, y/o modelos de area. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.1 Multiplicar o dividir para resolver problemas verbales con comparaciones multiplicativas, por ej., representar el problema utilizando dibujos y ecuaciones con un símbolo para el número desconocido; distinguir la comparación multiplicativa de la comparación de suma. Multiplican o dividen para resolver problemas verbales que incluyen comparaciones multiplicativas, por ejemplo, para representar el problema usando dibujos y ecuaciones con un símbolo para el número desconocido, distinguen una comparación multiplicativa de una comparación de suma. 

            05-01: Using Patterns to Divide
            
               Develop the Concept: Visual
               
                  Using Patterns to Divide: Visual Learning
                    Curriculum Standards: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. 

               Assess & Differentiate
               
                  05-01: Digital Quick Check
                    Curriculum Standards: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. 

            05-02: Estimating Quotients with 2-Digit Divisors
            
               Develop the Concept: Visual
               
                  Estimating Quotients with 2-Digit Divisors: Visual Learning
                    Curriculum Standards: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. 

               Assess & Differentiate
               
                  05-02: Digital Quick Check
                    Curriculum Standards: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. 

            05-03: Connecting Models and Symbols
            
               Develop the Concept: Visual
               
                  Connecting Models and Symbols: Visual Learning
                    Curriculum Standards: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. 

               Assess & Differentiate
               
                  05-03: Digital Quick Check
                    Curriculum Standards: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. 

            05-04: Dividing by Multiples of 10
            
               Develop the Concept: Visual
               
                  Dividing by Multiples of 10: Visual Learning
                    Curriculum Standards: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. 

               Assess & Differentiate
               
                  05-04: Digital Quick Check
                    Curriculum Standards: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. 

            05-05: 1-Digit Quotients
            
               Develop the Concept: Visual
               
                  1-Digit Quotients: Visual Learning
                    Curriculum Standards: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. 

               Assess & Differentiate
               
                  05-05: Digital Quick Check
                    Curriculum Standards: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. 

            05-06: 2-Digit Quotients
            
               Develop the Concept: Visual
               
                  2-Digit Quotients: Visual Learning
                    Curriculum Standards: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. 

               Assess & Differentiate
               
                  05-06: Digital Quick Check
                    Curriculum Standards: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. 

            05-07: Dividing with Greater Numbers
            
               Develop the Concept: Visual
               
                  Dividing with Greater Numbers: Visual Learning
                    Curriculum Standards: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. 

               Assess & Differentiate
               
                  05-07: Digital Quick Check
                    Curriculum Standards: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. 

            05-08: Problem Solving: Missing or Extra Information
            
               Develop the Concept: Visual
               
                  Problem Solving: Missing or Extra Information: Visual Learning
                    Curriculum Standards: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. 

               Assess & Differentiate
               
                  05-08: Digital Quick Check
                    Curriculum Standards: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. 

            Topic 05: Online Topic Test
              Curriculum Standards: Solve with proficiency for quotients of up to a four-digit dividend by a two-digit divisor using strategies and the standard algorithm. Solve with proficiency for quotients of up to a four-digit dividend by a two-digit divisor using strategies and the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Estimate to determine solutions to mathematical and real-world problems involving addition, subtraction, multiplication, or division. Estimate to determine solutions to mathematical and real-world problems involving addition, subtraction, multiplication, or division. Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution. Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution. 

            Alternate Test

            Digital Enhanced Topic Test

            Enhanced Topic Test

         Topic 06: Multiplying Decimals
         
            Multiplying Two Decimals

            Topic 06: Online Topic Readiness
              Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. Add and subtract positive rational numbers fluently. Add and subtract positive rational numbers fluently. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. Explain informally why the numbers will continue to alternate in this way. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. Explain informally why the numbers will continue to alternate in this way. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. Generar un patrón de números o figuras que siga una regla dada. Identificar características aparentes de la regla que no estaban explícitas en la regla misma. Por ejemplo, dada la regla “Sumar 3” y el número 1 para comenzar, generar términos en la sucesión resultante y observar que los términos parecen alternarse entre números impares y pares. Explicar informalmente por qué los números seguirán alternándose de esta manera. Generan un patrón de números o figuras que sigue una regla dada. Identifican las características aparentes del patrón que no eran explícitas en la regla misma. Por ejemplo, dada la regla “Añadir 3” y con el número 1 para comenzar, generan términos en la secuencia resultante y observan que los términos parecen alternarse entre números impares y pares. Explican informalmente porqué los números continuarán alternándose de esta manera. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. Interpretar una ecuación de multiplicación como una comparación, por ej., interpretar 35 = 5 × 7 como un enunciado de que 35 es 5 veces 7 y 7 veces 5. Representar enunciados verbales de comparaciones multiplicativas como ecuaciones de multiplicación. Interpretan una ecuación de multiplicación como una comparación, por ejemplo, 35 = 5x7 como un enunciados de que 35 es 5 veces 7, y 7 veces 5. Representan enunciados verbales de comparaciones multiplicativas como ecuaciones de multiplicación. Multiplican o dividen para resolver problemas verbales que incluyen comparaciones multiplicativas, por ejemplo, para representar el problema usando dibujos y ecuaciones con un símbolo para el número desconocido, distinguen una comparación multiplicativa de una comparación de suma. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar cocientes y residuos de números enteros no negativos a partir de divisiones con dividendos de hasta cuatro dígitos y divisores de un dígito, utilizando las estrategias basadas en el valor de posición y/o la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y/o modelos de área. Hallan cocientes y residuos de números enteros, a partir de divisiones con dividendos de hasta cuatro dígitos y divisores de un dígito, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares, y/o modelos de área. Resuelven problemas verbales de pasos múltiples con números enteros, cuya respuestas son números enteros, usando las cuatro operaciones, incluyendo problemas en los que los residuos deben ser interpretados. Representan estos problemas usando ecuaciones con una letra que representa la cantidad desconocida. Evalúan si las respuestas son razonables usando cálculos mentales y estrategias de estimación incluyendo el redondeo. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 = 70 x 10 by applying concepts of place value and division. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 = 70 x 10 by applying concepts of place value and division. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. Reconocer que en un número entero no negativo de múltiples dígitos, un dígito en determinado lugar representa diez veces lo que representa en el lugar a su derecha. Por ejemplo, reconocer que 700 ÷ 70 = 10 aplicando conceptos de valor de posición y de división. Reconocen que en un número entero de dígitos múltiples, un dígito en determinado lugar representa diez veces lo que representa en el lugar a su derecha. Por ejemplo, reconocen que 700 ÷ 70 = 10 al aplicar conceptos de valor de posición y de división. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Sumar y restar con fluidez los números enteros no negativos con múltiples dígitos utilizando el algoritmo convencional. Suman y restan con fluidez los números enteros con dígitos múltiples utilizando el algoritmo convencional. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using ., 5, and , symbols to record the results of comparisons. Leen y escriben números enteros con dígitos múltiples usando numerales en base diez, los nombres de los números, y sus formas desarrolladas. Comparan dos números de dígitos múltiples basándose en el valor de los dígitos en cada lugar, utilizando los símbolos >, = y < para anotar los resultados de las comparaciones. 

            06-01: Multiplying Decimals by 10, 100, or 1,000
            
               Develop the Concept: Visual
               
                  Multiplying Decimals by 10, 100, or 1,000: Visual Learning
                    Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Explicar los patrones en la cantidad de ceros que tiene un producto cuando se multiplica un número por una potencia de 10, y explicar los patrones al mover el punto decimal cuando hay que multiplicar o dividir un número decimal por una potencia de 10. Utilizar números enteros no negativos como exponentes para denotar la potencia de 10. Explican los patrones en la cantidad de ceros que tiene un producto cuando se multiplica un número por una potencia de 10, y explican los patrones en la posición del punto decimal cuando hay que multiplicar o dividir un decimal por una potencia de 10. Utilizan número enteros como exponentes para denotar la potencia de 10. 

               Assess & Differentiate
               
                  06-01: Digital Quick Check
                    Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Explicar los patrones en la cantidad de ceros que tiene un producto cuando se multiplica un número por una potencia de 10, y explicar los patrones al mover el punto decimal cuando hay que multiplicar o dividir un número decimal por una potencia de 10. Utilizar números enteros no negativos como exponentes para denotar la potencia de 10. Explican los patrones en la cantidad de ceros que tiene un producto cuando se multiplica un número por una potencia de 10, y explican los patrones en la posición del punto decimal cuando hay que multiplicar o dividir un decimal por una potencia de 10. Utilizan número enteros como exponentes para denotar la potencia de 10. 

            06-02: Estimating the Product of a Decimal and a Whole Number
            
               Develop the Concept: Visual
               
                  Estimating the Product of a Decimal and a Whole Number
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

               Assess & Differentiate
               
                  06-02: Digital Quick Check
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

            06-03: Number Sense: Decimal Multiplication
            
               Develop the Concept: Visual
               
                  Number Sense: Decimal Multiplication: Visual Learning
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

               Assess & Differentiate
               
                  06-03: Digital Quick Check
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

            06-04: Models for Multiplying Decimals
            
               Develop the Concept: Visual
               
                  Models for Multiplying Decimals: Visual Learning
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

               Assess & Differentiate
               
                  06-04: Digital Quick Check
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

            06-05: Multiplying a Decimal by a Whole Number
            
               Develop the Concept: Visual
               
                  Multiplying a Decimal by a Whole Number: Visual Learning
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

               Assess & Differentiate
               
                  06-05: Digital Quick Check
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

            06-06: Multiplying Two Decimals
            
               Develop the Concept: Visual
               
                  Multiplying Two Decimals: Visual Learning
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

               Assess & Differentiate
               
                  06-06: Digital Quick Check
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

            06-07: Problem Solving: Multiple-Step Problems
            
               Develop the Concept: Visual
               
                  Problem Solving: Multiple-Step Problems: Visual Learning
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

               Assess & Differentiate
               
                  06-07: Digital Quick Check
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

            Topic 06: Online Topic Test
              Curriculum Standards: Apply mathematics to problems arising in everyday life, society, and the workplace. Apply mathematics to problems arising in everyday life, society, and the workplace. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. Estimate to determine solutions to mathematical and real-world problems involving addition, subtraction, multiplication, or division. Estimate to determine solutions to mathematical and real-world problems involving addition, subtraction, multiplication, or division. Represent multiplication of decimals with products to the hundredths using objects and pictorial models, including area models. Represent multiplication of decimals with products to the hundredths using objects and pictorial models, including area models. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Explicar los patrones en la cantidad de ceros que tiene un producto cuando se multiplica un número por una potencia de 10, y explicar los patrones al mover el punto decimal cuando hay que multiplicar o dividir un número decimal por una potencia de 10. Utilizar números enteros no negativos como exponentes para denotar la potencia de 10. Explican los patrones en la cantidad de ceros que tiene un producto cuando se multiplica un número por una potencia de 10, y explican los patrones en la posición del punto decimal cuando hay que multiplicar o dividir un decimal por una potencia de 10. Utilizan número enteros como exponentes para denotar la potencia de 10. Solve for products of decimals to the hundredths, including situations involving money, using strategies based on place-value understandings, properties of operations, and the relationship to the multiplication of whole numbers. Solve for products of decimals to the hundredths, including situations involving money, using strategies based on place-value understandings, properties of operations, and the relationship to the multiplication of whole numbers. 

            Alternate Test

            Digital Enhanced Topic Test

            Enhanced Topic Test

         Topic 07: Dividing Decimals
         
            Topic 07: Online Topic Readiness
              Curriculum Standards: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Multiplicar un número entero no negativo de hasta cuatro dígitos por un número entero no negativo de un dígito, y multiplicar dos números de dos dígitos utilizando estrategias basadas en el valor de posición y las propiedades de las operaciones. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y/o modelos de área. Multiplican un número entero de hasta cuatro dígitos por un número entero de un dígito, y multiplican dos números de dos dígitos, utilizando estrategias basadas en el valor de posición y las propiedades de operaciones. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares, y/o modelos de area. Use strategies and algorithms, including the standard algorithm, to multiply up to a four-digit number by a one-digit number and to multiply a two-digit number by a two-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties. Use strategies and algorithms, including the standard algorithm, to multiply up to a four-digit number by a one-digit number and to multiply a two-digit number by a two-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties. Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Utilizar la comprensión del valor de posición para redondear números decimales a cualquier lugar de redondeo. Utilizan el entendimiento del valor de posición para redondear decimales a cualquier lugar. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100 ; describe a length as 0.62 meters; locate 0.62 on a number line diagram. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100 ; describe a length as 0.62 meters; locate 0.62 on a number line diagram. Use decimal notation for fractions with denominators 10 or 100. Utilizar la notación decimal para las fracciones con denominadores de 10 ó 100. Por ejemplo, reescribir 0.62 como 62/100; describir una longitud como 0.62 metros; localizar 0.62 en una recta numérica. Utilizan la notación decimal para las fracciones con denominadores de 10 ó 100. Por ejemplo, al escribir 0.62 como 62/100; al describir una longitud como 0.62 metros; al localizar 0.62 en una recta numérica. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. Represent the product of 2 two-digit numbers using arrays, area models, or equations, including perfect squares through 15 by 15. Represent the product of 2 two-digit numbers using arrays, area models, or equations, including perfect squares through 15 by 15. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Explicar los patrones en la cantidad de ceros que tiene un producto cuando se multiplica un número por una potencia de 10, y explicar los patrones al mover el punto decimal cuando hay que multiplicar o dividir un número decimal por una potencia de 10. Utilizar números enteros no negativos como exponentes para denotar la potencia de 10. Explican los patrones en la cantidad de ceros que tiene un producto cuando se multiplica un número por una potencia de 10, y explican los patrones en la posición del punto decimal cuando hay que multiplicar o dividir un decimal por una potencia de 10. Utilizan número enteros como exponentes para denotar la potencia de 10. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar cocientes y residuos de números enteros no negativos a partir de divisiones con dividendos de hasta cuatro dígitos y divisores de un dígito, utilizando las estrategias basadas en el valor de posición y/o la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y/o modelos de área. Hallan cocientes y residuos de números enteros, a partir de divisiones con dividendos de hasta cuatro dígitos y divisores de un dígito, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares, y/o modelos de área. 

            07-01: Dividing Decimals by 10, 100, or 1,000
            
               Develop the Concept: Visual
               
                  Dividing Decimals by 10, 100, or 1,000: Visual Learning
                    Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Explicar los patrones en la cantidad de ceros que tiene un producto cuando se multiplica un número por una potencia de 10, y explicar los patrones al mover el punto decimal cuando hay que multiplicar o dividir un número decimal por una potencia de 10. Utilizar números enteros no negativos como exponentes para denotar la potencia de 10. Explican los patrones en la cantidad de ceros que tiene un producto cuando se multiplica un número por una potencia de 10, y explican los patrones en la posición del punto decimal cuando hay que multiplicar o dividir un decimal por una potencia de 10. Utilizan número enteros como exponentes para denotar la potencia de 10. 

               Assess & Differentiate
               
                  07-01: Digital Quick Check
                    Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Explicar los patrones en la cantidad de ceros que tiene un producto cuando se multiplica un número por una potencia de 10, y explicar los patrones al mover el punto decimal cuando hay que multiplicar o dividir un número decimal por una potencia de 10. Utilizar números enteros no negativos como exponentes para denotar la potencia de 10. Explican los patrones en la cantidad de ceros que tiene un producto cuando se multiplica un número por una potencia de 10, y explican los patrones en la posición del punto decimal cuando hay que multiplicar o dividir un decimal por una potencia de 10. Utilizan número enteros como exponentes para denotar la potencia de 10. 

            07-02: Estimating Decimal Quotients
            
               Develop the Concept: Visual
               
                  Estimating Decimal Quotients: Visual Learning
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

               Assess & Differentiate
               
                  07-02: Digital Quick Check
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

            07-03: Number Sense: Decimal Division
            
               Develop the Concept: Visual
               
                  Number Sense: Decimal Division: Visual Learning
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

               Assess & Differentiate
               
                  07-03: Digital Quick Check
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

            07-04: Dividing by a Whole Number
            
               Develop the Concept: Visual
               
                  Dividing by a Whole Number: Visual Learning
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

               Assess & Differentiate
               
                  07-04: Digital Quick Check
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

            07-05: Dividing a Whole Number by a Decimal
            
               Develop the Concept: Visual
               
                  Dividing a Whole Number by a Decimal: Visual Learning
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

               Assess & Differentiate
               
                  07-05: Digital Quick Check
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

            07-06: Dividing a Decimal by a Decimal
            
               Develop the Concept: Visual
               
                  Dividing a Decimal by a Decimal: Visual Learning
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

               Assess & Differentiate
               
                  07-06: Digital Quick Check
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

            07-07: Problem Solving: Multiple-Step Problems
            
               Develop the Concept: Visual
               
                  Problem Solving: Multiple-Step Problems: Visual Learning
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

               Assess & Differentiate
               
                  07-07: Digital Quick Check
                    Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. 

            Topic 07: Online Topic Test
              Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. Estimate to determine solutions to mathematical and real-world problems involving addition, subtraction, multiplication, or division. Estimate to determine solutions to mathematical and real-world problems involving addition, subtraction, multiplication, or division. Solve for quotients of decimals to the hundredths, up to four-digit dividends and two-digit whole number divisors, using strategies and algorithms, including the standard algorithm. Solve for quotients of decimals to the hundredths, up to four-digit dividends and two-digit whole number divisors, using strategies and algorithms, including the standard algorithm. Represent quotients of decimals to the hundredths, up to four-digit dividends and two-digit whole number divisors, using objects and pictorial models, including area models. Represent quotients of decimals to the hundredths, up to four-digit dividends and two-digit whole number divisors, using objects and pictorial models, including area models. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Explicar los patrones en la cantidad de ceros que tiene un producto cuando se multiplica un número por una potencia de 10, y explicar los patrones al mover el punto decimal cuando hay que multiplicar o dividir un número decimal por una potencia de 10. Utilizar números enteros no negativos como exponentes para denotar la potencia de 10. Explican los patrones en la cantidad de ceros que tiene un producto cuando se multiplica un número por una potencia de 10, y explican los patrones en la posición del punto decimal cuando hay que multiplicar o dividir un decimal por una potencia de 10. Utilizan número enteros como exponentes para denotar la potencia de 10. 

            Alternate Test

            Digital Enhanced Topic Test

            Enhanced Topic Test

         Topic 08: Numerical Expressions, Patterns, and Relationships
         
            Expressions Rock

            Topic 08: Online Topic Readiness
              Curriculum Standards: Use strategies and algorithms, including the standard algorithm, to multiply a two-digit number by a one-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties. Use strategies and algorithms, including the standard algorithm, to multiply a two-digit number by a one-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties. Add and subtract positive rational numbers fluently. Add and subtract positive rational numbers fluently. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. Determine if two given fractions are equivalent using a variety of methods. Determine if two given fractions are equivalent using a variety of methods. Recognize the difference between additive and multiplicative numerical patterns given in a table or graph. Recognize the difference between additive and multiplicative numerical patterns given in a table or graph. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Multiplicar un número entero no negativo de hasta cuatro dígitos por un número entero no negativo de un dígito, y multiplicar dos números de dos dígitos utilizando estrategias basadas en el valor de posición y las propiedades de las operaciones. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y/o modelos de área. Multiplican un número entero de hasta cuatro dígitos por un número entero de un dígito, y multiplican dos números de dos dígitos, utilizando estrategias basadas en el valor de posición y las propiedades de operaciones. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares, y/o modelos de area. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar cocientes y residuos de números enteros no negativos a partir de divisiones con dividendos de hasta cuatro dígitos y divisores de un dígito, utilizando las estrategias basadas en el valor de posición y/o la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y/o modelos de área. Hallan cocientes y residuos de números enteros, a partir de divisiones con dividendos de hasta cuatro dígitos y divisores de un dígito, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares, y/o modelos de área. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule U1Add 3Ue and the starting number 0, and given the rule U1Add 6Ue and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule _Add 3? and the starting number 0, and given the rule _Add 6? and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule ñAdd 3î and the starting number 0, and given the rule ñAdd 6î and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generar dos patrones numéricos a partir de dos reglas dadas. Identificar la relación aparente entre los términos correspondientes. Formar pares ordenados con los términos correspondientes de ambos patrones y graficar los pares ordenados en un plano de coordenadas. Por ejemplo, dada la regla “Sumar 3” y el número 0 inicial, y dada la regla “Sumar 6” y el número 0 inicial, generar los términos en cada secuencia y observar que cada término de una secuencia es el doble que el término correspondiente en la otra secuencia. Explicar informalmente por qué esto es así. Generan dos patrones numéricos utilizando dos reglas dadas. Identifican la relación aparente entre términos correspondientes. Forman pares ordenados que consisten de los términos correspondientes de ambos patrones, y marcan los pares ordenados en un plano de coordenadas. Por ejemplo, dada la regla “Sumar 3” y el número inicial 0, y dada la regla “Sumar 6” y el número inicial 0, generan los términos en cada secuencia y observan que cada término de una secuencia, es el doble que el término correspondiente en la otra secuencia. Explican informalmente por qué esto es así. Use strategies and algorithms, including the standard algorithm, to divide up to a four-digit dividend by a one-digit divisor. Use strategies and algorithms, including the standard algorithm, to divide up to a four-digit dividend by a one-digit divisor. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. Explain informally why the numbers will continue to alternate in this way. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. Explain informally why the numbers will continue to alternate in this way. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. Generar un patrón de números o figuras que siga una regla dada. Identificar características aparentes de la regla que no estaban explícitas en la regla misma. Por ejemplo, dada la regla “Sumar 3” y el número 1 para comenzar, generar términos en la sucesión resultante y observar que los términos parecen alternarse entre números impares y pares. Explicar informalmente por qué los números seguirán alternándose de esta manera. Generan un patrón de números o figuras que sigue una regla dada. Identifican las características aparentes del patrón que no eran explícitas en la regla misma. Por ejemplo, dada la regla “Añadir 3” y con el número 1 para comenzar, generan términos en la secuencia resultante y observan que los términos parecen alternarse entre números impares y pares. Explican informalmente porqué los números continuarán alternándose de esta manera. 

            08-01: Variables and Expressions
            
               Develop the Concept: Visual
               
                  Variables and Expressions: Visual Learning
                    Curriculum Standards: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation U1add 8 and 7, then multiply by 2Ue as 2 x (8 +7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation _add 8 and 7, then multiply by 2? as 2 x (8 +7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation ñadd 8 and 7, then multiply by 2î as 2 x (8 +7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. Escribir expresiones simples que contengan cálculos numéricos e interpretar expresiones numéricas sin evaluarlas. Por ejemplo, expresar el cálculo “suma 8 más 7, luego multiplica por 2” como 2 x (8 + 7). Reconocer que 3 x (18,932 + 921) es tres veces mayor que 18,932 + 921, sin tener que calcular la suma o producto indicado. Escriben expresiones simples que contengan cálculos numéricos, e interpretan expresiones numéricas sin evaluarlas. Por ejemplo, expresan el cálculo “suma 8 más 7, luego multiplica por 2” como 2 x (8 + 7). Reconocen que 3 x (18,932 + 921) es tres veces mayor que 18,932 + 921, sin tener que calcular la suma o producto indicado. 

               Assess & Differentiate
               
                  08-01: Digital Quick Check
                    Curriculum Standards: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation U1add 8 and 7, then multiply by 2Ue as 2 x (8 +7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation _add 8 and 7, then multiply by 2? as 2 x (8 +7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation ñadd 8 and 7, then multiply by 2î as 2 x (8 +7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. Escribir expresiones simples que contengan cálculos numéricos e interpretar expresiones numéricas sin evaluarlas. Por ejemplo, expresar el cálculo “suma 8 más 7, luego multiplica por 2” como 2 x (8 + 7). Reconocer que 3 x (18,932 + 921) es tres veces mayor que 18,932 + 921, sin tener que calcular la suma o producto indicado. Escriben expresiones simples que contengan cálculos numéricos, e interpretan expresiones numéricas sin evaluarlas. Por ejemplo, expresan el cálculo “suma 8 más 7, luego multiplica por 2” como 2 x (8 + 7). Reconocen que 3 x (18,932 + 921) es tres veces mayor que 18,932 + 921, sin tener que calcular la suma o producto indicado. 

            08-02: Order of Operations
            
               Develop the Concept: Visual
               
                  Order of Operations: Visual Learning
                    Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Utilizar paréntesis, corchetes o llaves en las expresiones numéricas y evaluar las expresiones con estos símbolos. Utilizan paréntesis, corchetes o llaves en expresiones numéricas, y evaluan expresiones con estos símbolos. 

               Assess & Differentiate
               
                  08-02: Digital Quick Check
                    Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Utilizar paréntesis, corchetes o llaves en las expresiones numéricas y evaluar las expresiones con estos símbolos. Utilizan paréntesis, corchetes o llaves en expresiones numéricas, y evaluan expresiones con estos símbolos. 

            08-03: Evaluating Expressions
            
               Develop the Concept: Visual
               
                  Evaluating Expressions: Visual Learning
                    Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Utilizar paréntesis, corchetes o llaves en las expresiones numéricas y evaluar las expresiones con estos símbolos. Utilizan paréntesis, corchetes o llaves en expresiones numéricas, y evaluan expresiones con estos símbolos. 

               Assess & Differentiate
               
                  08-03: Digital Quick Check
                    Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Utilizar paréntesis, corchetes o llaves en las expresiones numéricas y evaluar las expresiones con estos símbolos. Utilizan paréntesis, corchetes o llaves en expresiones numéricas, y evaluan expresiones con estos símbolos. 

            08-04: Addition and Subtraction Expressions
            
               Develop the Concept: Visual
               
                  Addition and Subtraction Expressions: Visual Learning
                    Curriculum Standards: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule U1Add 3Ue and the starting number 0, and given the rule U1Add 6Ue and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule _Add 3? and the starting number 0, and given the rule _Add 6? and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule ñAdd 3î and the starting number 0, and given the rule ñAdd 6î and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generar dos patrones numéricos a partir de dos reglas dadas. Identificar la relación aparente entre los términos correspondientes. Formar pares ordenados con los términos correspondientes de ambos patrones y graficar los pares ordenados en un plano de coordenadas. Por ejemplo, dada la regla “Sumar 3” y el número 0 inicial, y dada la regla “Sumar 6” y el número 0 inicial, generar los términos en cada secuencia y observar que cada término de una secuencia es el doble que el término correspondiente en la otra secuencia. Explicar informalmente por qué esto es así. Generan dos patrones numéricos utilizando dos reglas dadas. Identifican la relación aparente entre términos correspondientes. Forman pares ordenados que consisten de los términos correspondientes de ambos patrones, y marcan los pares ordenados en un plano de coordenadas. Por ejemplo, dada la regla “Sumar 3” y el número inicial 0, y dada la regla “Sumar 6” y el número inicial 0, generan los términos en cada secuencia y observan que cada término de una secuencia, es el doble que el término correspondiente en la otra secuencia. Explican informalmente por qué esto es así. 

               Assess & Differentiate
               
                  08-04: Digital Quick Check
                    Curriculum Standards: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule U1Add 3Ue and the starting number 0, and given the rule U1Add 6Ue and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule _Add 3? and the starting number 0, and given the rule _Add 6? and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule ñAdd 3î and the starting number 0, and given the rule ñAdd 6î and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generar dos patrones numéricos a partir de dos reglas dadas. Identificar la relación aparente entre los términos correspondientes. Formar pares ordenados con los términos correspondientes de ambos patrones y graficar los pares ordenados en un plano de coordenadas. Por ejemplo, dada la regla “Sumar 3” y el número 0 inicial, y dada la regla “Sumar 6” y el número 0 inicial, generar los términos en cada secuencia y observar que cada término de una secuencia es el doble que el término correspondiente en la otra secuencia. Explicar informalmente por qué esto es así. Generan dos patrones numéricos utilizando dos reglas dadas. Identifican la relación aparente entre términos correspondientes. Forman pares ordenados que consisten de los términos correspondientes de ambos patrones, y marcan los pares ordenados en un plano de coordenadas. Por ejemplo, dada la regla “Sumar 3” y el número inicial 0, y dada la regla “Sumar 6” y el número inicial 0, generan los términos en cada secuencia y observan que cada término de una secuencia, es el doble que el término correspondiente en la otra secuencia. Explican informalmente por qué esto es así. 

            08-05: Multiplication and Division Expressions
            
               Develop the Concept: Visual
               
                  Multiplication and Division Expressions: Visual Learning
                    Curriculum Standards: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule U1Add 3Ue and the starting number 0, and given the rule U1Add 6Ue and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule _Add 3? and the starting number 0, and given the rule _Add 6? and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule ñAdd 3î and the starting number 0, and given the rule ñAdd 6î and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generar dos patrones numéricos a partir de dos reglas dadas. Identificar la relación aparente entre los términos correspondientes. Formar pares ordenados con los términos correspondientes de ambos patrones y graficar los pares ordenados en un plano de coordenadas. Por ejemplo, dada la regla “Sumar 3” y el número 0 inicial, y dada la regla “Sumar 6” y el número 0 inicial, generar los términos en cada secuencia y observar que cada término de una secuencia es el doble que el término correspondiente en la otra secuencia. Explicar informalmente por qué esto es así. Generan dos patrones numéricos utilizando dos reglas dadas. Identifican la relación aparente entre términos correspondientes. Forman pares ordenados que consisten de los términos correspondientes de ambos patrones, y marcan los pares ordenados en un plano de coordenadas. Por ejemplo, dada la regla “Sumar 3” y el número inicial 0, y dada la regla “Sumar 6” y el número inicial 0, generan los términos en cada secuencia y observan que cada término de una secuencia, es el doble que el término correspondiente en la otra secuencia. Explican informalmente por qué esto es así. 

               Assess & Differentiate
               
                  08-05: Digital Quick Check
                    Curriculum Standards: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule U1Add 3Ue and the starting number 0, and given the rule U1Add 6Ue and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule _Add 3? and the starting number 0, and given the rule _Add 6? and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule ñAdd 3î and the starting number 0, and given the rule ñAdd 6î and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generar dos patrones numéricos a partir de dos reglas dadas. Identificar la relación aparente entre los términos correspondientes. Formar pares ordenados con los términos correspondientes de ambos patrones y graficar los pares ordenados en un plano de coordenadas. Por ejemplo, dada la regla “Sumar 3” y el número 0 inicial, y dada la regla “Sumar 6” y el número 0 inicial, generar los términos en cada secuencia y observar que cada término de una secuencia es el doble que el término correspondiente en la otra secuencia. Explicar informalmente por qué esto es así. Generan dos patrones numéricos utilizando dos reglas dadas. Identifican la relación aparente entre términos correspondientes. Forman pares ordenados que consisten de los términos correspondientes de ambos patrones, y marcan los pares ordenados en un plano de coordenadas. Por ejemplo, dada la regla “Sumar 3” y el número inicial 0, y dada la regla “Sumar 6” y el número inicial 0, generan los términos en cada secuencia y observan que cada término de una secuencia, es el doble que el término correspondiente en la otra secuencia. Explican informalmente por qué esto es así. 

            08-06: Patterns: Extending Tables
            
               Develop the Concept: Visual
               
                  Patterns: Extending Tables: Visual Learning
                    Curriculum Standards: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule U1Add 3Ue and the starting number 0, and given the rule U1Add 6Ue and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule _Add 3? and the starting number 0, and given the rule _Add 6? and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule ñAdd 3î and the starting number 0, and given the rule ñAdd 6î and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generar dos patrones numéricos a partir de dos reglas dadas. Identificar la relación aparente entre los términos correspondientes. Formar pares ordenados con los términos correspondientes de ambos patrones y graficar los pares ordenados en un plano de coordenadas. Por ejemplo, dada la regla “Sumar 3” y el número 0 inicial, y dada la regla “Sumar 6” y el número 0 inicial, generar los términos en cada secuencia y observar que cada término de una secuencia es el doble que el término correspondiente en la otra secuencia. Explicar informalmente por qué esto es así. Generan dos patrones numéricos utilizando dos reglas dadas. Identifican la relación aparente entre términos correspondientes. Forman pares ordenados que consisten de los términos correspondientes de ambos patrones, y marcan los pares ordenados en un plano de coordenadas. Por ejemplo, dada la regla “Sumar 3” y el número inicial 0, y dada la regla “Sumar 6” y el número inicial 0, generan los términos en cada secuencia y observan que cada término de una secuencia, es el doble que el término correspondiente en la otra secuencia. Explican informalmente por qué esto es así. 

               Assess & Differentiate
               
                  08-06: Digital Quick Check
                    Curriculum Standards: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule U1Add 3Ue and the starting number 0, and given the rule U1Add 6Ue and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule _Add 3? and the starting number 0, and given the rule _Add 6? and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule ñAdd 3î and the starting number 0, and given the rule ñAdd 6î and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generar dos patrones numéricos a partir de dos reglas dadas. Identificar la relación aparente entre los términos correspondientes. Formar pares ordenados con los términos correspondientes de ambos patrones y graficar los pares ordenados en un plano de coordenadas. Por ejemplo, dada la regla “Sumar 3” y el número 0 inicial, y dada la regla “Sumar 6” y el número 0 inicial, generar los términos en cada secuencia y observar que cada término de una secuencia es el doble que el término correspondiente en la otra secuencia. Explicar informalmente por qué esto es así. Generan dos patrones numéricos utilizando dos reglas dadas. Identifican la relación aparente entre términos correspondientes. Forman pares ordenados que consisten de los términos correspondientes de ambos patrones, y marcan los pares ordenados en un plano de coordenadas. Por ejemplo, dada la regla “Sumar 3” y el número inicial 0, y dada la regla “Sumar 6” y el número inicial 0, generan los términos en cada secuencia y observan que cada término de una secuencia, es el doble que el término correspondiente en la otra secuencia. Explican informalmente por qué esto es así. 

            08-07: Problem Solving: Use Reasoning
            
               Develop the Concept: Visual
               
                  Problem Solving: Use Reasoning: Visual Learning
                    Curriculum Standards: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation U1add 8 and 7, then multiply by 2Ue as 2 x (8 +7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation _add 8 and 7, then multiply by 2? as 2 x (8 +7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation ñadd 8 and 7, then multiply by 2î as 2 x (8 +7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. Escribir expresiones simples que contengan cálculos numéricos e interpretar expresiones numéricas sin evaluarlas. Por ejemplo, expresar el cálculo “suma 8 más 7, luego multiplica por 2” como 2 x (8 + 7). Reconocer que 3 x (18,932 + 921) es tres veces mayor que 18,932 + 921, sin tener que calcular la suma o producto indicado. Escriben expresiones simples que contengan cálculos numéricos, e interpretan expresiones numéricas sin evaluarlas. Por ejemplo, expresan el cálculo “suma 8 más 7, luego multiplica por 2” como 2 x (8 + 7). Reconocen que 3 x (18,932 + 921) es tres veces mayor que 18,932 + 921, sin tener que calcular la suma o producto indicado. 

               Assess & Differentiate
               
                  08-07: Digital Quick Check
                    Curriculum Standards: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation U1add 8 and 7, then multiply by 2Ue as 2 x (8 +7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation _add 8 and 7, then multiply by 2? as 2 x (8 +7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation ñadd 8 and 7, then multiply by 2î as 2 x (8 +7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. Escribir expresiones simples que contengan cálculos numéricos e interpretar expresiones numéricas sin evaluarlas. Por ejemplo, expresar el cálculo “suma 8 más 7, luego multiplica por 2” como 2 x (8 + 7). Reconocer que 3 x (18,932 + 921) es tres veces mayor que 18,932 + 921, sin tener que calcular la suma o producto indicado. Escriben expresiones simples que contengan cálculos numéricos, e interpretan expresiones numéricas sin evaluarlas. Por ejemplo, expresan el cálculo “suma 8 más 7, luego multiplica por 2” como 2 x (8 + 7). Reconocen que 3 x (18,932 + 921) es tres veces mayor que 18,932 + 921, sin tener que calcular la suma o producto indicado. 

            Topic 08: Online Topic Test
              Curriculum Standards: Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution. Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate. Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution. Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation U1add 8 and 7, then multiply by 2Ue as 2 x (8 +7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation _add 8 and 7, then multiply by 2? as 2 x (8 +7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation ñadd 8 and 7, then multiply by 2î as 2 x (8 +7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. Escribir expresiones simples que contengan cálculos numéricos e interpretar expresiones numéricas sin evaluarlas. Por ejemplo, expresar el cálculo “suma 8 más 7, luego multiplica por 2” como 2 x (8 + 7). Reconocer que 3 x (18,932 + 921) es tres veces mayor que 18,932 + 921, sin tener que calcular la suma o producto indicado. Escriben expresiones simples que contengan cálculos numéricos, e interpretan expresiones numéricas sin evaluarlas. Por ejemplo, expresan el cálculo “suma 8 más 7, luego multiplica por 2” como 2 x (8 + 7). Reconocen que 3 x (18,932 + 921) es tres veces mayor que 18,932 + 921, sin tener que calcular la suma o producto indicado. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule U1Add 3Ue and the starting number 0, and given the rule U1Add 6Ue and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule _Add 3? and the starting number 0, and given the rule _Add 6? and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule ñAdd 3î and the starting number 0, and given the rule ñAdd 6î and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generar dos patrones numéricos a partir de dos reglas dadas. Identificar la relación aparente entre los términos correspondientes. Formar pares ordenados con los términos correspondientes de ambos patrones y graficar los pares ordenados en un plano de coordenadas. Por ejemplo, dada la regla “Sumar 3” y el número 0 inicial, y dada la regla “Sumar 6” y el número 0 inicial, generar los términos en cada secuencia y observar que cada término de una secuencia es el doble que el término correspondiente en la otra secuencia. Explicar informalmente por qué esto es así. Generan dos patrones numéricos utilizando dos reglas dadas. Identifican la relación aparente entre términos correspondientes. Forman pares ordenados que consisten de los términos correspondientes de ambos patrones, y marcan los pares ordenados en un plano de coordenadas. Por ejemplo, dada la regla “Sumar 3” y el número inicial 0, y dada la regla “Sumar 6” y el número inicial 0, generan los términos en cada secuencia y observan que cada término de una secuencia, es el doble que el término correspondiente en la otra secuencia. Explican informalmente por qué esto es así. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Utilizar paréntesis, corchetes o llaves en las expresiones numéricas y evaluar las expresiones con estos símbolos. Utilizan paréntesis, corchetes o llaves en expresiones numéricas, y evaluan expresiones con estos símbolos. Describe the meaning of parentheses and brackets in a numeric expression. Describe the meaning of parentheses and brackets in a numeric expression. Recognize the difference between additive and multiplicative numerical patterns given in a table or graph. Recognize the difference between additive and multiplicative numerical patterns given in a table or graph. 

            Alternate Test

            Digital Enhanced Topic Test

            Enhanced Topic Test

         Grade 5: Online Topics 05-08: Benchmark Test
           Curriculum Standards: Solve with proficiency for quotients of up to a four-digit dividend by a two-digit divisor using strategies and the standard algorithm. Solve with proficiency for quotients of up to a four-digit dividend by a two-digit divisor using strategies and the standard algorithm. Simplify numerical expressions that do not involve exponents, including up to two levels of grouping. Simplify numerical expressions that do not involve exponents, including up to two levels of grouping. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. Estimate to determine solutions to mathematical and real-world problems involving addition, subtraction, multiplication, or division. Estimate to determine solutions to mathematical and real-world problems involving addition, subtraction, multiplication, or division. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule U1Add 3Ue and the starting number 0, and given the rule U1Add 6Ue and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule _Add 3? and the starting number 0, and given the rule _Add 6? and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule ñAdd 3î and the starting number 0, and given the rule ñAdd 6î and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generar dos patrones numéricos a partir de dos reglas dadas. Identificar la relación aparente entre los términos correspondientes. Formar pares ordenados con los términos correspondientes de ambos patrones y graficar los pares ordenados en un plano de coordenadas. Por ejemplo, dada la regla “Sumar 3” y el número 0 inicial, y dada la regla “Sumar 6” y el número 0 inicial, generar los términos en cada secuencia y observar que cada término de una secuencia es el doble que el término correspondiente en la otra secuencia. Explicar informalmente por qué esto es así. Generan dos patrones numéricos utilizando dos reglas dadas. Identifican la relación aparente entre términos correspondientes. Forman pares ordenados que consisten de los términos correspondientes de ambos patrones, y marcan los pares ordenados en un plano de coordenadas. Por ejemplo, dada la regla “Sumar 3” y el número inicial 0, y dada la regla “Sumar 6” y el número inicial 0, generan los términos en cada secuencia y observan que cada término de una secuencia, es el doble que el término correspondiente en la otra secuencia. Explican informalmente por qué esto es así. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Utilizar paréntesis, corchetes o llaves en las expresiones numéricas y evaluar las expresiones con estos símbolos. Utilizan paréntesis, corchetes o llaves en expresiones numéricas, y evaluan expresiones con estos símbolos. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Explicar los patrones en la cantidad de ceros que tiene un producto cuando se multiplica un número por una potencia de 10, y explicar los patrones al mover el punto decimal cuando hay que multiplicar o dividir un número decimal por una potencia de 10. Utilizar números enteros no negativos como exponentes para denotar la potencia de 10. Explican los patrones en la cantidad de ceros que tiene un producto cuando se multiplica un número por una potencia de 10, y explican los patrones en la posición del punto decimal cuando hay que multiplicar o dividir un decimal por una potencia de 10. Utilizan número enteros como exponentes para denotar la potencia de 10. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation U1add 8 and 7, then multiply by 2Ue as 2 x (8 +7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation _add 8 and 7, then multiply by 2? as 2 x (8 +7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation ñadd 8 and 7, then multiply by 2î as 2 x (8 +7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. Escribir expresiones simples que contengan cálculos numéricos e interpretar expresiones numéricas sin evaluarlas. Por ejemplo, expresar el cálculo “suma 8 más 7, luego multiplica por 2” como 2 x (8 + 7). Reconocer que 3 x (18,932 + 921) es tres veces mayor que 18,932 + 921, sin tener que calcular la suma o producto indicado. Escriben expresiones simples que contengan cálculos numéricos, e interpretan expresiones numéricas sin evaluarlas. Por ejemplo, expresan el cálculo “suma 8 más 7, luego multiplica por 2” como 2 x (8 + 7). Reconocen que 3 x (18,932 + 921) es tres veces mayor que 18,932 + 921, sin tener que calcular la suma o producto indicado. 

         Topic 09: Adding and Subtracting Fractions
         
            Adding and Subtracting Fractions

            Topic 09: Online Topic Readiness
              Curriculum Standards: Solve with proficiency for quotients of up to a four-digit dividend by a two-digit divisor using strategies and the standard algorithm. Solve with proficiency for quotients of up to a four-digit dividend by a two-digit divisor using strategies and the standard algorithm. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.1 Multiplicar o dividir para resolver problemas verbales con comparaciones multiplicativas, por ej., representar el problema utilizando dibujos y ecuaciones con un símbolo para el número desconocido; distinguir la comparación multiplicativa de la comparación de suma. Multiplican o dividen para resolver problemas verbales que incluyen comparaciones multiplicativas, por ejemplo, para representar el problema usando dibujos y ecuaciones con un símbolo para el número desconocido, distinguen una comparación multiplicativa de una comparación de suma. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. Interpretar una ecuación de multiplicación como una comparación, por ej., interpretar 35 = 5 × 7 como un enunciado de que 35 es 5 veces 7 y 7 veces 5. Representar enunciados verbales de comparaciones multiplicativas como ecuaciones de multiplicación. Interpretan una ecuación de multiplicación como una comparación, por ejemplo, 35 = 5x7 como un enunciados de que 35 es 5 veces 7, y 7 veces 5. Representan enunciados verbales de comparaciones multiplicativas como ecuaciones de multiplicación. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 x (1/4), recording the conclusion by the equation 5/4 = 5 x (1/4). Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 x (1/4), recording the conclusion by the equation 5/4 = 5 x (1/4). Aplicar y ampliar los conocimientos previos sobre la multiplicación para multiplicar una fracción por un número entero no negativo. Entender que una fracción a/b es un múltiplo de 1/b. Por ejemplo, utilizar un modelo visual de fracciones para representar 5/4 como el producto 5 × (1/4), anotando la conclusión mediante la ecuación 5/4 = 5 × (1/4). Entienden que una fracción a/b es un múltiplo de 1/b. Por ejemplo, utilizan un modelo visual de fracciones para representar 5/4 como el producto 5 × (1/4), anotando la conclusión mediante la ecuación 5/4 = 5 × (1/4). Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100 , and add 3/10 + 4/100 = 34/100. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100 ; describe a length as 0.62 meters; locate 0.62 on a number line diagram. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100 , and add 3/10 + 4/100 = 34/100 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.4 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. Expresar una fracción con denominador 10 como una fracción equivalente con denominador 100 y utilizar esta técnica para sumar dos fracciones con denominadores respectivos de 10 y 100.4 Por ejemplo, expresar 3/10 como 30/100 y sumar 3/10 + 4/100 = 34/100. Expresan una fracción con denominador 10 como una fracción equivalente con denominador 1000, y utilizan esta técnica para sumar dos fracciones con denominadores respectivos de 10 y 1000. Por ejemplo, expresan 3/10 como 30/100 y suman 3/10 + 4/100 = 34/100. Utilizan la notación decimal para las fracciones con denominadores de 10 ó 100. Por ejemplo, al escribir 0.62 como 62/100; al describir una longitud como 0.62 metros; al localizar 0.62 en una recta numérica. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar cocientes y residuos de números enteros no negativos a partir de divisiones con dividendos de hasta cuatro dígitos y divisores de un dígito, utilizando las estrategias basadas en el valor de posición y/o la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y/o modelos de área. Hallan cocientes y residuos de números enteros, a partir de divisiones con dividendos de hasta cuatro dígitos y divisores de un dígito, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares, y/o modelos de área. Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Utilizar la comprensión del valor de posición para redondear números decimales a cualquier lugar de redondeo. Utilizan el entendimiento del valor de posición para redondear decimales a cualquier lugar. Use strategies and algorithms, including the standard algorithm, to divide up to a four-digit dividend by a one-digit divisor. Use strategies and algorithms, including the standard algorithm, to divide up to a four-digit dividend by a one-digit divisor. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Resuelven problemas verbales de pasos múltiples con números enteros, cuya respuestas son números enteros, usando las cuatro operaciones, incluyendo problemas en los que los residuos deben ser interpretados. Representan estos problemas usando ecuaciones con una letra que representa la cantidad desconocida. Evalúan si las respuestas son razonables usando cálculos mentales y estrategias de estimación incluyendo el redondeo. 

            09-01: Problem Solving: Writing to Explain
            
               Develop the Concept: Visual
               
                  Problem Solving: Writing to Explain: Visual Learning
                    Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 , by observing that 3/7 < 1/2 . Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 , by observing that 3/7 < 1/2 . Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Resolver problemas verbales de suma y resta de fracciones que se refieran a un todo, incluyendo casos de denominadores distintos; por ejemplo, empleando modelos visuales de fracciones o ecuaciones para representar el problema. Utilizar las fracciones de referencia y el sentido numérico para hacer cálculos mentales y evaluar la lógica de las respuestas. Por ejemplo, reconocer como incorrecto el resultado 2/5 + 1/2 = 3/7, observando que 3/7 < 1/2. Resuelven problemas verbales de suma y resta de fracciones que se refieran a un entero, incluyendo casos de denominadores distintos, por ejemplo, al emplear modelos visuales de fracciones o ecuaciones para representar el problema. Utilizan las fracciones de referencia y el sentido numérico para hacer cálculos mentales y evaluar la lógica de las respuestas. Por ejemplo, reconocen como incorrecto el resultado 2/5 + 1/2 = 3/7, observando que 3/7 < 1/2. 

               Assess & Differentiate
               
                  09-01: Digital Quick Check
                    Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 , by observing that 3/7 < 1/2 . Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 , by observing that 3/7 < 1/2 . Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Resolver problemas verbales de suma y resta de fracciones que se refieran a un todo, incluyendo casos de denominadores distintos; por ejemplo, empleando modelos visuales de fracciones o ecuaciones para representar el problema. Utilizar las fracciones de referencia y el sentido numérico para hacer cálculos mentales y evaluar la lógica de las respuestas. Por ejemplo, reconocer como incorrecto el resultado 2/5 + 1/2 = 3/7, observando que 3/7 < 1/2. Resuelven problemas verbales de suma y resta de fracciones que se refieran a un entero, incluyendo casos de denominadores distintos, por ejemplo, al emplear modelos visuales de fracciones o ecuaciones para representar el problema. Utilizan las fracciones de referencia y el sentido numérico para hacer cálculos mentales y evaluar la lógica de las respuestas. Por ejemplo, reconocen como incorrecto el resultado 2/5 + 1/2 = 3/7, observando que 3/7 < 1/2. 

            09-02: Estimating Sums and Differences of Fractions
            
               Develop the Concept: Visual
               
                  Estimating Sums and Differences of Fractions: Visual Learning
                    Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 , by observing that 3/7 < 1/2 . Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 , by observing that 3/7 < 1/2 . Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Resolver problemas verbales de suma y resta de fracciones que se refieran a un todo, incluyendo casos de denominadores distintos; por ejemplo, empleando modelos visuales de fracciones o ecuaciones para representar el problema. Utilizar las fracciones de referencia y el sentido numérico para hacer cálculos mentales y evaluar la lógica de las respuestas. Por ejemplo, reconocer como incorrecto el resultado 2/5 + 1/2 = 3/7, observando que 3/7 < 1/2. Resuelven problemas verbales de suma y resta de fracciones que se refieran a un entero, incluyendo casos de denominadores distintos, por ejemplo, al emplear modelos visuales de fracciones o ecuaciones para representar el problema. Utilizan las fracciones de referencia y el sentido numérico para hacer cálculos mentales y evaluar la lógica de las respuestas. Por ejemplo, reconocen como incorrecto el resultado 2/5 + 1/2 = 3/7, observando que 3/7 < 1/2. 

               Assess & Differentiate
               
                  09-02: Digital Quick Check
                    Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 , by observing that 3/7 < 1/2 . Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 , by observing that 3/7 < 1/2 . Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Resolver problemas verbales de suma y resta de fracciones que se refieran a un todo, incluyendo casos de denominadores distintos; por ejemplo, empleando modelos visuales de fracciones o ecuaciones para representar el problema. Utilizar las fracciones de referencia y el sentido numérico para hacer cálculos mentales y evaluar la lógica de las respuestas. Por ejemplo, reconocer como incorrecto el resultado 2/5 + 1/2 = 3/7, observando que 3/7 < 1/2. Resuelven problemas verbales de suma y resta de fracciones que se refieran a un entero, incluyendo casos de denominadores distintos, por ejemplo, al emplear modelos visuales de fracciones o ecuaciones para representar el problema. Utilizan las fracciones de referencia y el sentido numérico para hacer cálculos mentales y evaluar la lógica de las respuestas. Por ejemplo, reconocen como incorrecto el resultado 2/5 + 1/2 = 3/7, observando que 3/7 < 1/2. 

            09-03: Adding Fractions with Unlike Denominators
            
               Develop the Concept: Visual
               
                  Adding Fractions with Unlike Denominators: Visual Learning
                    Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Sumar y restar fracciones con denominadores distintos (inclusive números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) /bd). Suman y restan fracciones con denominadores distintos (incluyendo números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) / bd) 

               Assess & Differentiate
               
                  09-03: Digital Quick Check
                    Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Sumar y restar fracciones con denominadores distintos (inclusive números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) /bd). Suman y restan fracciones con denominadores distintos (incluyendo números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) / bd) 

            09-04: Subtracting Fractions with Unlike Denominators
            
               Develop the Concept: Visual
               
                  Subtracting Fractions with Unlike Denominators: Visual Learning
                    Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Sumar y restar fracciones con denominadores distintos (inclusive números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) /bd). Suman y restan fracciones con denominadores distintos (incluyendo números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) / bd) 

               Assess & Differentiate
               
                  09-04: Digital Quick Check
                    Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Sumar y restar fracciones con denominadores distintos (inclusive números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) /bd). Suman y restan fracciones con denominadores distintos (incluyendo números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) / bd) 

            09-05: More Adding and Subtracting Fractions
            
               Develop the Concept: Visual
               
                  More Adding and Subtracting Fractions: Visual Learning
                    Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Sumar y restar fracciones con denominadores distintos (inclusive números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) /bd). Suman y restan fracciones con denominadores distintos (incluyendo números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) / bd) 

               Assess & Differentiate
               
                  09-05: Digital Quick Check
                    Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Sumar y restar fracciones con denominadores distintos (inclusive números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) /bd). Suman y restan fracciones con denominadores distintos (incluyendo números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) / bd) 

            09-06: Solving Problems with Fractions
            
               Develop the Concept: Visual
               
                  Solving Problems with Fractions: Visual Learning
                    Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Sumar y restar fracciones con denominadores distintos (inclusive números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) /bd). Suman y restan fracciones con denominadores distintos (incluyendo números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) / bd) 

               Assess & Differentiate
               
                  09-06: Digital Quick Check
                    Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Sumar y restar fracciones con denominadores distintos (inclusive números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) /bd). Suman y restan fracciones con denominadores distintos (incluyendo números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) / bd) 

            09-07: Problem Solving: Draw a Picture and Write an Equation
            
               Develop the Concept: Visual
               
                  Problem Solving: Draw a Picture and Write an Equation: Visual Learning
                    Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 , by observing that 3/7 < 1/2 . Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 , by observing that 3/7 < 1/2 . Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Resolver problemas verbales de suma y resta de fracciones que se refieran a un todo, incluyendo casos de denominadores distintos; por ejemplo, empleando modelos visuales de fracciones o ecuaciones para representar el problema. Utilizar las fracciones de referencia y el sentido numérico para hacer cálculos mentales y evaluar la lógica de las respuestas. Por ejemplo, reconocer como incorrecto el resultado 2/5 + 1/2 = 3/7, observando que 3/7 < 1/2. Resuelven problemas verbales de suma y resta de fracciones que se refieran a un entero, incluyendo casos de denominadores distintos, por ejemplo, al emplear modelos visuales de fracciones o ecuaciones para representar el problema. Utilizan las fracciones de referencia y el sentido numérico para hacer cálculos mentales y evaluar la lógica de las respuestas. Por ejemplo, reconocen como incorrecto el resultado 2/5 + 1/2 = 3/7, observando que 3/7 < 1/2. 

               Assess & Differentiate
               
                  09-07: Digital Quick Check
                    Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 , by observing that 3/7 < 1/2 . Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 , by observing that 3/7 < 1/2 . Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Resolver problemas verbales de suma y resta de fracciones que se refieran a un todo, incluyendo casos de denominadores distintos; por ejemplo, empleando modelos visuales de fracciones o ecuaciones para representar el problema. Utilizar las fracciones de referencia y el sentido numérico para hacer cálculos mentales y evaluar la lógica de las respuestas. Por ejemplo, reconocer como incorrecto el resultado 2/5 + 1/2 = 3/7, observando que 3/7 < 1/2. Resuelven problemas verbales de suma y resta de fracciones que se refieran a un entero, incluyendo casos de denominadores distintos, por ejemplo, al emplear modelos visuales de fracciones o ecuaciones para representar el problema. Utilizan las fracciones de referencia y el sentido numérico para hacer cálculos mentales y evaluar la lógica de las respuestas. Por ejemplo, reconocen como incorrecto el resultado 2/5 + 1/2 = 3/7, observando que 3/7 < 1/2. 

            Topic 09: Online Topic Test
              Curriculum Standards: Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution. Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate. Create and use representations to organize, record, and communicate mathematical ideas. Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution. Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate. Create and use representations to organize, record, and communicate mathematical ideas. Represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects and pictorial models and properties of operations. Represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects and pictorial models and properties of operations. Add and subtract positive rational numbers fluently. Add and subtract positive rational numbers fluently. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 , by observing that 3/7 < 1/2 . Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 , by observing that 3/7 < 1/2 . Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Resolver problemas verbales de suma y resta de fracciones que se refieran a un todo, incluyendo casos de denominadores distintos; por ejemplo, empleando modelos visuales de fracciones o ecuaciones para representar el problema. Utilizar las fracciones de referencia y el sentido numérico para hacer cálculos mentales y evaluar la lógica de las respuestas. Por ejemplo, reconocer como incorrecto el resultado 2/5 + 1/2 = 3/7, observando que 3/7 < 1/2. Resuelven problemas verbales de suma y resta de fracciones que se refieran a un entero, incluyendo casos de denominadores distintos, por ejemplo, al emplear modelos visuales de fracciones o ecuaciones para representar el problema. Utilizan las fracciones de referencia y el sentido numérico para hacer cálculos mentales y evaluar la lógica de las respuestas. Por ejemplo, reconocen como incorrecto el resultado 2/5 + 1/2 = 3/7, observando que 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Sumar y restar fracciones con denominadores distintos (inclusive números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) /bd). Suman y restan fracciones con denominadores distintos (incluyendo números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) / bd) Estimate to determine solutions to mathematical and real-world problems involving addition, subtraction, multiplication, or division. Estimate to determine solutions to mathematical and real-world problems involving addition, subtraction, multiplication, or division. 

            Alternate Test

            Digital Enhanced Topic Test

            Enhanced Topic Test

         Topic 10: Adding and Subtracting Mixed Numbers
         
            Muffin Fractions

            Topic 10: Online Topic Readiness
              Curriculum Standards: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, <, and justify the conclusions, e.g., by using a visual fraction model. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, <, and justify the conclusions, e.g., by using a visual fraction model. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. Comparar dos fracciones con numeradores distintos y denominadores distintos, por ej., creando denominadores o numeradores comunes o comparándolas a una fracción de referencia como 1/2. Reconocer que las comparaciones son válidas solamente cuando las dos fracciones se refieren al mismo entero. Anotar los resultados de las comparaciones con los símbolos >, = ó <, y justificar las conclusiones, por ej., utilizando un modelo visual de fracciones. Comparan dos fracciones con numeradores distintos y denominadores distintos, por ejemplo, al crear denominadores o numeradores comunes, o al comparar una fracción de referencia como 1/2. Reconocen que las comparaciones son válidas solamente cuando las dos fracciones se refieren al mismo entero. Anotan los resultados de las comparaciones con los símbolos >, = ó <, y justifican las conclusiones, por ejemplo, utilizando un modelo visual de fracciones. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8.  2-1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8.  2-1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition  by an equation. Justify decompositions,  e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 =
8/8 + 8/8 + 1/8. Entender una fracción a/b cuando a > 1 como una suma de fracciones 1/b. Descomponer de varias maneras una fracción en una suma de fracciones con el mismo denominador, anotando cada descomposición como una ecuación. Justificar las descomposiciones, por ej., utilizando un modelo visual de fracciones. Ejemplos: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. Descomponen de varias maneras una fracción en una suma de fracciones con el mismo denominador, anotando cada descomposición con una ecuación. Justifican las descomposiciones, por ejemplo, utilizando un modelo visual de fracciones. Ejemplos: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8; 21/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. Represent problems using an input-output table and numerical expressions to generate a number pattern that follows a given rule representing the relationship of the values in the resulting sequence and their position in the sequence. Represent problems using an input-output table and numerical expressions to generate a number pattern that follows a given rule representing the relationship of the values in the resulting sequence and their position in the sequence. Add and subtract positive rational numbers fluently. Add and subtract positive rational numbers fluently. Compare two fractions with different numerators and different denominators and represent the comparison using the symbols >, =, or < . Compare two fractions with different numerators and different denominators and represent the comparison using the symbols >, =, or < . Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. Explain informally why the numbers will continue to alternate in this way. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. Explain informally why the numbers will continue to alternate in this way. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. Generar un patrón de números o figuras que siga una regla dada. Identificar características aparentes de la regla que no estaban explícitas en la regla misma. Por ejemplo, dada la regla “Sumar 3” y el número 1 para comenzar, generar términos en la sucesión resultante y observar que los términos parecen alternarse entre números impares y pares. Explicar informalmente por qué los números seguirán alternándose de esta manera. Generan un patrón de números o figuras que sigue una regla dada. Identifican las características aparentes del patrón que no eran explícitas en la regla misma. Por ejemplo, dada la regla “Añadir 3” y con el número 1 para comenzar, generan términos en la secuencia resultante y observan que los términos parecen alternarse entre números impares y pares. Explican informalmente porqué los números continuarán alternándose de esta manera. Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Hallar todos los pares de factores de un número entero no negativo con rango de 1 a 100. Reconocer que un número entero no negativo es un múltiplo de cada uno de sus factores. Determinar si cierto número entero no negativo con rango de 1 a 100 es un múltiplo de cierto número de un dígito. Determinar si cierto número entero no negativo con rango de 1 a 100 es primo o compuesto. Hallan todos los pares de factores de números enteros dentro del rango 1–100. Reconocen que un número entero es un múltiplo de cada uno de sus factores. Determinan si cierto número entero dentro del rango 1–100 es un múltiplo de cierto número de un solo dígito. Determinan si un número entero dentro del rango 1–100 es primo o compuesto. 

            10-01: Estimating Sums and Differences of Mixed Numbers
            
               Develop the Concept: Visual
               
                  Estimating Sums and Differences of Mixed Numbers: Visual Learning
                    Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 , by observing that 3/7 < 1/2 . Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 , by observing that 3/7 < 1/2 . Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Resolver problemas verbales de suma y resta de fracciones que se refieran a un todo, incluyendo casos de denominadores distintos; por ejemplo, empleando modelos visuales de fracciones o ecuaciones para representar el problema. Utilizar las fracciones de referencia y el sentido numérico para hacer cálculos mentales y evaluar la lógica de las respuestas. Por ejemplo, reconocer como incorrecto el resultado 2/5 + 1/2 = 3/7, observando que 3/7 < 1/2. Resuelven problemas verbales de suma y resta de fracciones que se refieran a un entero, incluyendo casos de denominadores distintos, por ejemplo, al emplear modelos visuales de fracciones o ecuaciones para representar el problema. Utilizan las fracciones de referencia y el sentido numérico para hacer cálculos mentales y evaluar la lógica de las respuestas. Por ejemplo, reconocen como incorrecto el resultado 2/5 + 1/2 = 3/7, observando que 3/7 < 1/2. 

               Assess & Differentiate
               
                  10-01: Digital Quick Check
                    Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 , by observing that 3/7 < 1/2 . Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 , by observing that 3/7 < 1/2 . Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Resolver problemas verbales de suma y resta de fracciones que se refieran a un todo, incluyendo casos de denominadores distintos; por ejemplo, empleando modelos visuales de fracciones o ecuaciones para representar el problema. Utilizar las fracciones de referencia y el sentido numérico para hacer cálculos mentales y evaluar la lógica de las respuestas. Por ejemplo, reconocer como incorrecto el resultado 2/5 + 1/2 = 3/7, observando que 3/7 < 1/2. Resuelven problemas verbales de suma y resta de fracciones que se refieran a un entero, incluyendo casos de denominadores distintos, por ejemplo, al emplear modelos visuales de fracciones o ecuaciones para representar el problema. Utilizan las fracciones de referencia y el sentido numérico para hacer cálculos mentales y evaluar la lógica de las respuestas. Por ejemplo, reconocen como incorrecto el resultado 2/5 + 1/2 = 3/7, observando que 3/7 < 1/2. 

            10-02: Modeling Addition and Subtraction of Mixed Numbers
            
               Develop the Concept: Visual
               
                  Modeling Addition and Subtraction of Mixed Numbers: Visual Learning
                    Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 , by observing that 3/7 < 1/2 . Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 , by observing that 3/7 < 1/2 . Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Resolver problemas verbales de suma y resta de fracciones que se refieran a un todo, incluyendo casos de denominadores distintos; por ejemplo, empleando modelos visuales de fracciones o ecuaciones para representar el problema. Utilizar las fracciones de referencia y el sentido numérico para hacer cálculos mentales y evaluar la lógica de las respuestas. Por ejemplo, reconocer como incorrecto el resultado 2/5 + 1/2 = 3/7, observando que 3/7 < 1/2. Resuelven problemas verbales de suma y resta de fracciones que se refieran a un entero, incluyendo casos de denominadores distintos, por ejemplo, al emplear modelos visuales de fracciones o ecuaciones para representar el problema. Utilizan las fracciones de referencia y el sentido numérico para hacer cálculos mentales y evaluar la lógica de las respuestas. Por ejemplo, reconocen como incorrecto el resultado 2/5 + 1/2 = 3/7, observando que 3/7 < 1/2. 

               Assess & Differentiate
               
                  10-02: Digital Quick Check
                    Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 , by observing that 3/7 < 1/2 . Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 , by observing that 3/7 < 1/2 . Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Resolver problemas verbales de suma y resta de fracciones que se refieran a un todo, incluyendo casos de denominadores distintos; por ejemplo, empleando modelos visuales de fracciones o ecuaciones para representar el problema. Utilizar las fracciones de referencia y el sentido numérico para hacer cálculos mentales y evaluar la lógica de las respuestas. Por ejemplo, reconocer como incorrecto el resultado 2/5 + 1/2 = 3/7, observando que 3/7 < 1/2. Resuelven problemas verbales de suma y resta de fracciones que se refieran a un entero, incluyendo casos de denominadores distintos, por ejemplo, al emplear modelos visuales de fracciones o ecuaciones para representar el problema. Utilizan las fracciones de referencia y el sentido numérico para hacer cálculos mentales y evaluar la lógica de las respuestas. Por ejemplo, reconocen como incorrecto el resultado 2/5 + 1/2 = 3/7, observando que 3/7 < 1/2. 

            10-03: Adding Mixed Numbers
            
               Develop the Concept: Visual
               
                  Adding Mixed Numbers: Visual Learning
                    Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Sumar y restar fracciones con denominadores distintos (inclusive números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) /bd). Suman y restan fracciones con denominadores distintos (incluyendo números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) / bd) 

               Assess & Differentiate
               
                  10-03: Digital Quick Check
                    Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Sumar y restar fracciones con denominadores distintos (inclusive números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) /bd). Suman y restan fracciones con denominadores distintos (incluyendo números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) / bd) 

            10-04: Subtracting Mixed Numbers
            
               Develop the Concept: Visual
               
                  Subtracting Mixed Numbers: Visual Learning
                    Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Sumar y restar fracciones con denominadores distintos (inclusive números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) /bd). Suman y restan fracciones con denominadores distintos (incluyendo números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) / bd) 

               Assess & Differentiate
               
                  10-04: Digital Quick Check
                    Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Sumar y restar fracciones con denominadores distintos (inclusive números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) /bd). Suman y restan fracciones con denominadores distintos (incluyendo números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) / bd) 

            10-05: More Adding and Subtracting Mixed Numbers
            
               Develop the Concept: Visual
               
                  More Adding and Subtracting Mixed Numbers: Visual Learning
                    Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Sumar y restar fracciones con denominadores distintos (inclusive números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) /bd). Suman y restan fracciones con denominadores distintos (incluyendo números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) / bd) 

               Assess & Differentiate
               
                  10-05: Digital Quick Check
                    Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Sumar y restar fracciones con denominadores distintos (inclusive números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) /bd). Suman y restan fracciones con denominadores distintos (incluyendo números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) / bd) 

            10-06: Problem Solving: Draw a Picture and Write an Equation
            
               Develop the Concept: Visual
               
                  Problem Solving: Draw a Picture and Write an Equation: Visual Learning
                    Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Sumar y restar fracciones con denominadores distintos (inclusive números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) /bd). Suman y restan fracciones con denominadores distintos (incluyendo números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) / bd) 

               Assess & Differentiate
               
                  10-06: Digital Quick Check
                    Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Sumar y restar fracciones con denominadores distintos (inclusive números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) /bd). Suman y restan fracciones con denominadores distintos (incluyendo números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) / bd) 

            Topic 10: Online Topic Test
              Curriculum Standards: Represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects and pictorial models and properties of operations. Represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects and pictorial models and properties of operations. Add and subtract positive rational numbers fluently. Add and subtract positive rational numbers fluently. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 , by observing that 3/7 < 1/2 . Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 , by observing that 3/7 < 1/2 . Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Resolver problemas verbales de suma y resta de fracciones que se refieran a un todo, incluyendo casos de denominadores distintos; por ejemplo, empleando modelos visuales de fracciones o ecuaciones para representar el problema. Utilizar las fracciones de referencia y el sentido numérico para hacer cálculos mentales y evaluar la lógica de las respuestas. Por ejemplo, reconocer como incorrecto el resultado 2/5 + 1/2 = 3/7, observando que 3/7 < 1/2. Resuelven problemas verbales de suma y resta de fracciones que se refieran a un entero, incluyendo casos de denominadores distintos, por ejemplo, al emplear modelos visuales de fracciones o ecuaciones para representar el problema. Utilizan las fracciones de referencia y el sentido numérico para hacer cálculos mentales y evaluar la lógica de las respuestas. Por ejemplo, reconocen como incorrecto el resultado 2/5 + 1/2 = 3/7, observando que 3/7 < 1/2. Estimate to determine solutions to mathematical and real-world problems involving addition, subtraction, multiplication, or division. Estimate to determine solutions to mathematical and real-world problems involving addition, subtraction, multiplication, or division. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Sumar y restar fracciones con denominadores distintos (inclusive números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) /bd). Suman y restan fracciones con denominadores distintos (incluyendo números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) / bd) 

            Alternate Test

            Digital Enhanced Topic Test

            Enhanced Topic Test

         Topic 11: Multiplying and Dividing Fractions and Mixed Numbers
         
            Multiplying Fractions

            Topic 11: Online Topic Readiness
              Curriculum Standards: Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Entender una fracción a/b cuando a > 1 como una suma de fracciones 1/b. Sumar y restar números mixtos con el mismo denominador, por ej., reemplazando cada número mixto por una fracción equivalente, y/o utilizando las propiedades de las operaciones y la relación entre la suma y la resta. Suman y restan números mixtos con el mismo denominador, por ejemplo, al reemplazar cada número mixto por una fracción equivalente, y/o al utilizar las propiedades de las operaciones y la relación entre la suma y la resta. Represent and solve addition and subtraction of fractions with equal denominators using objects and pictorial models that build to the number line and properties of operations. Represent and solve addition and subtraction of fractions with equal denominators using objects and pictorial models that build to the number line and properties of operations. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 , by observing that 3/7 < 1/2 . Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 , by observing that 3/7 < 1/2 . Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Resolver problemas verbales de suma y resta de fracciones que se refieran a un todo, incluyendo casos de denominadores distintos; por ejemplo, empleando modelos visuales de fracciones o ecuaciones para representar el problema. Utilizar las fracciones de referencia y el sentido numérico para hacer cálculos mentales y evaluar la lógica de las respuestas. Por ejemplo, reconocer como incorrecto el resultado 2/5 + 1/2 = 3/7, observando que 3/7 < 1/2. Resuelven problemas verbales de suma y resta de fracciones que se refieran a un entero, incluyendo casos de denominadores distintos, por ejemplo, al emplear modelos visuales de fracciones o ecuaciones para representar el problema. Utilizan las fracciones de referencia y el sentido numérico para hacer cálculos mentales y evaluar la lógica de las respuestas. Por ejemplo, reconocen como incorrecto el resultado 2/5 + 1/2 = 3/7, observando que 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Sumar y restar fracciones con denominadores distintos (inclusive números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) /bd). Suman y restan fracciones con denominadores distintos (incluyendo números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) / bd) Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Entender una fracción a/b cuando a > 1 como una suma de fracciones 1/b. Entender la suma y la resta de fracciones como la unión y separación de partes que se refieren a un mismo entero. Entienden la suma y la resta de fracciones como la unión y la separación de partes que se refieren a un mismo entero. Resuelven problemas verbales sobre sumas y restas de fracciones relacionados a un mismo entero y con el mismo denominador, por ejemplo, utilizando modelos visuales de fracciones y ecuaciones para representar el problema. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Hallar todos los pares de factores de un número entero no negativo con rango de 1 a 100. Reconocer que un número entero no negativo es un múltiplo de cada uno de sus factores. Determinar si cierto número entero no negativo con rango de 1 a 100 es un múltiplo de cierto número de un dígito. Determinar si cierto número entero no negativo con rango de 1 a 100 es primo o compuesto. Hallan todos los pares de factores de números enteros dentro del rango 1–100. Reconocen que un número entero es un múltiplo de cada uno de sus factores. Determinan si cierto número entero dentro del rango 1–100 es un múltiplo de cierto número de un solo dígito. Determinan si un número entero dentro del rango 1–100 es primo o compuesto. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. Entienden que un múltiplo de a/b es un múltiplo de 1/b, y utilizan este entendimiento para multiplicar una fracción por un número entero. Resuelven problemas verbales relacionados a la multiplicación de una fracción por un número entero, por ejemplo, utilizan modelos visuales de fracciones y ecuaciones para representar el problema. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. 

            11-01: Multiplying Fractions and Whole Numbers
            
               Develop the Concept: Visual
               
                  Multiplying Fractions and Whole Numbers: Visual Learning
                    Curriculum Standards: Interpret the product (a/b) x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷ b. For example, use a visual fraction model to show (2/3) x 4 = 8/3 , and create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd.) Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷ b. For example, use a visual fraction model to show (2/3) x 4 = 8/3 , and create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd.) Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q … b. For example, use a visual fraction model to show (2/3) x 4 = 8/3 , and create a story context for this equation. Do the same with (2/3) x ( 4/5) = 8/15. (In general, (a/b) x (c/d ) = ac/bd.) Aplicar y ampliar los conocimientos previos sobre la multiplicación para multiplicar una fracción o un número entero por una fracción. Interpretar el producto (a/b) × q como a partes de la repartición de q en partes iguales de b; de manera equivalente, como el resultado de la secuencia de operaciones a × q ÷ b. Por ejemplo, emplear un modelo visual de fracciones para representar (2/3) × 4 = 8/3, e inventar un contexto para esta ecuación. Hacer lo mismo con (2/3) ×(4/5) = 8/15. (En general, (a/b) ×(c/d) = ac/bd). Interpretan el producto (a/b) × q como tantas partes a de la repartición de q en partes iguales de b; de manera equivalente, como el resultado de la secuencia de operaciones a × q ÷ b. Por ejemplo, al emplear un modelo visual de fracciones para representar (2/3) × 4 = 8/3, y crear un contexto para esta ecuación. Hacen lo mismo con (2/3) × (4/5) = 8/15. (En general, (a /b) × (c /d) = ac/bd). 

               Assess & Differentiate
               
                  11-01: Digital Quick Check
                    Curriculum Standards: Interpret the product (a/b) x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷ b. For example, use a visual fraction model to show (2/3) x 4 = 8/3 , and create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd.) Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷ b. For example, use a visual fraction model to show (2/3) x 4 = 8/3 , and create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd.) Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q … b. For example, use a visual fraction model to show (2/3) x 4 = 8/3 , and create a story context for this equation. Do the same with (2/3) x ( 4/5) = 8/15. (In general, (a/b) x (c/d ) = ac/bd.) Aplicar y ampliar los conocimientos previos sobre la multiplicación para multiplicar una fracción o un número entero por una fracción. Interpretar el producto (a/b) × q como a partes de la repartición de q en partes iguales de b; de manera equivalente, como el resultado de la secuencia de operaciones a × q ÷ b. Por ejemplo, emplear un modelo visual de fracciones para representar (2/3) × 4 = 8/3, e inventar un contexto para esta ecuación. Hacer lo mismo con (2/3) ×(4/5) = 8/15. (En general, (a/b) ×(c/d) = ac/bd). Interpretan el producto (a/b) × q como tantas partes a de la repartición de q en partes iguales de b; de manera equivalente, como el resultado de la secuencia de operaciones a × q ÷ b. Por ejemplo, al emplear un modelo visual de fracciones para representar (2/3) × 4 = 8/3, y crear un contexto para esta ecuación. Hacen lo mismo con (2/3) × (4/5) = 8/15. (En general, (a /b) × (c /d) = ac/bd). 

            11-02: Multiplication as Scaling
            
               Develop the Concept: Visual
               
                  Multiplication as Scaling: Visual Learning
                    Curriculum Standards: Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n x a) /(n x b) to the effect of multiplying a/b by 1. Interpret multiplication as scaling (resizing), by: Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n x a) /(n x b) to the effect of multiplying a/b by 1. Interpret multiplication as scaling (resizing), by: Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n x a) /(n x b) to the effect of multiplying a/b by 1. Interpretar la multiplicación como poner a escala (cambiar el tamaño de) algo al: Explicar por qué al multiplicar un determinado número por una fracción mayor que 1 se obtiene un producto mayor que el número dado (reconocer la multiplicación de números enteros no negativos mayores que 1 como un caso común); explicar por qué la multiplicación de determinado número por una fracción menor que 1 resulta en un producto menor que el número dado; y relacionar el principio de las fracciones equivalentes a/b = (n × a)/(n × b) con el fin de multiplicar a/b por 1. Explican por qué al multiplicar un determinado número por una fracción mayor que 1 se obtiene un producto mayor que el número dado (reconocen la multiplicación de números enteros mayores que 1 como un caso común); explican por qué la multiplicación de determinado número por una fracción menor que 1 resulta en un producto menor que el número dado; y relacionan el principio de las fracciones equivalentes a/b = (n x a) / (n x b) con el fin de multiplicar a/ b por 1. 

               Assess & Differentiate
               
                  11-02: Digital Quick Check
                    Curriculum Standards: Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n x a) /(n x b) to the effect of multiplying a/b by 1. Interpret multiplication as scaling (resizing), by: Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n x a) /(n x b) to the effect of multiplying a/b by 1. Interpret multiplication as scaling (resizing), by: Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n x a) /(n x b) to the effect of multiplying a/b by 1. Interpretar la multiplicación como poner a escala (cambiar el tamaño de) algo al: Explicar por qué al multiplicar un determinado número por una fracción mayor que 1 se obtiene un producto mayor que el número dado (reconocer la multiplicación de números enteros no negativos mayores que 1 como un caso común); explicar por qué la multiplicación de determinado número por una fracción menor que 1 resulta en un producto menor que el número dado; y relacionar el principio de las fracciones equivalentes a/b = (n × a)/(n × b) con el fin de multiplicar a/b por 1. Explican por qué al multiplicar un determinado número por una fracción mayor que 1 se obtiene un producto mayor que el número dado (reconocen la multiplicación de números enteros mayores que 1 como un caso común); explican por qué la multiplicación de determinado número por una fracción menor que 1 resulta en un producto menor que el número dado; y relacionan el principio de las fracciones equivalentes a/b = (n x a) / (n x b) con el fin de multiplicar a/ b por 1. 

            11-03: Estimating Products
            
               Develop the Concept: Visual
               
                  Estimating Products: Visual Learning
                    Curriculum Standards: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Interpret multiplication as scaling (resizing), by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Interpret multiplication as scaling (resizing), by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Interpretar la multiplicación como poner a escala (cambiar el tamaño de) algo al: Comparar el tamaño de un producto al tamaño de un factor en base al tamaño del otro factor, sin efectuar la multiplicación indicada. Comparan el tamaño de un producto al tamaño de un factor en base al tamaño del otro factor, sin efectuar la multiplicación indicada. 

               Assess & Differentiate
               
                  11-03: Digital Quick Check
                    Curriculum Standards: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Interpret multiplication as scaling (resizing), by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Interpret multiplication as scaling (resizing), by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Interpretar la multiplicación como poner a escala (cambiar el tamaño de) algo al: Comparar el tamaño de un producto al tamaño de un factor en base al tamaño del otro factor, sin efectuar la multiplicación indicada. Comparan el tamaño de un producto al tamaño de un factor en base al tamaño del otro factor, sin efectuar la multiplicación indicada. 

            11-04: Multiplying Two Fractions
            
               Develop the Concept: Visual
               
                  Multiplying Two Fractions: Visual Learning
                    Curriculum Standards: Interpret the product (a/b) x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷ b. For example, use a visual fraction model to show (2/3) x 4 = 8/3 , and create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd.) Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷ b. For example, use a visual fraction model to show (2/3) x 4 = 8/3 , and create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd.) Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q … b. For example, use a visual fraction model to show (2/3) x 4 = 8/3 , and create a story context for this equation. Do the same with (2/3) x ( 4/5) = 8/15. (In general, (a/b) x (c/d ) = ac/bd.) Aplicar y ampliar los conocimientos previos sobre la multiplicación para multiplicar una fracción o un número entero por una fracción. Interpretar el producto (a/b) × q como a partes de la repartición de q en partes iguales de b; de manera equivalente, como el resultado de la secuencia de operaciones a × q ÷ b. Por ejemplo, emplear un modelo visual de fracciones para representar (2/3) × 4 = 8/3, e inventar un contexto para esta ecuación. Hacer lo mismo con (2/3) ×(4/5) = 8/15. (En general, (a/b) ×(c/d) = ac/bd). Interpretan el producto (a/b) × q como tantas partes a de la repartición de q en partes iguales de b; de manera equivalente, como el resultado de la secuencia de operaciones a × q ÷ b. Por ejemplo, al emplear un modelo visual de fracciones para representar (2/3) × 4 = 8/3, y crear un contexto para esta ecuación. Hacen lo mismo con (2/3) × (4/5) = 8/15. (En general, (a /b) × (c /d) = ac/bd). 

               Assess & Differentiate
               
                  11-04: Digital Quick Check
                    Curriculum Standards: Interpret the product (a/b) x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷ b. For example, use a visual fraction model to show (2/3) x 4 = 8/3 , and create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd.) Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷ b. For example, use a visual fraction model to show (2/3) x 4 = 8/3 , and create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd.) Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q … b. For example, use a visual fraction model to show (2/3) x 4 = 8/3 , and create a story context for this equation. Do the same with (2/3) x ( 4/5) = 8/15. (In general, (a/b) x (c/d ) = ac/bd.) Aplicar y ampliar los conocimientos previos sobre la multiplicación para multiplicar una fracción o un número entero por una fracción. Interpretar el producto (a/b) × q como a partes de la repartición de q en partes iguales de b; de manera equivalente, como el resultado de la secuencia de operaciones a × q ÷ b. Por ejemplo, emplear un modelo visual de fracciones para representar (2/3) × 4 = 8/3, e inventar un contexto para esta ecuación. Hacer lo mismo con (2/3) ×(4/5) = 8/15. (En general, (a/b) ×(c/d) = ac/bd). Interpretan el producto (a/b) × q como tantas partes a de la repartición de q en partes iguales de b; de manera equivalente, como el resultado de la secuencia de operaciones a × q ÷ b. Por ejemplo, al emplear un modelo visual de fracciones para representar (2/3) × 4 = 8/3, y crear un contexto para esta ecuación. Hacen lo mismo con (2/3) × (4/5) = 8/15. (En general, (a /b) × (c /d) = ac/bd). 

            11-05: Area Models
            
               Develop the Concept: Visual
               
                  Area Models: Visual Learning
                    Curriculum Standards: Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Aplicar y ampliar los conocimientos previos sobre la multiplicación para multiplicar una fracción o un número entero por una fracción. Hallar el área de un rectángulo cuyos lados se miden en unidades fraccionarias, cubriéndolo con unidades cuadradas de la unidad fraccionaria correspondiente a sus lados, y demostrar que el área sería la misma que se hallaría si se multiplicaran las longitudes de los lados. Multiplicar los números fraccionarios de las longitudes de los lados para hallar el área de rectángulos y representar los productos de las fracciones como áreas rectangulares. Hallan el área de un rectángulo cuyos lados se miden en unidades fraccionarias, cubriéndolo con unidades cuadradas de la unidad fraccionaria correspondiente a sus lados, y demuestran que el área sería la misma que se hallaría si se multiplicaran las longitudes de los lados. Multiplican los números fraccionarios de las longitudes de los lados para hallar el área de rectángulos, y representar los productos de las fracciones como áreas rectangulares. 

               Assess & Differentiate
               
                  11-05: Digital Quick Check
                    Curriculum Standards: Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Aplicar y ampliar los conocimientos previos sobre la multiplicación para multiplicar una fracción o un número entero por una fracción. Hallar el área de un rectángulo cuyos lados se miden en unidades fraccionarias, cubriéndolo con unidades cuadradas de la unidad fraccionaria correspondiente a sus lados, y demostrar que el área sería la misma que se hallaría si se multiplicaran las longitudes de los lados. Multiplicar los números fraccionarios de las longitudes de los lados para hallar el área de rectángulos y representar los productos de las fracciones como áreas rectangulares. Hallan el área de un rectángulo cuyos lados se miden en unidades fraccionarias, cubriéndolo con unidades cuadradas de la unidad fraccionaria correspondiente a sus lados, y demuestran que el área sería la misma que se hallaría si se multiplicaran las longitudes de los lados. Multiplican los números fraccionarios de las longitudes de los lados para hallar el área de rectángulos, y representar los productos de las fracciones como áreas rectangulares. 

            11-06: Multiplying Mixed Numbers
            
               Develop the Concept: Visual
               
                  Multiplying Mixed Numbers: Visual Learning
                    Curriculum Standards: Interpret the product (a/b) x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷ b. For example, use a visual fraction model to show (2/3) x 4 = 8/3 , and create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd.) Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷ b. For example, use a visual fraction model to show (2/3) x 4 = 8/3 , and create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd.) Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q … b. For example, use a visual fraction model to show (2/3) x 4 = 8/3 , and create a story context for this equation. Do the same with (2/3) x ( 4/5) = 8/15. (In general, (a/b) x (c/d ) = ac/bd.) Aplicar y ampliar los conocimientos previos sobre la multiplicación para multiplicar una fracción o un número entero por una fracción. Interpretar el producto (a/b) × q como a partes de la repartición de q en partes iguales de b; de manera equivalente, como el resultado de la secuencia de operaciones a × q ÷ b. Por ejemplo, emplear un modelo visual de fracciones para representar (2/3) × 4 = 8/3, e inventar un contexto para esta ecuación. Hacer lo mismo con (2/3) ×(4/5) = 8/15. (En general, (a/b) ×(c/d) = ac/bd). Interpretan el producto (a/b) × q como tantas partes a de la repartición de q en partes iguales de b; de manera equivalente, como el resultado de la secuencia de operaciones a × q ÷ b. Por ejemplo, al emplear un modelo visual de fracciones para representar (2/3) × 4 = 8/3, y crear un contexto para esta ecuación. Hacen lo mismo con (2/3) × (4/5) = 8/15. (En general, (a /b) × (c /d) = ac/bd). 

               Assess & Differentiate
               
                  11-06: Digital Quick Check
                    Curriculum Standards: Interpret the product (a/b) x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷ b. For example, use a visual fraction model to show (2/3) x 4 = 8/3 , and create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd.) Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷ b. For example, use a visual fraction model to show (2/3) x 4 = 8/3 , and create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd.) Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q … b. For example, use a visual fraction model to show (2/3) x 4 = 8/3 , and create a story context for this equation. Do the same with (2/3) x ( 4/5) = 8/15. (In general, (a/b) x (c/d ) = ac/bd.) Aplicar y ampliar los conocimientos previos sobre la multiplicación para multiplicar una fracción o un número entero por una fracción. Interpretar el producto (a/b) × q como a partes de la repartición de q en partes iguales de b; de manera equivalente, como el resultado de la secuencia de operaciones a × q ÷ b. Por ejemplo, emplear un modelo visual de fracciones para representar (2/3) × 4 = 8/3, e inventar un contexto para esta ecuación. Hacer lo mismo con (2/3) ×(4/5) = 8/15. (En general, (a/b) ×(c/d) = ac/bd). Interpretan el producto (a/b) × q como tantas partes a de la repartición de q en partes iguales de b; de manera equivalente, como el resultado de la secuencia de operaciones a × q ÷ b. Por ejemplo, al emplear un modelo visual de fracciones para representar (2/3) × 4 = 8/3, y crear un contexto para esta ecuación. Hacen lo mismo con (2/3) × (4/5) = 8/15. (En general, (a /b) × (c /d) = ac/bd). 

            11-07: Problem Solving: Multiple-Step Problems
            
               Develop the Concept: Visual
               
                  Problem Solving: Multiple-Step Problems: Visual Learning
                    Curriculum Standards: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Resolver problemas de la vida diaria relacionados a la multiplicación de fracciones y números mixtos, por ej., al usar modelos visuales de fracciones o ecuaciones para representar el problema. Resuelven problemas del mundo real relacionados a la multiplicación de fracciones y números mixtos, por ejemplo, al usar modelos visuales de fracciones o ecuaciones para representar el problema. 

               Assess & Differentiate
               
                  11-07: Digital Quick Check
                    Curriculum Standards: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Resolver problemas de la vida diaria relacionados a la multiplicación de fracciones y números mixtos, por ej., al usar modelos visuales de fracciones o ecuaciones para representar el problema. Resuelven problemas del mundo real relacionados a la multiplicación de fracciones y números mixtos, por ejemplo, al usar modelos visuales de fracciones o ecuaciones para representar el problema. 

            11-08: Fractions and Division
            
               Develop the Concept: Visual
               
                  Fractions and Division: Visual Learning
                    Curriculum Standards: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a…b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpretar una fracción como la división del numerador por el denominador (a/b = a ÷ b). Resolver problemas verbales relativos a la división de números enteros no negativos que resulten en fracciones, números mixtos por ej., empleando modelos visuales de fracciones o ecuaciones para representar el problema.  Por ejemplo, interpretar 3/4 como el resultado de la división de 3 por 4, notando que 3/4 multiplicado por 4 es igual a 3, y que cuando se comparten igualmente 3 enteros entre 4 personas, cada una termina con una parte de 3/4 de tamaño. Si 9 personas quieren compartir por igual y en base al peso un saco de arroz de 50 libras, ¿cuántas libras de arroz debe recibir cada persona? ¿Entre qué números enteros no negativos se encuentra la respuesta? Interpretan una fracción como la división del numerador por el denominador (a/b = a ÷ b). Resuelven problemas verbales relacionados a la división de números enteros que resulten en fracciones o números mixtos por ejemplo, emplean modelos visuales de fracciones o ecuaciones para representar el problema. 

               Assess & Differentiate
               
                  11-08: Digital Quick Check
                    Curriculum Standards: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a…b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpretar una fracción como la división del numerador por el denominador (a/b = a ÷ b). Resolver problemas verbales relativos a la división de números enteros no negativos que resulten en fracciones, números mixtos por ej., empleando modelos visuales de fracciones o ecuaciones para representar el problema.  Por ejemplo, interpretar 3/4 como el resultado de la división de 3 por 4, notando que 3/4 multiplicado por 4 es igual a 3, y que cuando se comparten igualmente 3 enteros entre 4 personas, cada una termina con una parte de 3/4 de tamaño. Si 9 personas quieren compartir por igual y en base al peso un saco de arroz de 50 libras, ¿cuántas libras de arroz debe recibir cada persona? ¿Entre qué números enteros no negativos se encuentra la respuesta? Interpretan una fracción como la división del numerador por el denominador (a/b = a ÷ b). Resuelven problemas verbales relacionados a la división de números enteros que resulten en fracciones o números mixtos por ejemplo, emplean modelos visuales de fracciones o ecuaciones para representar el problema. 

            11-09: Fractions, Mixed Numbers, and Decimals as Quotients
            
               Develop the Concept: Visual
               
                  Fractions, Mixed Numbers, and Decimals as Quotients
                    Curriculum Standards: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a…b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpretar una fracción como la división del numerador por el denominador (a/b = a ÷ b). Resolver problemas verbales relativos a la división de números enteros no negativos que resulten en fracciones, números mixtos por ej., empleando modelos visuales de fracciones o ecuaciones para representar el problema.  Por ejemplo, interpretar 3/4 como el resultado de la división de 3 por 4, notando que 3/4 multiplicado por 4 es igual a 3, y que cuando se comparten igualmente 3 enteros entre 4 personas, cada una termina con una parte de 3/4 de tamaño. Si 9 personas quieren compartir por igual y en base al peso un saco de arroz de 50 libras, ¿cuántas libras de arroz debe recibir cada persona? ¿Entre qué números enteros no negativos se encuentra la respuesta? Interpretan una fracción como la división del numerador por el denominador (a/b = a ÷ b). Resuelven problemas verbales relacionados a la división de números enteros que resulten en fracciones o números mixtos por ejemplo, emplean modelos visuales de fracciones o ecuaciones para representar el problema. 

               Assess & Differentiate
               
                  11-09: Digital Quick Check
                    Curriculum Standards: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a…b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpretar una fracción como la división del numerador por el denominador (a/b = a ÷ b). Resolver problemas verbales relativos a la división de números enteros no negativos que resulten en fracciones, números mixtos por ej., empleando modelos visuales de fracciones o ecuaciones para representar el problema.  Por ejemplo, interpretar 3/4 como el resultado de la división de 3 por 4, notando que 3/4 multiplicado por 4 es igual a 3, y que cuando se comparten igualmente 3 enteros entre 4 personas, cada una termina con una parte de 3/4 de tamaño. Si 9 personas quieren compartir por igual y en base al peso un saco de arroz de 50 libras, ¿cuántas libras de arroz debe recibir cada persona? ¿Entre qué números enteros no negativos se encuentra la respuesta? Interpretan una fracción como la división del numerador por el denominador (a/b = a ÷ b). Resuelven problemas verbales relacionados a la división de números enteros que resulten en fracciones o números mixtos por ejemplo, emplean modelos visuales de fracciones o ecuaciones para representar el problema. 

            11-10: Dividing Whole Numbers by Unit Fractions
            
               Develop the Concept: Visual
               
                  Dividing Whole Numbers by Unit Fractions: Visual Learning
                    Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ 1/5 , and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 x (1/5) = 4. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ 1/5 , and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 x (1/5) = 4. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 … 1/5 , and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 … (1/5 ) = 20 because 20 x (1/5 ) = 4. Aplicar y ampliar los conocimientos previos sobre la división para dividir fracciones unitarias por números enteros no negativos y números enteros no negativos por fracciones unitarias. Interpretar la división de un número entero no negativo por una fracción unitaria y calcular este tipo de cocientes. Por ejemplo, inventar un contexto para 4 ÷ (1/5), y utilizar un modelo visual de fracciones para expresar el cociente. Utilizar la relación entre la multiplicación y la división para explicar que 4 ÷ (1/5) =20 porque 20 ×(1/5)= 4. Interpretan la división de un número entero entre una fracción unitaria y calculan sus cocientes. Por ejemplo, crean en el contexto de un cuento 4 ÷ (1/5), y utilizan un modelo visual de fracciones para expresar el cociente. Utilizan la relación entre la multiplicación y la división para explicar que 4 ÷ (1/5) =20 porque 20 ×(1/5)= 4. 

               Assess & Differentiate
               
                  11-10: Digital Quick Check
                    Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ 1/5 , and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 x (1/5) = 4. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ 1/5 , and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 x (1/5) = 4. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 … 1/5 , and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 … (1/5 ) = 20 because 20 x (1/5 ) = 4. Aplicar y ampliar los conocimientos previos sobre la división para dividir fracciones unitarias por números enteros no negativos y números enteros no negativos por fracciones unitarias. Interpretar la división de un número entero no negativo por una fracción unitaria y calcular este tipo de cocientes. Por ejemplo, inventar un contexto para 4 ÷ (1/5), y utilizar un modelo visual de fracciones para expresar el cociente. Utilizar la relación entre la multiplicación y la división para explicar que 4 ÷ (1/5) =20 porque 20 ×(1/5)= 4. Interpretan la división de un número entero entre una fracción unitaria y calculan sus cocientes. Por ejemplo, crean en el contexto de un cuento 4 ÷ (1/5), y utilizan un modelo visual de fracciones para expresar el cociente. Utilizan la relación entre la multiplicación y la división para explicar que 4 ÷ (1/5) =20 porque 20 ×(1/5)= 4. 

            11-11: Dividing Unit Fractions by Non-Zero Whole Numbers
            
               Develop the Concept: Visual
               
                  Dividing Unit Fractions by Non-Zero Whole Numbers: Visual Learning
                    Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) x 4 = 1/3. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) x 4 = 1/3 . Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) … 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) … 4 = 1/12 because (1/12 ) x 4 = 1/3 . Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb. of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Aplicar y ampliar los conocimientos previos sobre la división para dividir fracciones unitarias por números enteros no negativos y números enteros no negativos por fracciones unitarias. Interpretar la división de una fracción unitaria por un número entero no negativo distinto a cero y calcular este tipo de cocientes. Por ejemplo, inventar un contexto para (1/3) ÷ 4, y utilizar un modelo visual de fracciones para expresar el cociente. Utilizar la relación entre la multiplicación y la división para explicar que (1/3) ÷ 4 = 1/12 porque (1/12) × 4 = 1/3. Aplicar y ampliar los conocimientos previos sobre la división para dividir fracciones unitarias por números enteros no negativos y números enteros no negativos por fracciones unitarias. Resolver problemas de la vida diaria relacionados a la división de fracciones unitarias por números enteros no negativos distintos de cero y a la división de números enteros no negativos por fracciones unitarias, por ej., utilizando modelos visuales de fracciones y ecuaciones para representar el problema. Por ejemplo, ¿cuánto chocolate tendrá cada persona si 3 personas comparten ½ libra de chocolate en partes iguales?¿Cuántas porciones de 1/3 de taza hay en 2 tazas de pasas? Interpretan la división de una fracción unitaria entre un número entero distinto al cero, y calculan sus cocientes. Por ejemplo, crean el contexto de un cuento para (1/3) ÷ 4, y utilizan un modelo visual de fracciones para expresar el cociente. Utilizan la relación entre la multiplicación y la división para explicar que (1/3) ÷ 4 = 1/12 porque (1/12) × 4 = 1/3. Resuelven problemas del mundo real relacionados a la división de fracciones unitarias entre números enteros distintos al cero y la división de números enteros entre fracciones unitarias, por ejemplo, utilizan modelos visuales de fracciones y ecuaciones para representar el problema. Por ejemplo, ¿cuánto chocolate tendrá cada persona si 3 personas comparten ½ libra de chocolate en partes iguales?¿Cuántas porciones de 1/3 de taza hay en 2 tazas de pasas? Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb. of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? 

               Assess & Differentiate
               
                  11-11: Digital Quick Check
                    Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) x 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb. of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) x 4 = 1/3 . Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) … 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) … 4 = 1/12 because (1/12 ) x 4 = 1/3 . Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb. of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Aplicar y ampliar los conocimientos previos sobre la división para dividir fracciones unitarias por números enteros no negativos y números enteros no negativos por fracciones unitarias. Interpretar la división de una fracción unitaria por un número entero no negativo distinto a cero y calcular este tipo de cocientes. Por ejemplo, inventar un contexto para (1/3) ÷ 4, y utilizar un modelo visual de fracciones para expresar el cociente. Utilizar la relación entre la multiplicación y la división para explicar que (1/3) ÷ 4 = 1/12 porque (1/12) × 4 = 1/3. Aplicar y ampliar los conocimientos previos sobre la división para dividir fracciones unitarias por números enteros no negativos y números enteros no negativos por fracciones unitarias. Resolver problemas de la vida diaria relacionados a la división de fracciones unitarias por números enteros no negativos distintos de cero y a la división de números enteros no negativos por fracciones unitarias, por ej., utilizando modelos visuales de fracciones y ecuaciones para representar el problema. Por ejemplo, ¿cuánto chocolate tendrá cada persona si 3 personas comparten ½ libra de chocolate en partes iguales?¿Cuántas porciones de 1/3 de taza hay en 2 tazas de pasas? Interpretan la división de una fracción unitaria entre un número entero distinto al cero, y calculan sus cocientes. Por ejemplo, crean el contexto de un cuento para (1/3) ÷ 4, y utilizan un modelo visual de fracciones para expresar el cociente. Utilizan la relación entre la multiplicación y la división para explicar que (1/3) ÷ 4 = 1/12 porque (1/12) × 4 = 1/3. Resuelven problemas del mundo real relacionados a la división de fracciones unitarias entre números enteros distintos al cero y la división de números enteros entre fracciones unitarias, por ejemplo, utilizan modelos visuales de fracciones y ecuaciones para representar el problema. Por ejemplo, ¿cuánto chocolate tendrá cada persona si 3 personas comparten ½ libra de chocolate en partes iguales?¿Cuántas porciones de 1/3 de taza hay en 2 tazas de pasas? 

            11-12: Problem Solving: Draw a Picture and Write an Equation
            
               Develop the Concept: Visual
               
                  Problem Solving: Draw a Picture and Write an Equation: Visual Learning
                    Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) x 4 = 1/3. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) x 4 = 1/3 . Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) … 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) … 4 = 1/12 because (1/12 ) x 4 = 1/3 . Aplicar y ampliar los conocimientos previos sobre la división para dividir fracciones unitarias por números enteros no negativos y números enteros no negativos por fracciones unitarias. Interpretar la división de una fracción unitaria por un número entero no negativo distinto a cero y calcular este tipo de cocientes. Por ejemplo, inventar un contexto para (1/3) ÷ 4, y utilizar un modelo visual de fracciones para expresar el cociente. Utilizar la relación entre la multiplicación y la división para explicar que (1/3) ÷ 4 = 1/12 porque (1/12) × 4 = 1/3. Interpretan la división de una fracción unitaria entre un número entero distinto al cero, y calculan sus cocientes. Por ejemplo, crean el contexto de un cuento para (1/3) ÷ 4, y utilizan un modelo visual de fracciones para expresar el cociente. Utilizan la relación entre la multiplicación y la división para explicar que (1/3) ÷ 4 = 1/12 porque (1/12) × 4 = 1/3. 

               Assess & Differentiate
               
                  11-12: Digital Quick Check
                    Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) x 4 = 1/3. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) x 4 = 1/3 . Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) … 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) … 4 = 1/12 because (1/12 ) x 4 = 1/3 . Aplicar y ampliar los conocimientos previos sobre la división para dividir fracciones unitarias por números enteros no negativos y números enteros no negativos por fracciones unitarias. Interpretar la división de una fracción unitaria por un número entero no negativo distinto a cero y calcular este tipo de cocientes. Por ejemplo, inventar un contexto para (1/3) ÷ 4, y utilizar un modelo visual de fracciones para expresar el cociente. Utilizar la relación entre la multiplicación y la división para explicar que (1/3) ÷ 4 = 1/12 porque (1/12) × 4 = 1/3. Interpretan la división de una fracción unitaria entre un número entero distinto al cero, y calculan sus cocientes. Por ejemplo, crean el contexto de un cuento para (1/3) ÷ 4, y utilizan un modelo visual de fracciones para expresar el cociente. Utilizan la relación entre la multiplicación y la división para explicar que (1/3) ÷ 4 = 1/12 porque (1/12) × 4 = 1/3. 

            Topic 11: Online Topic Test
              Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ 1/5 , and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 x (1/5) = 4. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ 1/5 , and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 x (1/5) = 4. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 … 1/5 , and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 … (1/5 ) = 20 because 20 x (1/5 ) = 4. Aplicar y ampliar los conocimientos previos sobre la división para dividir fracciones unitarias por números enteros no negativos y números enteros no negativos por fracciones unitarias. Interpretar la división de un número entero no negativo por una fracción unitaria y calcular este tipo de cocientes. Por ejemplo, inventar un contexto para 4 ÷ (1/5), y utilizar un modelo visual de fracciones para expresar el cociente. Utilizar la relación entre la multiplicación y la división para explicar que 4 ÷ (1/5) =20 porque 20 ×(1/5)= 4. Interpretan la división de un número entero entre una fracción unitaria y calculan sus cocientes. Por ejemplo, crean en el contexto de un cuento 4 ÷ (1/5), y utilizan un modelo visual de fracciones para expresar el cociente. Utilizan la relación entre la multiplicación y la división para explicar que 4 ÷ (1/5) =20 porque 20 ×(1/5)= 4. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n x a) /(n x b) to the effect of multiplying a/b by 1. Interpret multiplication as scaling (resizing), by: Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n x a) /(n x b) to the effect of multiplying a/b by 1. Interpret multiplication as scaling (resizing), by: Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n x a) /(n x b) to the effect of multiplying a/b by 1. Interpretar la multiplicación como poner a escala (cambiar el tamaño de) algo al: Explicar por qué al multiplicar un determinado número por una fracción mayor que 1 se obtiene un producto mayor que el número dado (reconocer la multiplicación de números enteros no negativos mayores que 1 como un caso común); explicar por qué la multiplicación de determinado número por una fracción menor que 1 resulta en un producto menor que el número dado; y relacionar el principio de las fracciones equivalentes a/b = (n × a)/(n × b) con el fin de multiplicar a/b por 1. Explican por qué al multiplicar un determinado número por una fracción mayor que 1 se obtiene un producto mayor que el número dado (reconocen la multiplicación de números enteros mayores que 1 como un caso común); explican por qué la multiplicación de determinado número por una fracción menor que 1 resulta en un producto menor que el número dado; y relacionan el principio de las fracciones equivalentes a/b = (n x a) / (n x b) con el fin de multiplicar a/ b por 1. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Interpret multiplication as scaling (resizing), by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Interpret multiplication as scaling (resizing), by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Interpretar la multiplicación como poner a escala (cambiar el tamaño de) algo al: Comparar el tamaño de un producto al tamaño de un factor en base al tamaño del otro factor, sin efectuar la multiplicación indicada. Comparan el tamaño de un producto al tamaño de un factor en base al tamaño del otro factor, sin efectuar la multiplicación indicada. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) x 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb. of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) x 4 = 1/3 . Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) … 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) … 4 = 1/12 because (1/12 ) x 4 = 1/3 . Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb. of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Aplicar y ampliar los conocimientos previos sobre la división para dividir fracciones unitarias por números enteros no negativos y números enteros no negativos por fracciones unitarias. Interpretar la división de una fracción unitaria por un número entero no negativo distinto a cero y calcular este tipo de cocientes. Por ejemplo, inventar un contexto para (1/3) ÷ 4, y utilizar un modelo visual de fracciones para expresar el cociente. Utilizar la relación entre la multiplicación y la división para explicar que (1/3) ÷ 4 = 1/12 porque (1/12) × 4 = 1/3. Aplicar y ampliar los conocimientos previos sobre la división para dividir fracciones unitarias por números enteros no negativos y números enteros no negativos por fracciones unitarias. Resolver problemas de la vida diaria relacionados a la división de fracciones unitarias por números enteros no negativos distintos de cero y a la división de números enteros no negativos por fracciones unitarias, por ej., utilizando modelos visuales de fracciones y ecuaciones para representar el problema. Por ejemplo, ¿cuánto chocolate tendrá cada persona si 3 personas comparten ½ libra de chocolate en partes iguales?¿Cuántas porciones de 1/3 de taza hay en 2 tazas de pasas? Interpretan la división de una fracción unitaria entre un número entero distinto al cero, y calculan sus cocientes. Por ejemplo, crean el contexto de un cuento para (1/3) ÷ 4, y utilizan un modelo visual de fracciones para expresar el cociente. Utilizan la relación entre la multiplicación y la división para explicar que (1/3) ÷ 4 = 1/12 porque (1/12) × 4 = 1/3. Resuelven problemas del mundo real relacionados a la división de fracciones unitarias entre números enteros distintos al cero y la división de números enteros entre fracciones unitarias, por ejemplo, utilizan modelos visuales de fracciones y ecuaciones para representar el problema. Por ejemplo, ¿cuánto chocolate tendrá cada persona si 3 personas comparten ½ libra de chocolate en partes iguales?¿Cuántas porciones de 1/3 de taza hay en 2 tazas de pasas? Interpret the product (a/b) x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷ b. For example, use a visual fraction model to show (2/3) x 4 = 8/3 , and create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd.) Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷ b. For example, use a visual fraction model to show (2/3) x 4 = 8/3 , and create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd.) Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q … b. For example, use a visual fraction model to show (2/3) x 4 = 8/3 , and create a story context for this equation. Do the same with (2/3) x ( 4/5) = 8/15. (In general, (a/b) x (c/d ) = ac/bd.) Aplicar y ampliar los conocimientos previos sobre la multiplicación para multiplicar una fracción o un número entero por una fracción. Interpretar el producto (a/b) × q como a partes de la repartición de q en partes iguales de b; de manera equivalente, como el resultado de la secuencia de operaciones a × q ÷ b. Por ejemplo, emplear un modelo visual de fracciones para representar (2/3) × 4 = 8/3, e inventar un contexto para esta ecuación. Hacer lo mismo con (2/3) ×(4/5) = 8/15. (En general, (a/b) ×(c/d) = ac/bd). Interpretan el producto (a/b) × q como tantas partes a de la repartición de q en partes iguales de b; de manera equivalente, como el resultado de la secuencia de operaciones a × q ÷ b. Por ejemplo, al emplear un modelo visual de fracciones para representar (2/3) × 4 = 8/3, y crear un contexto para esta ecuación. Hacen lo mismo con (2/3) × (4/5) = 8/15. (En general, (a /b) × (c /d) = ac/bd). Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Aplicar y ampliar los conocimientos previos sobre la multiplicación para multiplicar una fracción o un número entero por una fracción. Hallar el área de un rectángulo cuyos lados se miden en unidades fraccionarias, cubriéndolo con unidades cuadradas de la unidad fraccionaria correspondiente a sus lados, y demostrar que el área sería la misma que se hallaría si se multiplicaran las longitudes de los lados. Multiplicar los números fraccionarios de las longitudes de los lados para hallar el área de rectángulos y representar los productos de las fracciones como áreas rectangulares. Hallan el área de un rectángulo cuyos lados se miden en unidades fraccionarias, cubriéndolo con unidades cuadradas de la unidad fraccionaria correspondiente a sus lados, y demuestran que el área sería la misma que se hallaría si se multiplicaran las longitudes de los lados. Multiplican los números fraccionarios de las longitudes de los lados para hallar el área de rectángulos, y representar los productos de las fracciones como áreas rectangulares. Represent division of a unit fraction by a whole number and the division of a whole number by a unit fraction such as 1/3 ? 7 and 7 ? 1/3 using objects and pictorial models, including area models. Represent division of a unit fraction by a whole number and the division of a whole number by a unit fraction such as 1/3 ÷ 7 and 7 ÷ 1/3 using objects and pictorial models, including area models. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a…b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpretar una fracción como la división del numerador por el denominador (a/b = a ÷ b). Resolver problemas verbales relativos a la división de números enteros no negativos que resulten en fracciones, números mixtos por ej., empleando modelos visuales de fracciones o ecuaciones para representar el problema.  Por ejemplo, interpretar 3/4 como el resultado de la división de 3 por 4, notando que 3/4 multiplicado por 4 es igual a 3, y que cuando se comparten igualmente 3 enteros entre 4 personas, cada una termina con una parte de 3/4 de tamaño. Si 9 personas quieren compartir por igual y en base al peso un saco de arroz de 50 libras, ¿cuántas libras de arroz debe recibir cada persona? ¿Entre qué números enteros no negativos se encuentra la respuesta? Interpretan una fracción como la división del numerador por el denominador (a/b = a ÷ b). Resuelven problemas verbales relacionados a la división de números enteros que resulten en fracciones o números mixtos por ejemplo, emplean modelos visuales de fracciones o ecuaciones para representar el problema. 

            Alternate Test

            Digital Enhanced Topic Test

            Enhanced Topic Test

         Topic 12: Volume of Solids
         
            Volume Equations

            Topic 12: Online Topic Readiness
              Curriculum Standards: Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.1 Multiplicar o dividir para resolver problemas verbales con comparaciones multiplicativas, por ej., representar el problema utilizando dibujos y ecuaciones con un símbolo para el número desconocido; distinguir la comparación multiplicativa de la comparación de suma. Multiplican o dividen para resolver problemas verbales que incluyen comparaciones multiplicativas, por ejemplo, para representar el problema usando dibujos y ecuaciones con un símbolo para el número desconocido, distinguen una comparación multiplicativa de una comparación de suma. Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ... Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ... Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), Saber los tamaños relativos de las unidades de medición dentro de un sistema de unidades, incluyendo km, m, cm; kg, g; lb, oz.; L, mL; h, min, s. Dentro de un mismo sistema de medición, expresar las medidas en una unidad más grande en términos de una unidad más pequeña. Anotar las medidas equivalentes en una tabla de dos columnas. Por ejemplo, saber que 1 pie es 12 veces más largo que 1 pulg. Expresar la longitud de una culebra de 4 pies como 48 pulgs. Generar una tabla de conversión para pies y pulgadas con una lista de pares de números (1, 12), (2, 24), (3, 36), ... Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), Reconocen los tamaños relativos de las unidades de medición dentro de un sistema de unidades, incluyendo km, m, cm; kg, g; lb, oz.; L, mL; h, min, s. Dentro de un mismo sistema de medición, expresan las medidas en una unidad más grande en términos de una unidad más pequeña. Anotan las medidas equivalentes en una tabla de dos columnas. Por ejemplo, saben que 1 pie es 12 veces más largo que 1 pulgada. Expresan la longitud de una culebra de 4 pies como 48 pulgadas. Generan una tabla de conversión para pies y pulgadas con una lista de pares de números (1, 12), (2, 24), (3, 36), … Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Utilizan las cuatro operaciones para resolver problemas verbales sobre distancias, intervalos de tiempo, volúmenes líquidos, masas de objetos y dinero, incluyendo problemas con fracciones simples o decimales, y problemas que requieren expresar las medidas dadas en una unidad más grande en términos de una unidad más pequeña. Representan cantidades medidas utilizando diagramas tales como rectas numéricas con escalas de medición. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding  and explain why a rounded solution is appropriate. Resolver problemas verbales de varios pasos con números enteros no negativos y cuyas respuestas son números enteros no negativos utilizando las cuatro operaciones, incluyendo aquellos problemas en los que los residuos deben ser interpretados. Representar estos problemas utilizando ecuaciones con una letra para representar la cantidad desconocida. Evaluar lo razonable de las respuestas utilizando el cálculo mental y las estrategias de estimación, incluyendo el redondeo. Resuelven problemas verbales de pasos múltiples con números enteros, cuya respuestas son números enteros, usando las cuatro operaciones, incluyendo problemas en los que los residuos deben ser interpretados. Representan estos problemas usando ecuaciones con una letra que representa la cantidad desconocida. Evalúan si las respuestas son razonables usando cálculos mentales y estrategias de estimación incluyendo el redondeo. Use strategies and algorithms, including the standard algorithm, to divide up to a four-digit dividend by a one-digit divisor. Use strategies and algorithms, including the standard algorithm, to divide up to a four-digit dividend by a one-digit divisor. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. Interpretar una ecuación de multiplicación como una comparación, por ej., interpretar 35 = 5 × 7 como un enunciado de que 35 es 5 veces 7 y 7 veces 5. Representar enunciados verbales de comparaciones multiplicativas como ecuaciones de multiplicación. Interpretan una ecuación de multiplicación como una comparación, por ejemplo, 35 = 5x7 como un enunciados de que 35 es 5 veces 7, y 7 veces 5. Representan enunciados verbales de comparaciones multiplicativas como ecuaciones de multiplicación. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. (Two dimensional shapes should include special triangles, e.g., equilateral, isosceles, scalene, and special quadrilaterals, e.g., rhombus, square, rectangle, parallelogram, trapezoid.) Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. Clasificar las figuras bidimensionales en base a la presencia o ausencia de rectas paralelas o perpendiculares, o en la presencia o ausencia de ángulos de un tamaño especificado. Reconocer que los triángulos rectos forman una categoría en sí e identificar triángulos rectos. Clasifican las figuras bidimensionales basándose en la presencia o ausencia de rectas paralelas o perpendiculares, o en la presencia o ausencia de ángulos de un tamaño especificado. Reconocen que los triángulos rectos forman una categoría en sí, e identifican triángulos rectos. (Las figuras bidimensionales deben incluir los triángulos especiales, por ejemplo, los triángulos equiláteros, isósceles y escalenos, y los cuadriláteros especiales, por ejemplo, los rombos, cuadrados, rectángulos, paralelogramos y trapecios.) Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar cocientes y residuos de números enteros no negativos a partir de divisiones con dividendos de hasta cuatro dígitos y divisores de un dígito, utilizando las estrategias basadas en el valor de posición y/o la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y/o modelos de área. Hallan cocientes y residuos de números enteros, a partir de divisiones con dividendos de hasta cuatro dígitos y divisores de un dígito, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares, y/o modelos de área. 

            12-01: Models and Volume
            
               Develop the Concept: Visual
               
                  Models and Volume: Visual Learning
                    Curriculum Standards: A cube with side length 1 unit, called a U1unit cube,Ue is said to have U1one cubic unitUe of volume, and can be used to measure volume. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A cube with side length 1 unit, called a _unit cube,? is said to have _one cubic unit? of volume, and can be used to measure volume. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A cube with side length 1 unit, called a ñunit cube,î is said to have ñone cubic unitî of volume, and can be used to measure volume. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Reconocer el volumen como un atributo de las figuras sólidas y entender los conceptos de la medición del volumen. Se dice que un cubo con lados de 1 unidad, llamado “bloque de unidad”, tiene “una unidad cúbica” de volumen, y ésta se puede utilizar para medir el volumen. Reconocer el volumen como un atributo de las figuras sólidas y entender los conceptos de la medición del volumen. Se dice que una figura sólida que se puede rellenar con n bloques de unidad sin dejar espacios o superposiciones tiene un volumen de n unidades cúbicas. Se dice que un cubo con lados de 1 unidad, llamado “unidad cúbica”, tiene “una unidad cúbica” de volumen, y ésta se puede utilizar para medir el volumen. Se dice que una figura sólida que se puede rellenar con la unidad cúbica n sin dejar espacios o superposiciones tiene un volumen de n unidades cúbicas. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. 

               Assess & Differentiate
               
                  12-01: Digital Quick Check
                    Curriculum Standards: A cube with side length 1 unit, called a U1unit cube,Ue is said to have U1one cubic unitUe of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A cube with side length 1 unit, called a _unit cube,? is said to have _one cubic unit? of volume, and can be used to measure volume. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A cube with side length 1 unit, called a ñunit cube,î is said to have ñone cubic unitî of volume, and can be used to measure volume. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Reconocer el volumen como un atributo de las figuras sólidas y entender los conceptos de la medición del volumen. Se dice que un cubo con lados de 1 unidad, llamado “bloque de unidad”, tiene “una unidad cúbica” de volumen, y ésta se puede utilizar para medir el volumen. Reconocer el volumen como un atributo de las figuras sólidas y entender los conceptos de la medición del volumen. Se dice que una figura sólida que se puede rellenar con n bloques de unidad sin dejar espacios o superposiciones tiene un volumen de n unidades cúbicas. Se dice que un cubo con lados de 1 unidad, llamado “unidad cúbica”, tiene “una unidad cúbica” de volumen, y ésta se puede utilizar para medir el volumen. Se dice que una figura sólida que se puede rellenar con la unidad cúbica n sin dejar espacios o superposiciones tiene un volumen de n unidades cúbicas. 

            12-02: Volume
            
               Develop the Concept: Visual
               
                  Volume: Visual Learning
                    Curriculum Standards: Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold wholenumber products as volumes, e.g., to represent the associative property of multiplication. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold wholenumber products as volumes, e.g., to represent the associative property of multiplication. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold wholenumber products as volumes, e.g., to represent the associative property of multiplication. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Apply the formulas V = l x w x h and V = b x h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. Relacionar el volumen con las operaciones de multiplicación y suma para resolver problemas matemáticos y de la vida diaria relativos al volumen. Hallar el volumen de un prisma rectangular recto con lados que se miden en números enteros no negativos, llenando el prisma con unidades cúbicas, y demostrar que el volumen es el mismo que se hallaría multiplicando la altura por el área de la base. Representar tres veces el producto de un número entero no negativo como un volumen, por ej., para representar la propiedad asociativa de la multiplicación. Relacionar el volumen con las operaciones de multiplicación y suma para resolver problemas matemáticos y de la vida diaria relativos al volumen. Aplicar las fórmulas V = l × a × h   y   V = b × h de los prismas rectangulares para hallar los volúmenes de prismas rectangulares rectos cuyos lados se miden en números enteros no negativos, en el contexto de resolver problemas matemáticos y de la vida diaria. Hallan el volumen de un prisma rectangular recto con lados que se miden en números enteros, llenando el prisma con unidades cúbicas, y demostrando que el volumen es el mismo que se hallaría multiplicando la altura por el área de la base. Representan tres veces el producto de un número entero como un volumen, por ejemplo, para representar la propiedad asociativa de la multiplicación. Aplican las fórmulas V = l × a × h y V = b × h de los prismas rectangulares para hallar los volúmenes de prismas rectangulares rectos cuyos lados se miden en números enteros, en el contexto de resolver problemas matemáticos y del mundo real. Apply the formulas V = l x w x h and V = b x h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. 

               Assess & Differentiate
               
                  12-02: Digital Quick Check
                    Curriculum Standards: Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold wholenumber products as volumes, e.g., to represent the associative property of multiplication. Apply the formulas V = l x w x h and V = b x h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold wholenumber products as volumes, e.g., to represent the associative property of multiplication. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold wholenumber products as volumes, e.g., to represent the associative property of multiplication. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Apply the formulas V = l x w x h and V = b x h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. Relacionar el volumen con las operaciones de multiplicación y suma para resolver problemas matemáticos y de la vida diaria relativos al volumen. Hallar el volumen de un prisma rectangular recto con lados que se miden en números enteros no negativos, llenando el prisma con unidades cúbicas, y demostrar que el volumen es el mismo que se hallaría multiplicando la altura por el área de la base. Representar tres veces el producto de un número entero no negativo como un volumen, por ej., para representar la propiedad asociativa de la multiplicación. Relacionar el volumen con las operaciones de multiplicación y suma para resolver problemas matemáticos y de la vida diaria relativos al volumen. Aplicar las fórmulas V = l × a × h   y   V = b × h de los prismas rectangulares para hallar los volúmenes de prismas rectangulares rectos cuyos lados se miden en números enteros no negativos, en el contexto de resolver problemas matemáticos y de la vida diaria. Hallan el volumen de un prisma rectangular recto con lados que se miden en números enteros, llenando el prisma con unidades cúbicas, y demostrando que el volumen es el mismo que se hallaría multiplicando la altura por el área de la base. Representan tres veces el producto de un número entero como un volumen, por ejemplo, para representar la propiedad asociativa de la multiplicación. Aplican las fórmulas V = l × a × h y V = b × h de los prismas rectangulares para hallar los volúmenes de prismas rectangulares rectos cuyos lados se miden en números enteros, en el contexto de resolver problemas matemáticos y del mundo real. 

            12-03: Combining Volumes
            
               Develop the Concept: Visual
               
                  Combining Volumes: Visual Learning
                    Curriculum Standards: Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. Relacionar el volumen con las operaciones de multiplicación y suma para resolver problemas matemáticos y de la vida diaria relativos al volumen. Reconocer que el volumen se puede sumar. Hallar el volumen de figuras sólidas compuestas de dos prismas rectangulares rectos no superpuestos, sumando los volúmenes de las partes que no se sobreponen, y aplicar esta técnica para resolver problemas de la vida diaria. Reconocen el volumen como una suma. Hallan el volumen de figuras sólidas compuestas de dos prismas rectangulares rectos que no se sobrepongan, sumando los volúmenes de las partes que no se sobreponen, y aplican esta técnica para resolver problemas del mundo real. 

               Assess & Differentiate
               
                  12-03: Digital Quick Check
                    Curriculum Standards: Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. Relacionar el volumen con las operaciones de multiplicación y suma para resolver problemas matemáticos y de la vida diaria relativos al volumen. Reconocer que el volumen se puede sumar. Hallar el volumen de figuras sólidas compuestas de dos prismas rectangulares rectos no superpuestos, sumando los volúmenes de las partes que no se sobreponen, y aplicar esta técnica para resolver problemas de la vida diaria. Reconocen el volumen como una suma. Hallan el volumen de figuras sólidas compuestas de dos prismas rectangulares rectos que no se sobrepongan, sumando los volúmenes de las partes que no se sobreponen, y aplican esta técnica para resolver problemas del mundo real. 

            12-04: Problem Solving: Use Objects and Reasoning
            
               Develop the Concept: Visual
               
                  Problem Solving: Use Objects and Reasoning: Visual Learning
                    Curriculum Standards: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Medir volúmenes contando unidades cúbicas, utilizando centímetros cúbicos, pulgadas cúbicas, pies cúbicos y otras unidades improvisadas. Miden volúmenes contando unidades cúbicas, utilizando centímetros cúbicos, pulgadas cúbicas, pies cúbicos, y otras unidades improvisadas. 

               Assess & Differentiate
               
                  12-04: Digital Quick Check
                    Curriculum Standards: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Medir volúmenes contando unidades cúbicas, utilizando centímetros cúbicos, pulgadas cúbicas, pies cúbicos y otras unidades improvisadas. Miden volúmenes contando unidades cúbicas, utilizando centímetros cúbicos, pulgadas cúbicas, pies cúbicos, y otras unidades improvisadas. 

            Topic 12: Online Topic Test
              Curriculum Standards: Use concrete objects and pictorial models to develop the formulas for the volume of a rectangular prism, including the special form for a cube (V = l x w x h, V = s x s x s, and V = Bh). Use concrete objects and pictorial models to develop the formulas for the volume of a rectangular prism, including the special form for a cube (V = l × w × h, V = s × s × s, and V = Bh). Represent and solve problems related to perimeter and/or area and related to volume. Represent and solve problems related to perimeter and/or area and related to volume. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. Relacionar el volumen con las operaciones de multiplicación y suma para resolver problemas matemáticos y de la vida diaria relativos al volumen. Reconocer que el volumen se puede sumar. Hallar el volumen de figuras sólidas compuestas de dos prismas rectangulares rectos no superpuestos, sumando los volúmenes de las partes que no se sobreponen, y aplicar esta técnica para resolver problemas de la vida diaria. Reconocen el volumen como una suma. Hallan el volumen de figuras sólidas compuestas de dos prismas rectangulares rectos que no se sobrepongan, sumando los volúmenes de las partes que no se sobreponen, y aplican esta técnica para resolver problemas del mundo real. Recognize a cube with side length of one unit as a unit cube having one cubic unit of volume and the volume of a three-dimensional figure as the number of unit cubes (n cubic units) needed to fill it with no gaps or overlaps if possible. Determine the volume of a rectangular prism with whole number side lengths in problems related to the number of layers times the number of unit cubes in the area of the base. Recognize a cube with side length of one unit as a unit cube having one cubic unit of volume and the volume of a three-dimensional figure as the number of unit cubes (n cubic units) needed to fill it with no gaps or overlaps if possible. Determine the volume of a rectangular prism with whole number side lengths in problems related to the number of layers times the number of unit cubes in the area of the base. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold wholenumber products as volumes, e.g., to represent the associative property of multiplication. Apply the formulas V = l x w x h and V = b x h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold wholenumber products as volumes, e.g., to represent the associative property of multiplication. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold wholenumber products as volumes, e.g., to represent the associative property of multiplication. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Apply the formulas V = l x w x h and V = b x h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. Relacionar el volumen con las operaciones de multiplicación y suma para resolver problemas matemáticos y de la vida diaria relativos al volumen. Hallar el volumen de un prisma rectangular recto con lados que se miden en números enteros no negativos, llenando el prisma con unidades cúbicas, y demostrar que el volumen es el mismo que se hallaría multiplicando la altura por el área de la base. Representar tres veces el producto de un número entero no negativo como un volumen, por ej., para representar la propiedad asociativa de la multiplicación. Relacionar el volumen con las operaciones de multiplicación y suma para resolver problemas matemáticos y de la vida diaria relativos al volumen. Aplicar las fórmulas V = l × a × h   y   V = b × h de los prismas rectangulares para hallar los volúmenes de prismas rectangulares rectos cuyos lados se miden en números enteros no negativos, en el contexto de resolver problemas matemáticos y de la vida diaria. Hallan el volumen de un prisma rectangular recto con lados que se miden en números enteros, llenando el prisma con unidades cúbicas, y demostrando que el volumen es el mismo que se hallaría multiplicando la altura por el área de la base. Representan tres veces el producto de un número entero como un volumen, por ejemplo, para representar la propiedad asociativa de la multiplicación. Aplican las fórmulas V = l × a × h y V = b × h de los prismas rectangulares para hallar los volúmenes de prismas rectangulares rectos cuyos lados se miden en números enteros, en el contexto de resolver problemas matemáticos y del mundo real. A cube with side length 1 unit, called a U1unit cube,Ue is said to have U1one cubic unitUe of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A cube with side length 1 unit, called a _unit cube,? is said to have _one cubic unit? of volume, and can be used to measure volume. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A cube with side length 1 unit, called a ñunit cube,î is said to have ñone cubic unitî of volume, and can be used to measure volume. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Reconocer el volumen como un atributo de las figuras sólidas y entender los conceptos de la medición del volumen. Se dice que un cubo con lados de 1 unidad, llamado “bloque de unidad”, tiene “una unidad cúbica” de volumen, y ésta se puede utilizar para medir el volumen. Reconocer el volumen como un atributo de las figuras sólidas y entender los conceptos de la medición del volumen. Se dice que una figura sólida que se puede rellenar con n bloques de unidad sin dejar espacios o superposiciones tiene un volumen de n unidades cúbicas. Se dice que un cubo con lados de 1 unidad, llamado “unidad cúbica”, tiene “una unidad cúbica” de volumen, y ésta se puede utilizar para medir el volumen. Se dice que una figura sólida que se puede rellenar con la unidad cúbica n sin dejar espacios o superposiciones tiene un volumen de n unidades cúbicas. 

            Alternate Test

            Digital Enhanced Topic Test

            Enhanced Topic Test

         Grade 5: Online Topics 09-12: Benchmark Test
           Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 , by observing that 3/7 < 1/2 . Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 , by observing that 3/7 < 1/2 . Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Resolver problemas verbales de suma y resta de fracciones que se refieran a un todo, incluyendo casos de denominadores distintos; por ejemplo, empleando modelos visuales de fracciones o ecuaciones para representar el problema. Utilizar las fracciones de referencia y el sentido numérico para hacer cálculos mentales y evaluar la lógica de las respuestas. Por ejemplo, reconocer como incorrecto el resultado 2/5 + 1/2 = 3/7, observando que 3/7 < 1/2. Resuelven problemas verbales de suma y resta de fracciones que se refieran a un entero, incluyendo casos de denominadores distintos, por ejemplo, al emplear modelos visuales de fracciones o ecuaciones para representar el problema. Utilizan las fracciones de referencia y el sentido numérico para hacer cálculos mentales y evaluar la lógica de las respuestas. Por ejemplo, reconocen como incorrecto el resultado 2/5 + 1/2 = 3/7, observando que 3/7 < 1/2. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Interpret multiplication as scaling (resizing), by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Interpret multiplication as scaling (resizing), by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Interpretar la multiplicación como poner a escala (cambiar el tamaño de) algo al: Comparar el tamaño de un producto al tamaño de un factor en base al tamaño del otro factor, sin efectuar la multiplicación indicada. Comparan el tamaño de un producto al tamaño de un factor en base al tamaño del otro factor, sin efectuar la multiplicación indicada. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. Relacionar el volumen con las operaciones de multiplicación y suma para resolver problemas matemáticos y de la vida diaria relativos al volumen. Reconocer que el volumen se puede sumar. Hallar el volumen de figuras sólidas compuestas de dos prismas rectangulares rectos no superpuestos, sumando los volúmenes de las partes que no se sobreponen, y aplicar esta técnica para resolver problemas de la vida diaria. Reconocen el volumen como una suma. Hallan el volumen de figuras sólidas compuestas de dos prismas rectangulares rectos que no se sobrepongan, sumando los volúmenes de las partes que no se sobreponen, y aplican esta técnica para resolver problemas del mundo real. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) x 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb. of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) x 4 = 1/3 . Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) … 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) … 4 = 1/12 because (1/12 ) x 4 = 1/3 . Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb. of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Aplicar y ampliar los conocimientos previos sobre la división para dividir fracciones unitarias por números enteros no negativos y números enteros no negativos por fracciones unitarias. Interpretar la división de una fracción unitaria por un número entero no negativo distinto a cero y calcular este tipo de cocientes. Por ejemplo, inventar un contexto para (1/3) ÷ 4, y utilizar un modelo visual de fracciones para expresar el cociente. Utilizar la relación entre la multiplicación y la división para explicar que (1/3) ÷ 4 = 1/12 porque (1/12) × 4 = 1/3. Aplicar y ampliar los conocimientos previos sobre la división para dividir fracciones unitarias por números enteros no negativos y números enteros no negativos por fracciones unitarias. Resolver problemas de la vida diaria relacionados a la división de fracciones unitarias por números enteros no negativos distintos de cero y a la división de números enteros no negativos por fracciones unitarias, por ej., utilizando modelos visuales de fracciones y ecuaciones para representar el problema. Por ejemplo, ¿cuánto chocolate tendrá cada persona si 3 personas comparten ½ libra de chocolate en partes iguales?¿Cuántas porciones de 1/3 de taza hay en 2 tazas de pasas? Interpretan la división de una fracción unitaria entre un número entero distinto al cero, y calculan sus cocientes. Por ejemplo, crean el contexto de un cuento para (1/3) ÷ 4, y utilizan un modelo visual de fracciones para expresar el cociente. Utilizan la relación entre la multiplicación y la división para explicar que (1/3) ÷ 4 = 1/12 porque (1/12) × 4 = 1/3. Resuelven problemas del mundo real relacionados a la división de fracciones unitarias entre números enteros distintos al cero y la división de números enteros entre fracciones unitarias, por ejemplo, utilizan modelos visuales de fracciones y ecuaciones para representar el problema. Por ejemplo, ¿cuánto chocolate tendrá cada persona si 3 personas comparten ½ libra de chocolate en partes iguales?¿Cuántas porciones de 1/3 de taza hay en 2 tazas de pasas? Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold wholenumber products as volumes, e.g., to represent the associative property of multiplication. Apply the formulas V = l x w x h and V = b x h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold wholenumber products as volumes, e.g., to represent the associative property of multiplication. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold wholenumber products as volumes, e.g., to represent the associative property of multiplication. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Apply the formulas V = l x w x h and V = b x h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. Relacionar el volumen con las operaciones de multiplicación y suma para resolver problemas matemáticos y de la vida diaria relativos al volumen. Hallar el volumen de un prisma rectangular recto con lados que se miden en números enteros no negativos, llenando el prisma con unidades cúbicas, y demostrar que el volumen es el mismo que se hallaría multiplicando la altura por el área de la base. Representar tres veces el producto de un número entero no negativo como un volumen, por ej., para representar la propiedad asociativa de la multiplicación. Relacionar el volumen con las operaciones de multiplicación y suma para resolver problemas matemáticos y de la vida diaria relativos al volumen. Aplicar las fórmulas V = l × a × h   y   V = b × h de los prismas rectangulares para hallar los volúmenes de prismas rectangulares rectos cuyos lados se miden en números enteros no negativos, en el contexto de resolver problemas matemáticos y de la vida diaria. Hallan el volumen de un prisma rectangular recto con lados que se miden en números enteros, llenando el prisma con unidades cúbicas, y demostrando que el volumen es el mismo que se hallaría multiplicando la altura por el área de la base. Representan tres veces el producto de un número entero como un volumen, por ejemplo, para representar la propiedad asociativa de la multiplicación. Aplican las fórmulas V = l × a × h y V = b × h de los prismas rectangulares para hallar los volúmenes de prismas rectangulares rectos cuyos lados se miden en números enteros, en el contexto de resolver problemas matemáticos y del mundo real. Interpret the product (a/b) x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷ b. For example, use a visual fraction model to show (2/3) x 4 = 8/3 , and create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd.) Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷ b. For example, use a visual fraction model to show (2/3) x 4 = 8/3 , and create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd.) Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q … b. For example, use a visual fraction model to show (2/3) x 4 = 8/3 , and create a story context for this equation. Do the same with (2/3) x ( 4/5) = 8/15. (In general, (a/b) x (c/d ) = ac/bd.) Aplicar y ampliar los conocimientos previos sobre la multiplicación para multiplicar una fracción o un número entero por una fracción. Interpretar el producto (a/b) × q como a partes de la repartición de q en partes iguales de b; de manera equivalente, como el resultado de la secuencia de operaciones a × q ÷ b. Por ejemplo, emplear un modelo visual de fracciones para representar (2/3) × 4 = 8/3, e inventar un contexto para esta ecuación. Hacer lo mismo con (2/3) ×(4/5) = 8/15. (En general, (a/b) ×(c/d) = ac/bd). Interpretan el producto (a/b) × q como tantas partes a de la repartición de q en partes iguales de b; de manera equivalente, como el resultado de la secuencia de operaciones a × q ÷ b. Por ejemplo, al emplear un modelo visual de fracciones para representar (2/3) × 4 = 8/3, y crear un contexto para esta ecuación. Hacen lo mismo con (2/3) × (4/5) = 8/15. (En general, (a /b) × (c /d) = ac/bd). A cube with side length 1 unit, called a U1unit cube,Ue is said to have U1one cubic unitUe of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A cube with side length 1 unit, called a _unit cube,? is said to have _one cubic unit? of volume, and can be used to measure volume. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A cube with side length 1 unit, called a ñunit cube,î is said to have ñone cubic unitî of volume, and can be used to measure volume. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Reconocer el volumen como un atributo de las figuras sólidas y entender los conceptos de la medición del volumen. Se dice que un cubo con lados de 1 unidad, llamado “bloque de unidad”, tiene “una unidad cúbica” de volumen, y ésta se puede utilizar para medir el volumen. Reconocer el volumen como un atributo de las figuras sólidas y entender los conceptos de la medición del volumen. Se dice que una figura sólida que se puede rellenar con n bloques de unidad sin dejar espacios o superposiciones tiene un volumen de n unidades cúbicas. Se dice que un cubo con lados de 1 unidad, llamado “unidad cúbica”, tiene “una unidad cúbica” de volumen, y ésta se puede utilizar para medir el volumen. Se dice que una figura sólida que se puede rellenar con la unidad cúbica n sin dejar espacios o superposiciones tiene un volumen de n unidades cúbicas. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Sumar y restar fracciones con denominadores distintos (inclusive números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) /bd). Suman y restan fracciones con denominadores distintos (incluyendo números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) / bd) Represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects and pictorial models and properties of operations. Represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects and pictorial models and properties of operations. Estimate to determine solutions to mathematical and real-world problems involving addition, subtraction, multiplication, or division. Estimate to determine solutions to mathematical and real-world problems involving addition, subtraction, multiplication, or division. Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution. Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate. Create and use representations to organize, record, and communicate mathematical ideas. Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution. Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate. Create and use representations to organize, record, and communicate mathematical ideas. Represent and solve multiplication of a whole number and a fraction that refers to the same whole using objects and pictorial models, including area models. Represent and solve multiplication of a whole number and a fraction that refers to the same whole using objects and pictorial models, including area models. Represent and solve problems related to perimeter and/or area and related to volume. Represent and solve problems related to perimeter and/or area and related to volume. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Aplicar y ampliar los conocimientos previos sobre la multiplicación para multiplicar una fracción o un número entero por una fracción. Hallar el área de un rectángulo cuyos lados se miden en unidades fraccionarias, cubriéndolo con unidades cuadradas de la unidad fraccionaria correspondiente a sus lados, y demostrar que el área sería la misma que se hallaría si se multiplicaran las longitudes de los lados. Multiplicar los números fraccionarios de las longitudes de los lados para hallar el área de rectángulos y representar los productos de las fracciones como áreas rectangulares. Hallan el área de un rectángulo cuyos lados se miden en unidades fraccionarias, cubriéndolo con unidades cuadradas de la unidad fraccionaria correspondiente a sus lados, y demuestran que el área sería la misma que se hallaría si se multiplicaran las longitudes de los lados. Multiplican los números fraccionarios de las longitudes de los lados para hallar el área de rectángulos, y representar los productos de las fracciones como áreas rectangulares. Represent division of a unit fraction by a whole number and the division of a whole number by a unit fraction such as 1/3 ? 7 and 7 ? 1/3 using objects and pictorial models, including area models. Represent division of a unit fraction by a whole number and the division of a whole number by a unit fraction such as 1/3 ÷ 7 and 7 ÷ 1/3 using objects and pictorial models, including area models. 

         Topic 13: Units of Measure
         
            Converting Measurements

            Topic 13: Online Topic Readiness
              Curriculum Standards: Solve problems related to perimeter and area of rectangles where dimensions are whole numbers. Solve problems related to perimeter and area of rectangles where dimensions are whole numbers. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold wholenumber products as volumes, e.g., to represent the associative property of multiplication. Apply the formulas V = l x w x h and V = b x h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold wholenumber products as volumes, e.g., to represent the associative property of multiplication. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold wholenumber products as volumes, e.g., to represent the associative property of multiplication. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Apply the formulas V = l x w x h and V = b x h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. Relacionar el volumen con las operaciones de multiplicación y suma para resolver problemas matemáticos y de la vida diaria relativos al volumen. Hallar el volumen de un prisma rectangular recto con lados que se miden en números enteros no negativos, llenando el prisma con unidades cúbicas, y demostrar que el volumen es el mismo que se hallaría multiplicando la altura por el área de la base. Representar tres veces el producto de un número entero no negativo como un volumen, por ej., para representar la propiedad asociativa de la multiplicación. Relacionar el volumen con las operaciones de multiplicación y suma para resolver problemas matemáticos y de la vida diaria relativos al volumen. Aplicar las fórmulas V = l × a × h   y   V = b × h de los prismas rectangulares para hallar los volúmenes de prismas rectangulares rectos cuyos lados se miden en números enteros no negativos, en el contexto de resolver problemas matemáticos y de la vida diaria. Hallan el volumen de un prisma rectangular recto con lados que se miden en números enteros, llenando el prisma con unidades cúbicas, y demostrando que el volumen es el mismo que se hallaría multiplicando la altura por el área de la base. Representan tres veces el producto de un número entero como un volumen, por ejemplo, para representar la propiedad asociativa de la multiplicación. Aplican las fórmulas V = l × a × h y V = b × h de los prismas rectangulares para hallar los volúmenes de prismas rectangulares rectos cuyos lados se miden en números enteros, en el contexto de resolver problemas matemáticos y del mundo real. Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ... Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ... Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), Saber los tamaños relativos de las unidades de medición dentro de un sistema de unidades, incluyendo km, m, cm; kg, g; lb, oz.; L, mL; h, min, s. Dentro de un mismo sistema de medición, expresar las medidas en una unidad más grande en términos de una unidad más pequeña. Anotar las medidas equivalentes en una tabla de dos columnas. Por ejemplo, saber que 1 pie es 12 veces más largo que 1 pulg. Expresar la longitud de una culebra de 4 pies como 48 pulgs. Generar una tabla de conversión para pies y pulgadas con una lista de pares de números (1, 12), (2, 24), (3, 36), ... Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), Reconocen los tamaños relativos de las unidades de medición dentro de un sistema de unidades, incluyendo km, m, cm; kg, g; lb, oz.; L, mL; h, min, s. Dentro de un mismo sistema de medición, expresan las medidas en una unidad más grande en términos de una unidad más pequeña. Anotan las medidas equivalentes en una tabla de dos columnas. Por ejemplo, saben que 1 pie es 12 veces más largo que 1 pulgada. Expresan la longitud de una culebra de 4 pies como 48 pulgadas. Generan una tabla de conversión para pies y pulgadas con una lista de pares de números (1, 12), (2, 24), (3, 36), … Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. Represent and interpret data. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. Aplicar fórmulas de área y perímetro de rectángulos para resolver problemas matemáticos y de la vida diaria. Por ejemplo, hallar el ancho de una habitación rectangular dadas el área del piso y la longitud, usando la fórmula del área como una ecuación de multiplicación con un factor desconocido. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. Aplican fórmulas de área y perímetro de rectángulos para resolver problemas matemáticos y del mundo real. Por ejemplo, hallan el ancho de una habitación rectangular dadas el área y la longitud del piso, usando la fórmula del área como una ecuación de multiplicación con un factor desconocido Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. Convert measurements within the same measurement system, customary or metric, from a smaller unit into a larger unit or a larger unit into a smaller unit when given other equivalent measures represented in a table. Convert measurements within the same measurement system, customary or metric, from a smaller unit into a larger unit or a larger unit into a smaller unit when given other equivalent measures represented in a table. Use concrete objects and pictorial models to develop the formulas for the volume of a rectangular prism, including the special form for a cube (V = l x w x h, V = s x s x s, and V = Bh). Use concrete objects and pictorial models to develop the formulas for the volume of a rectangular prism, including the special form for a cube (V = l × w × h, V = s × s × s, and V = Bh). Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. (Two dimensional shapes should include special triangles, e.g., equilateral, isosceles, scalene, and special quadrilaterals, e.g., rhombus, square, rectangle, parallelogram, trapezoid.) Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. Dibujar puntos, rectas, segmentos de rectas, semirrectas, ángulos (rectos, agudos, obtusos) y rectas perpendiculares y paralelas. Identificar estos elementos en las figuras bidimensionales. Dibujan puntos, rectas, segmentos de rectas, semirrectas, ángulos (rectos, agudos, obtusos), y rectas perpendiculares y paralelas. Identifican estos elementos en las figuras bidimensionales. Clasifican las figuras bidimensionales basándose en la presencia o ausencia de rectas paralelas o perpendiculares, o en la presencia o ausencia de ángulos de un tamaño especificado. Reconocen que los triángulos rectos forman una categoría en sí, e identifican triángulos rectos. (Las figuras bidimensionales deben incluir los triángulos especiales, por ejemplo, los triángulos equiláteros, isósceles y escalenos, y los cuadriláteros especiales, por ejemplo, los rombos, cuadrados, rectángulos, paralelogramos y trapecios.) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Utilizan las cuatro operaciones para resolver problemas verbales sobre distancias, intervalos de tiempo, volúmenes líquidos, masas de objetos y dinero, incluyendo problemas con fracciones simples o decimales, y problemas que requieren expresar las medidas dadas en una unidad más grande en términos de una unidad más pequeña. Representan cantidades medidas utilizando diagramas tales como rectas numéricas con escalas de medición. Identify relative sizes of measurement units within the customary and metric systems. Identify relative sizes of measurement units within the customary and metric systems. 

            13-01: Converting Customary Units of Length
            
               Develop the Concept: Visual
               
                  Converting Customary Units of Length: Visual Learning
                    Curriculum Standards: Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convertir unidades de medida estándar de diferentes tamaños dentro de un sistema de medición determinado (por ej., convertir 5 cm a 0.05 m), y utilizar estas conversiones para resolver problemas de varios pasos de la vida diaria. Convierten unidades de medición estándar de diferentes tamaños dentro de un sistema de medición dado (por ejemplo, convierten 5 cm en 0.05 m), y utilizan estas conversiones en la solución de problemas de varios pasos y del mundo real. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. 

               Assess & Differentiate
               
                  13-01: Digital Quick Check
                    Curriculum Standards: Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convertir unidades de medida estándar de diferentes tamaños dentro de un sistema de medición determinado (por ej., convertir 5 cm a 0.05 m), y utilizar estas conversiones para resolver problemas de varios pasos de la vida diaria. Convierten unidades de medición estándar de diferentes tamaños dentro de un sistema de medición dado (por ejemplo, convierten 5 cm en 0.05 m), y utilizan estas conversiones en la solución de problemas de varios pasos y del mundo real. 

            13-02: Converting Customary Units of Capacity
            
               Develop the Concept: Visual
               
                  Converting Customary Units of Capacity: Visual Learning
                    Curriculum Standards: Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convertir unidades de medida estándar de diferentes tamaños dentro de un sistema de medición determinado (por ej., convertir 5 cm a 0.05 m), y utilizar estas conversiones para resolver problemas de varios pasos de la vida diaria. Convierten unidades de medición estándar de diferentes tamaños dentro de un sistema de medición dado (por ejemplo, convierten 5 cm en 0.05 m), y utilizan estas conversiones en la solución de problemas de varios pasos y del mundo real. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. 

               Assess & Differentiate
               
                  13-02: Digital Quick Check
                    Curriculum Standards: Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convertir unidades de medida estándar de diferentes tamaños dentro de un sistema de medición determinado (por ej., convertir 5 cm a 0.05 m), y utilizar estas conversiones para resolver problemas de varios pasos de la vida diaria. Convierten unidades de medición estándar de diferentes tamaños dentro de un sistema de medición dado (por ejemplo, convierten 5 cm en 0.05 m), y utilizan estas conversiones en la solución de problemas de varios pasos y del mundo real. 

            13-03: Converting Customary Units of Weight
            
               Develop the Concept: Visual
               
                  Converting Customary Units of Weight: Visual Learning
                    Curriculum Standards: Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convertir unidades de medida estándar de diferentes tamaños dentro de un sistema de medición determinado (por ej., convertir 5 cm a 0.05 m), y utilizar estas conversiones para resolver problemas de varios pasos de la vida diaria. Convierten unidades de medición estándar de diferentes tamaños dentro de un sistema de medición dado (por ejemplo, convierten 5 cm en 0.05 m), y utilizan estas conversiones en la solución de problemas de varios pasos y del mundo real. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. 

               Assess & Differentiate
               
                  13-03: Digital Quick Check
                    Curriculum Standards: Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convertir unidades de medida estándar de diferentes tamaños dentro de un sistema de medición determinado (por ej., convertir 5 cm a 0.05 m), y utilizar estas conversiones para resolver problemas de varios pasos de la vida diaria. Convierten unidades de medición estándar de diferentes tamaños dentro de un sistema de medición dado (por ejemplo, convierten 5 cm en 0.05 m), y utilizan estas conversiones en la solución de problemas de varios pasos y del mundo real. 

            13-04: Converting Metric Units of Length
            
               Develop the Concept: Visual
               
                  Converting Metric Units of Length: Visual Learning
                    Curriculum Standards: Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convertir unidades de medida estándar de diferentes tamaños dentro de un sistema de medición determinado (por ej., convertir 5 cm a 0.05 m), y utilizar estas conversiones para resolver problemas de varios pasos de la vida diaria. Convierten unidades de medición estándar de diferentes tamaños dentro de un sistema de medición dado (por ejemplo, convierten 5 cm en 0.05 m), y utilizan estas conversiones en la solución de problemas de varios pasos y del mundo real. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. 

               Assess & Differentiate
               
                  13-04: Digital Quick Check
                    Curriculum Standards: Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convertir unidades de medida estándar de diferentes tamaños dentro de un sistema de medición determinado (por ej., convertir 5 cm a 0.05 m), y utilizar estas conversiones para resolver problemas de varios pasos de la vida diaria. Convierten unidades de medición estándar de diferentes tamaños dentro de un sistema de medición dado (por ejemplo, convierten 5 cm en 0.05 m), y utilizan estas conversiones en la solución de problemas de varios pasos y del mundo real. 

            13-05: Converting Metric Units of Capacity
            
               Develop the Concept: Visual
               
                  Converting Metric Units of Capacity: Visual Learning
                    Curriculum Standards: Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convertir unidades de medida estándar de diferentes tamaños dentro de un sistema de medición determinado (por ej., convertir 5 cm a 0.05 m), y utilizar estas conversiones para resolver problemas de varios pasos de la vida diaria. Convierten unidades de medición estándar de diferentes tamaños dentro de un sistema de medición dado (por ejemplo, convierten 5 cm en 0.05 m), y utilizan estas conversiones en la solución de problemas de varios pasos y del mundo real. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. 

               Assess & Differentiate
               
                  13-05: Digital Quick Check
                    Curriculum Standards: Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convertir unidades de medida estándar de diferentes tamaños dentro de un sistema de medición determinado (por ej., convertir 5 cm a 0.05 m), y utilizar estas conversiones para resolver problemas de varios pasos de la vida diaria. Convierten unidades de medición estándar de diferentes tamaños dentro de un sistema de medición dado (por ejemplo, convierten 5 cm en 0.05 m), y utilizan estas conversiones en la solución de problemas de varios pasos y del mundo real. 

            13-06: Converting Metric Units of Mass
            
               Develop the Concept: Visual
               
                  Converting Metric Units of Mass: Visual Learning
                    Curriculum Standards: Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convertir unidades de medida estándar de diferentes tamaños dentro de un sistema de medición determinado (por ej., convertir 5 cm a 0.05 m), y utilizar estas conversiones para resolver problemas de varios pasos de la vida diaria. Convierten unidades de medición estándar de diferentes tamaños dentro de un sistema de medición dado (por ejemplo, convierten 5 cm en 0.05 m), y utilizan estas conversiones en la solución de problemas de varios pasos y del mundo real. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. 

               Assess & Differentiate
               
                  13-06: Digital Quick Check
                    Curriculum Standards: Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convertir unidades de medida estándar de diferentes tamaños dentro de un sistema de medición determinado (por ej., convertir 5 cm a 0.05 m), y utilizar estas conversiones para resolver problemas de varios pasos de la vida diaria. Convierten unidades de medición estándar de diferentes tamaños dentro de un sistema de medición dado (por ejemplo, convierten 5 cm en 0.05 m), y utilizan estas conversiones en la solución de problemas de varios pasos y del mundo real. 

            13-07: Problem Solving: Multiple-Step Problems
            
               Develop the Concept: Visual
               
                  Problem Solving: Multiple-Step Problems: Visual Learning
                    Curriculum Standards: Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convertir unidades de medida estándar de diferentes tamaños dentro de un sistema de medición determinado (por ej., convertir 5 cm a 0.05 m), y utilizar estas conversiones para resolver problemas de varios pasos de la vida diaria. Convierten unidades de medición estándar de diferentes tamaños dentro de un sistema de medición dado (por ejemplo, convierten 5 cm en 0.05 m), y utilizan estas conversiones en la solución de problemas de varios pasos y del mundo real. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. 

               Assess & Differentiate
               
                  13-07: Digital Quick Check
                    Curriculum Standards: Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convertir unidades de medida estándar de diferentes tamaños dentro de un sistema de medición determinado (por ej., convertir 5 cm a 0.05 m), y utilizar estas conversiones para resolver problemas de varios pasos de la vida diaria. Convierten unidades de medición estándar de diferentes tamaños dentro de un sistema de medición dado (por ejemplo, convierten 5 cm en 0.05 m), y utilizan estas conversiones en la solución de problemas de varios pasos y del mundo real. 

            Topic 13: Online Topic Test
              Curriculum Standards: Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convertir unidades de medida estándar de diferentes tamaños dentro de un sistema de medición determinado (por ej., convertir 5 cm a 0.05 m), y utilizar estas conversiones para resolver problemas de varios pasos de la vida diaria. Convierten unidades de medición estándar de diferentes tamaños dentro de un sistema de medición dado (por ejemplo, convierten 5 cm en 0.05 m), y utilizan estas conversiones en la solución de problemas de varios pasos y del mundo real. Solve problems by calculating conversions within a measurement system, customary or metric. Solve problems by calculating conversions within a measurement system, customary or metric. 

            Alternate Test

            Digital Enhanced Topic Test

            Enhanced Topic Test

         Topic 14: Data
         
            Tally This!

            Topic 14: Online Topic Readiness
              Curriculum Standards: Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ... Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ... Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), Saber los tamaños relativos de las unidades de medición dentro de un sistema de unidades, incluyendo km, m, cm; kg, g; lb, oz.; L, mL; h, min, s. Dentro de un mismo sistema de medición, expresar las medidas en una unidad más grande en términos de una unidad más pequeña. Anotar las medidas equivalentes en una tabla de dos columnas. Por ejemplo, saber que 1 pie es 12 veces más largo que 1 pulg. Expresar la longitud de una culebra de 4 pies como 48 pulgs. Generar una tabla de conversión para pies y pulgadas con una lista de pares de números (1, 12), (2, 24), (3, 36), ... Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), Reconocen los tamaños relativos de las unidades de medición dentro de un sistema de unidades, incluyendo km, m, cm; kg, g; lb, oz.; L, mL; h, min, s. Dentro de un mismo sistema de medición, expresan las medidas en una unidad más grande en términos de una unidad más pequeña. Anotan las medidas equivalentes en una tabla de dos columnas. Por ejemplo, saben que 1 pie es 12 veces más largo que 1 pulgada. Expresan la longitud de una culebra de 4 pies como 48 pulgadas. Generan una tabla de conversión para pies y pulgadas con una lista de pares de números (1, 12), (2, 24), (3, 36), … Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Utilizan las cuatro operaciones para resolver problemas verbales sobre distancias, intervalos de tiempo, volúmenes líquidos, masas de objetos y dinero, incluyendo problemas con fracciones simples o decimales, y problemas que requieren expresar las medidas dadas en una unidad más grande en términos de una unidad más pequeña. Representan cantidades medidas utilizando diagramas tales como rectas numéricas con escalas de medición. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. Hacer un diagrama de puntos para representar un conjunto de datos de medidas en fracciones de una unidad (1/2, 1/4, 1/8). Resolver problemas sobre sumas y restas de fracciones utilizando la información presentada en los diagramas de puntos. Por ejemplo, utilizando un diagrama de puntos, hallar e interpretar la diferencia de longitud entre los ejemplares más largos y más cortos de una colección de insectos. Hacen un diagrama de puntos para representar un conjunto de datos de medidas en fracciones de una unidad (1/2, 1/4, 1/8). Resuelven problemas sobre sumas y restas de fracciones utilizando la información presentada en los diagramas de puntos. Por ejemplo, al utilizar un diagrama de puntos, hallan e interpretan la diferencia de longitud entre los ejemplares más largos y más cortos en una colección de insectos. Identify relative sizes of measurement units within the customary and metric systems. Identify relative sizes of measurement units within the customary and metric systems. 

            14-01: Line Plots
            
               Develop the Concept: Visual
               
                  Line Plots: Visual Learning
                    Curriculum Standards: Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8 ). Use operations on fractions for this grade to solve problems involving information presented in line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8 ). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8 ). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Hacer un diagrama de puntos para mostrar un conjunto de medidas en unidades fraccionarias (1/2, 1/4, 1/8). Efectuar operaciones con fracciones apropiadas a este grado, para resolver problemas relacionados con la información presentada en los diagramas de puntos. Por ejemplo, dadas diferentes medidas de líquido en vasos de laboratorio idénticos, hallar la cantidad de líquido que cada vaso contiene, si la cantidad total en todos los vasos fuera redistribuida igualmente. Hacen un diagrama de puntos para mostrar un conjunto de medidas en unidades fraccionarias (1/2, 1/4, 1/8). Efectúan operaciones con fracciones apropiadas a este grado, para resolver problemas relacionados con la información presentada en los diagramas de puntos. 

               Assess & Differentiate
               
                  14-01: Digital Quick Check
                    Curriculum Standards: Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8 ). Use operations on fractions for this grade to solve problems involving information presented in line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8 ). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8 ). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Hacer un diagrama de puntos para mostrar un conjunto de medidas en unidades fraccionarias (1/2, 1/4, 1/8). Efectuar operaciones con fracciones apropiadas a este grado, para resolver problemas relacionados con la información presentada en los diagramas de puntos. Por ejemplo, dadas diferentes medidas de líquido en vasos de laboratorio idénticos, hallar la cantidad de líquido que cada vaso contiene, si la cantidad total en todos los vasos fuera redistribuida igualmente. Hacen un diagrama de puntos para mostrar un conjunto de medidas en unidades fraccionarias (1/2, 1/4, 1/8). Efectúan operaciones con fracciones apropiadas a este grado, para resolver problemas relacionados con la información presentada en los diagramas de puntos. 

            14-02: Data from Surveys
            
               Develop the Concept: Visual
               
                  Data from Surveys: Visual Learning
                    Curriculum Standards: Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8 ). Use operations on fractions for this grade to solve problems involving information presented in line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8 ). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8 ). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Hacer un diagrama de puntos para mostrar un conjunto de medidas en unidades fraccionarias (1/2, 1/4, 1/8). Efectuar operaciones con fracciones apropiadas a este grado, para resolver problemas relacionados con la información presentada en los diagramas de puntos. Por ejemplo, dadas diferentes medidas de líquido en vasos de laboratorio idénticos, hallar la cantidad de líquido que cada vaso contiene, si la cantidad total en todos los vasos fuera redistribuida igualmente. Hacen un diagrama de puntos para mostrar un conjunto de medidas en unidades fraccionarias (1/2, 1/4, 1/8). Efectúan operaciones con fracciones apropiadas a este grado, para resolver problemas relacionados con la información presentada en los diagramas de puntos. 

               Assess & Differentiate
               
                  14-02: Digital Quick Check
                    Curriculum Standards: Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8 ). Use operations on fractions for this grade to solve problems involving information presented in line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8 ). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8 ). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Hacer un diagrama de puntos para mostrar un conjunto de medidas en unidades fraccionarias (1/2, 1/4, 1/8). Efectuar operaciones con fracciones apropiadas a este grado, para resolver problemas relacionados con la información presentada en los diagramas de puntos. Por ejemplo, dadas diferentes medidas de líquido en vasos de laboratorio idénticos, hallar la cantidad de líquido que cada vaso contiene, si la cantidad total en todos los vasos fuera redistribuida igualmente. Hacen un diagrama de puntos para mostrar un conjunto de medidas en unidades fraccionarias (1/2, 1/4, 1/8). Efectúan operaciones con fracciones apropiadas a este grado, para resolver problemas relacionados con la información presentada en los diagramas de puntos. 

            14-03: Making Line Plots
            
               Develop the Concept: Visual
               
                  Making Line Plots: Visual Learning
                    Curriculum Standards: Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8 ). Use operations on fractions for this grade to solve problems involving information presented in line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8 ). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8 ). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Hacer un diagrama de puntos para mostrar un conjunto de medidas en unidades fraccionarias (1/2, 1/4, 1/8). Efectuar operaciones con fracciones apropiadas a este grado, para resolver problemas relacionados con la información presentada en los diagramas de puntos. Por ejemplo, dadas diferentes medidas de líquido en vasos de laboratorio idénticos, hallar la cantidad de líquido que cada vaso contiene, si la cantidad total en todos los vasos fuera redistribuida igualmente. Hacen un diagrama de puntos para mostrar un conjunto de medidas en unidades fraccionarias (1/2, 1/4, 1/8). Efectúan operaciones con fracciones apropiadas a este grado, para resolver problemas relacionados con la información presentada en los diagramas de puntos. 

               Assess & Differentiate
               
                  14-03: Digital Quick Check
                    Curriculum Standards: Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8 ). Use operations on fractions for this grade to solve problems involving information presented in line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8 ). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8 ). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Hacer un diagrama de puntos para mostrar un conjunto de medidas en unidades fraccionarias (1/2, 1/4, 1/8). Efectuar operaciones con fracciones apropiadas a este grado, para resolver problemas relacionados con la información presentada en los diagramas de puntos. Por ejemplo, dadas diferentes medidas de líquido en vasos de laboratorio idénticos, hallar la cantidad de líquido que cada vaso contiene, si la cantidad total en todos los vasos fuera redistribuida igualmente. Hacen un diagrama de puntos para mostrar un conjunto de medidas en unidades fraccionarias (1/2, 1/4, 1/8). Efectúan operaciones con fracciones apropiadas a este grado, para resolver problemas relacionados con la información presentada en los diagramas de puntos. 

            14-04: Measurement Data
            
               Develop the Concept: Visual
               
                  Measurement Data: Visual Learning
                    Curriculum Standards: Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8 ). Use operations on fractions for this grade to solve problems involving information presented in line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8 ). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8 ). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Hacer un diagrama de puntos para mostrar un conjunto de medidas en unidades fraccionarias (1/2, 1/4, 1/8). Efectuar operaciones con fracciones apropiadas a este grado, para resolver problemas relacionados con la información presentada en los diagramas de puntos. Por ejemplo, dadas diferentes medidas de líquido en vasos de laboratorio idénticos, hallar la cantidad de líquido que cada vaso contiene, si la cantidad total en todos los vasos fuera redistribuida igualmente. Hacen un diagrama de puntos para mostrar un conjunto de medidas en unidades fraccionarias (1/2, 1/4, 1/8). Efectúan operaciones con fracciones apropiadas a este grado, para resolver problemas relacionados con la información presentada en los diagramas de puntos. 

               Assess & Differentiate
               
                  14-04: Digital Quick Check
                    Curriculum Standards: Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8 ). Use operations on fractions for this grade to solve problems involving information presented in line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8 ). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8 ). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Hacer un diagrama de puntos para mostrar un conjunto de medidas en unidades fraccionarias (1/2, 1/4, 1/8). Efectuar operaciones con fracciones apropiadas a este grado, para resolver problemas relacionados con la información presentada en los diagramas de puntos. Por ejemplo, dadas diferentes medidas de líquido en vasos de laboratorio idénticos, hallar la cantidad de líquido que cada vaso contiene, si la cantidad total en todos los vasos fuera redistribuida igualmente. Hacen un diagrama de puntos para mostrar un conjunto de medidas en unidades fraccionarias (1/2, 1/4, 1/8). Efectúan operaciones con fracciones apropiadas a este grado, para resolver problemas relacionados con la información presentada en los diagramas de puntos. 

            14-05: Problem Solving: Writing to Explain
            
               Develop the Concept: Visual
               
                  Problem Solving: Writing to Explain: Visual Learning
                    Curriculum Standards: Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Representar problemas matemáticos y de la vida diaria al graficar puntos en el primer cuadrante del plano de coordenadas e interpretar los valores de los puntos de las coordenadas según el contexto. Representan problemas matemáticos y del mundo real al representar gráficamente puntos en el primer cuadrante del plano de coordenadas e interpretan los valores de los puntos de las coordenadas según el Contexto. 

               Assess & Differentiate
               
                  14-05: Digital Quick Check
                    Curriculum Standards: Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Representar problemas matemáticos y de la vida diaria al graficar puntos en el primer cuadrante del plano de coordenadas e interpretar los valores de los puntos de las coordenadas según el contexto. Representan problemas matemáticos y del mundo real al representar gráficamente puntos en el primer cuadrante del plano de coordenadas e interpretan los valores de los puntos de las coordenadas según el Contexto. 

            Topic 14: Online Topic Test
              Curriculum Standards: Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8 ). Use operations on fractions for this grade to solve problems involving information presented in line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8 ). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8 ). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Hacer un diagrama de puntos para mostrar un conjunto de medidas en unidades fraccionarias (1/2, 1/4, 1/8). Efectuar operaciones con fracciones apropiadas a este grado, para resolver problemas relacionados con la información presentada en los diagramas de puntos. Por ejemplo, dadas diferentes medidas de líquido en vasos de laboratorio idénticos, hallar la cantidad de líquido que cada vaso contiene, si la cantidad total en todos los vasos fuera redistribuida igualmente. Hacen un diagrama de puntos para mostrar un conjunto de medidas en unidades fraccionarias (1/2, 1/4, 1/8). Efectúan operaciones con fracciones apropiadas a este grado, para resolver problemas relacionados con la información presentada en los diagramas de puntos. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Representar problemas matemáticos y de la vida diaria al graficar puntos en el primer cuadrante del plano de coordenadas e interpretar los valores de los puntos de las coordenadas según el contexto. Representan problemas matemáticos y del mundo real al representar gráficamente puntos en el primer cuadrante del plano de coordenadas e interpretan los valores de los puntos de las coordenadas según el Contexto. 

            Alternate Test

            Digital Enhanced Topic Test

            Enhanced Topic Test

         Topic 15: Classifying Plane Figures
         
            Topic 15: Online Topic Readiness
              Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. Estimate to determine solutions to mathematical and real-world problems involving addition, subtraction, multiplication, or division. Estimate to determine solutions to mathematical and real-world problems involving addition, subtraction, multiplication, or division. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. (Two dimensional shapes should include special triangles, e.g., equilateral, isosceles, scalene, and special quadrilaterals, e.g., rhombus, square, rectangle, parallelogram, trapezoid.) Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. Dibujar puntos, rectas, segmentos de rectas, semirrectas, ángulos (rectos, agudos, obtusos) y rectas perpendiculares y paralelas. Identificar estos elementos en las figuras bidimensionales. Dibujan puntos, rectas, segmentos de rectas, semirrectas, ángulos (rectos, agudos, obtusos), y rectas perpendiculares y paralelas. Identifican estos elementos en las figuras bidimensionales. Clasifican las figuras bidimensionales basándose en la presencia o ausencia de rectas paralelas o perpendiculares, o en la presencia o ausencia de ángulos de un tamaño especificado. Reconocen que los triángulos rectos forman una categoría en sí, e identifican triángulos rectos. (Las figuras bidimensionales deben incluir los triángulos especiales, por ejemplo, los triángulos equiláteros, isósceles y escalenos, y los cuadriláteros especiales, por ejemplo, los rombos, cuadrados, rectángulos, paralelogramos y trapecios.) Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule U1Add 3Ue and the starting number 0, and given the rule U1Add 6Ue and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule _Add 3? and the starting number 0, and given the rule _Add 6? and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule ñAdd 3î and the starting number 0, and given the rule ñAdd 6î and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generar dos patrones numéricos a partir de dos reglas dadas. Identificar la relación aparente entre los términos correspondientes. Formar pares ordenados con los términos correspondientes de ambos patrones y graficar los pares ordenados en un plano de coordenadas. Por ejemplo, dada la regla “Sumar 3” y el número 0 inicial, y dada la regla “Sumar 6” y el número 0 inicial, generar los términos en cada secuencia y observar que cada término de una secuencia es el doble que el término correspondiente en la otra secuencia. Explicar informalmente por qué esto es así. Generan dos patrones numéricos utilizando dos reglas dadas. Identifican la relación aparente entre términos correspondientes. Forman pares ordenados que consisten de los términos correspondientes de ambos patrones, y marcan los pares ordenados en un plano de coordenadas. Por ejemplo, dada la regla “Sumar 3” y el número inicial 0, y dada la regla “Sumar 6” y el número inicial 0, generan los términos en cada secuencia y observan que cada término de una secuencia, es el doble que el término correspondiente en la otra secuencia. Explican informalmente por qué esto es así. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. Clasificar las figuras bidimensionales en base a la presencia o ausencia de rectas paralelas o perpendiculares, o en la presencia o ausencia de ángulos de un tamaño especificado. Reconocer que los triángulos rectos forman una categoría en sí e identificar triángulos rectos. Round to the nearest 10, 100, or 1,000 or use compatible numbers to estimate solutions involving whole numbers. Round to the nearest 10, 100, or 1,000 or use compatible numbers to estimate solutions involving whole numbers. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Sumar y restar con fluidez los números enteros no negativos con múltiples dígitos utilizando el algoritmo convencional. Suman y restan con fluidez los números enteros con dígitos múltiples utilizando el algoritmo convencional. Use place value understanding to round multi-digit whole numbers to any place. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding  and explain why a rounded solution is appropriate. Resolver problemas verbales de varios pasos con números enteros no negativos y cuyas respuestas son números enteros no negativos utilizando las cuatro operaciones, incluyendo aquellos problemas en los que los residuos deben ser interpretados. Representar estos problemas utilizando ecuaciones con una letra para representar la cantidad desconocida. Evaluar lo razonable de las respuestas utilizando el cálculo mental y las estrategias de estimación, incluyendo el redondeo. Utilizan la comprensión del valor de posición para redondear números enteros con dígitos múltiples a cualquier lugar. Resuelven problemas verbales de pasos múltiples con números enteros, cuya respuestas son números enteros, usando las cuatro operaciones, incluyendo problemas en los que los residuos deben ser interpretados. Representan estos problemas usando ecuaciones con una letra que representa la cantidad desconocida. Evalúan si las respuestas son razonables usando cálculos mentales y estrategias de estimación incluyendo el redondeo. 

            15-01: Polygons
            
               Develop the Concept: Visual
               
                  Polygons: Visual Learning
                    Curriculum Standards: Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Clasificar las figuras bidimensionales dentro de una jerarquía, según sus propiedades. Clasifican las figuras bidimensionales dentro de una jerarquía, según sus propiedades. 

               Assess & Differentiate
               
                  15-01: Digital Quick Check
                    Curriculum Standards: Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Clasificar las figuras bidimensionales dentro de una jerarquía, según sus propiedades. Clasifican las figuras bidimensionales dentro de una jerarquía, según sus propiedades. 

            15-02: Triangles
            
               Develop the Concept: Visual
               
                  Triangles: Visual Learning
                    Curriculum Standards: Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Entender que los atributos que pertenecen a una categoría de figuras bidimensionales también pertenecen a todas las subcategorías de dicha categoría. Por ejemplo, todos los rectángulos tienen cuatro ángulos rectos y los cuadrados son rectángulos; por lo tanto, todos los cuadrados tienen cuatro ángulos rectos. Entienden que los atributos que pertenecen a una categoría de figuras bidimensionales también pertenecen a todas las subcategorías de dicha categoría. Por ejemplo, todos los rectángulos tienen cuatro ángulos rectos y los cuadrados son rectángulos; por lo tanto, todos los cuadrados tienen cuatro ángulos rectos. 

               Assess & Differentiate
               
                  15-02: Digital Quick Check
                    Curriculum Standards: Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Entender que los atributos que pertenecen a una categoría de figuras bidimensionales también pertenecen a todas las subcategorías de dicha categoría. Por ejemplo, todos los rectángulos tienen cuatro ángulos rectos y los cuadrados son rectángulos; por lo tanto, todos los cuadrados tienen cuatro ángulos rectos. Entienden que los atributos que pertenecen a una categoría de figuras bidimensionales también pertenecen a todas las subcategorías de dicha categoría. Por ejemplo, todos los rectángulos tienen cuatro ángulos rectos y los cuadrados son rectángulos; por lo tanto, todos los cuadrados tienen cuatro ángulos rectos. 

            15-03: Attributes of Quadrilaterals
            
               Develop the Concept: Visual
               
                  Attributes of Quadrilaterals: Visual Learning
                    Curriculum Standards: Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Entender que los atributos que pertenecen a una categoría de figuras bidimensionales también pertenecen a todas las subcategorías de dicha categoría. Por ejemplo, todos los rectángulos tienen cuatro ángulos rectos y los cuadrados son rectángulos; por lo tanto, todos los cuadrados tienen cuatro ángulos rectos. Entienden que los atributos que pertenecen a una categoría de figuras bidimensionales también pertenecen a todas las subcategorías de dicha categoría. Por ejemplo, todos los rectángulos tienen cuatro ángulos rectos y los cuadrados son rectángulos; por lo tanto, todos los cuadrados tienen cuatro ángulos rectos. 

               Assess & Differentiate
               
                  15-03: Digital Quick Check
                    Curriculum Standards: Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Entender que los atributos que pertenecen a una categoría de figuras bidimensionales también pertenecen a todas las subcategorías de dicha categoría. Por ejemplo, todos los rectángulos tienen cuatro ángulos rectos y los cuadrados son rectángulos; por lo tanto, todos los cuadrados tienen cuatro ángulos rectos. Entienden que los atributos que pertenecen a una categoría de figuras bidimensionales también pertenecen a todas las subcategorías de dicha categoría. Por ejemplo, todos los rectángulos tienen cuatro ángulos rectos y los cuadrados son rectángulos; por lo tanto, todos los cuadrados tienen cuatro ángulos rectos. 

            15-04: Special Quadrilaterals
            
               Develop the Concept: Visual
               
                  Special Quadrilaterals: Visual Learning
                    Curriculum Standards: Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Entender que los atributos que pertenecen a una categoría de figuras bidimensionales también pertenecen a todas las subcategorías de dicha categoría. Por ejemplo, todos los rectángulos tienen cuatro ángulos rectos y los cuadrados son rectángulos; por lo tanto, todos los cuadrados tienen cuatro ángulos rectos. Entienden que los atributos que pertenecen a una categoría de figuras bidimensionales también pertenecen a todas las subcategorías de dicha categoría. Por ejemplo, todos los rectángulos tienen cuatro ángulos rectos y los cuadrados son rectángulos; por lo tanto, todos los cuadrados tienen cuatro ángulos rectos. 

               Assess & Differentiate
               
                  15-04: Digital Quick Check
                    Curriculum Standards: Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Entender que los atributos que pertenecen a una categoría de figuras bidimensionales también pertenecen a todas las subcategorías de dicha categoría. Por ejemplo, todos los rectángulos tienen cuatro ángulos rectos y los cuadrados son rectángulos; por lo tanto, todos los cuadrados tienen cuatro ángulos rectos. Entienden que los atributos que pertenecen a una categoría de figuras bidimensionales también pertenecen a todas las subcategorías de dicha categoría. Por ejemplo, todos los rectángulos tienen cuatro ángulos rectos y los cuadrados son rectángulos; por lo tanto, todos los cuadrados tienen cuatro ángulos rectos. 

            15-05: Classifying Quadrilaterals
            
               Develop the Concept: Visual
               
                  Classifying Quadrilaterals: Visual Learning
                    Curriculum Standards: Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Clasificar las figuras bidimensionales dentro de una jerarquía, según sus propiedades. Clasifican las figuras bidimensionales dentro de una jerarquía, según sus propiedades. 

               Assess & Differentiate
               
                  15-05: Digital Quick Check
                    Curriculum Standards: Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Clasificar las figuras bidimensionales dentro de una jerarquía, según sus propiedades. Clasifican las figuras bidimensionales dentro de una jerarquía, según sus propiedades. 

            15-06: Problem Solving: Make and Test Generalizations
            
               Develop the Concept: Visual
               
                  Problem Solving: Make and Test Generalizations: Visual Learning
                    Curriculum Standards: Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Entender que los atributos que pertenecen a una categoría de figuras bidimensionales también pertenecen a todas las subcategorías de dicha categoría. Por ejemplo, todos los rectángulos tienen cuatro ángulos rectos y los cuadrados son rectángulos; por lo tanto, todos los cuadrados tienen cuatro ángulos rectos. Entienden que los atributos que pertenecen a una categoría de figuras bidimensionales también pertenecen a todas las subcategorías de dicha categoría. Por ejemplo, todos los rectángulos tienen cuatro ángulos rectos y los cuadrados son rectángulos; por lo tanto, todos los cuadrados tienen cuatro ángulos rectos. 

               Assess & Differentiate
               
                  15-06: Digital Quick Check
                    Curriculum Standards: Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Entender que los atributos que pertenecen a una categoría de figuras bidimensionales también pertenecen a todas las subcategorías de dicha categoría. Por ejemplo, todos los rectángulos tienen cuatro ángulos rectos y los cuadrados son rectángulos; por lo tanto, todos los cuadrados tienen cuatro ángulos rectos. Entienden que los atributos que pertenecen a una categoría de figuras bidimensionales también pertenecen a todas las subcategorías de dicha categoría. Por ejemplo, todos los rectángulos tienen cuatro ángulos rectos y los cuadrados son rectángulos; por lo tanto, todos los cuadrados tienen cuatro ángulos rectos. 

            Topic 15: Online Topic Test
              Curriculum Standards: Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Entender que los atributos que pertenecen a una categoría de figuras bidimensionales también pertenecen a todas las subcategorías de dicha categoría. Por ejemplo, todos los rectángulos tienen cuatro ángulos rectos y los cuadrados son rectángulos; por lo tanto, todos los cuadrados tienen cuatro ángulos rectos. Entienden que los atributos que pertenecen a una categoría de figuras bidimensionales también pertenecen a todas las subcategorías de dicha categoría. Por ejemplo, todos los rectángulos tienen cuatro ángulos rectos y los cuadrados son rectángulos; por lo tanto, todos los cuadrados tienen cuatro ángulos rectos. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Clasificar las figuras bidimensionales dentro de una jerarquía, según sus propiedades. Clasifican las figuras bidimensionales dentro de una jerarquía, según sus propiedades. Classify two-dimensional figures in a hierarchy of sets and subsets using graphic organizers based on their attributes and properties. Classify two-dimensional figures in a hierarchy of sets and subsets using graphic organizers based on their attributes and properties. Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate. Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate. 

            Alternate Test

            Digital Enhanced Topic Test

            Enhanced Topic Test

         Topic 16: Coordinate Geometry
         
            The Ordered Pair

            Topic 16: Online Topic Readiness
              Curriculum Standards: Explain why a fraction a/b is equivalent to a fraction (n - a) / (n - b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Explain why a fraction a / b is equivalent to a fraction (n - a) / (n - b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Explicar por qué la fracción a/b es equivalente a la fracción (n × a)/(n × b) utilizando modelos visuales de fracciones, observando que el número y el tamaño de las partes difiere aunque las dos fracciones en sí son del mismo tamaño. Utilizar este principio para reconocer y generar fracciones equivalentes. Explican por qué la fracción a/b es equivalente a la fracción (n × a)/(n × b) al utilizar modelos visuales de fracciones, poniendo atención a como el número y el tamaño de las partes difiere aún cuando ambas fracciones son del mismo tamaño. Utilizan este principio para reconocer y generar fracciones equivalentes Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, <, and justify the conclusions, e.g., by using a visual fraction model. Comparan dos fracciones con numeradores distintos y denominadores distintos, por ejemplo, al crear denominadores o numeradores comunes, o al comparar una fracción de referencia como 1/2. Reconocen que las comparaciones son válidas solamente cuando las dos fracciones se refieren al mismo entero. Anotan los resultados de las comparaciones con los símbolos >, = ó <, y justifican las conclusiones, por ejemplo, utilizando un modelo visual de fracciones. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100 ; describe a length as 0.62 meters; locate 0.62 on a number line diagram. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100 ; describe a length as 0.62 meters; locate 0.62 on a number line diagram. Use decimal notation for fractions with denominators 10 or 100. Utilizar la notación decimal para las fracciones con denominadores de 10 ó 100. Por ejemplo, reescribir 0.62 como 62/100; describir una longitud como 0.62 metros; localizar 0.62 en una recta numérica. Utilizan la notación decimal para las fracciones con denominadores de 10 ó 100. Por ejemplo, al escribir 0.62 como 62/100; al describir una longitud como 0.62 metros; al localizar 0.62 en una recta numérica. Represent fractions and decimals to the tenths or hundredths as distances from zero on a number line. Represent fractions and decimals to the tenths or hundredths as distances from zero on a number line. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8.  2-1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8.  2-1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition  by an equation. Justify decompositions,  e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 =
8/8 + 8/8 + 1/8. Entender una fracción a/b cuando a > 1 como una suma de fracciones 1/b. Descomponer de varias maneras una fracción en una suma de fracciones con el mismo denominador, anotando cada descomposición como una ecuación. Justificar las descomposiciones, por ej., utilizando un modelo visual de fracciones. Ejemplos: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. Descomponen de varias maneras una fracción en una suma de fracciones con el mismo denominador, anotando cada descomposición con una ecuación. Justifican las descomposiciones, por ejemplo, utilizando un modelo visual de fracciones. Ejemplos: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8; 21/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Utilizan las cuatro operaciones para resolver problemas verbales sobre distancias, intervalos de tiempo, volúmenes líquidos, masas de objetos y dinero, incluyendo problemas con fracciones simples o decimales, y problemas que requieren expresar las medidas dadas en una unidad más grande en términos de una unidad más pequeña. Representan cantidades medidas utilizando diagramas tales como rectas numéricas con escalas de medición. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100 , and add 3/10 + 4/100 = 34/100. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100 , and add 3/10 + 4/100 = 34/100 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.4 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. Expresar una fracción con denominador 10 como una fracción equivalente con denominador 100 y utilizar esta técnica para sumar dos fracciones con denominadores respectivos de 10 y 100.4 Por ejemplo, expresar 3/10 como 30/100 y sumar 3/10 + 4/100 = 34/100. Expresan una fracción con denominador 10 como una fracción equivalente con denominador 1000, y utilizan esta técnica para sumar dos fracciones con denominadores respectivos de 10 y 1000. Por ejemplo, expresan 3/10 como 30/100 y suman 3/10 + 4/100 = 34/100. 

            16-01: Ordered Pairs
            
               Develop the Concept: Visual
               
                  Ordered Pairs: Visual Learning
                    Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Utilizar un par de rectas numéricas perpendiculares, llamadas ejes, para definir un sistema de coordenadas, situando la intersección de las rectas (el origen) para que coincida con el 0 de cada recta y con un punto determinado en el plano que se pueda ubicar usando un par de números ordenados, llamados coordenadas. Entender que el primer número indica la distancia que se recorre desde el origen en dirección sobre un eje, y el segundo número indica la distancia que se recorre sobre el segundo eje, siguiendo la convención de que los nombre de los dos ejes y los de las coordenadas correspondan (por ej., el eje de las x y la coordenada x, el eje de las y la coordenada y). Utilizan un par de rectas numéricas perpendiculares, llamadas ejes, para definir un sistema de coordenadas, situando la intersección de las rectas (el origen) para que coincida con el 0 de cada recta y con un punto determinado en el plano que se pueda ubicar usando un par de números ordenados, llamados coordenadas. Entienden que el primer número indica la distancia que se recorre desde el origen en dirección sobre un eje, y el segundo número indica la distancia que se recorre sobre el segundo eje, siguiendo la convención de que los nombre de los dos ejes y los de las coordenadas correspondan (por ejemplo, el eje x con la coordenada x, el eje y con la coordenada y). 

               Assess & Differentiate
               
                  16-01: Digital Quick Check
                    Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Utilizar un par de rectas numéricas perpendiculares, llamadas ejes, para definir un sistema de coordenadas, situando la intersección de las rectas (el origen) para que coincida con el 0 de cada recta y con un punto determinado en el plano que se pueda ubicar usando un par de números ordenados, llamados coordenadas. Entender que el primer número indica la distancia que se recorre desde el origen en dirección sobre un eje, y el segundo número indica la distancia que se recorre sobre el segundo eje, siguiendo la convención de que los nombre de los dos ejes y los de las coordenadas correspondan (por ej., el eje de las x y la coordenada x, el eje de las y la coordenada y). Utilizan un par de rectas numéricas perpendiculares, llamadas ejes, para definir un sistema de coordenadas, situando la intersección de las rectas (el origen) para que coincida con el 0 de cada recta y con un punto determinado en el plano que se pueda ubicar usando un par de números ordenados, llamados coordenadas. Entienden que el primer número indica la distancia que se recorre desde el origen en dirección sobre un eje, y el segundo número indica la distancia que se recorre sobre el segundo eje, siguiendo la convención de que los nombre de los dos ejes y los de las coordenadas correspondan (por ejemplo, el eje x con la coordenada x, el eje y con la coordenada y). 

            16-02: Patterns and Graphing
            
               Develop the Concept: Visual
               
                  Patterns and Graphing: Visual Learning
                    Curriculum Standards: Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Representar problemas matemáticos y de la vida diaria al graficar puntos en el primer cuadrante del plano de coordenadas e interpretar los valores de los puntos de las coordenadas según el contexto. Representan problemas matemáticos y del mundo real al representar gráficamente puntos en el primer cuadrante del plano de coordenadas e interpretan los valores de los puntos de las coordenadas según el Contexto. 

               Assess & Differentiate
               
                  16-02: Digital Quick Check
                    Curriculum Standards: Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Representar problemas matemáticos y de la vida diaria al graficar puntos en el primer cuadrante del plano de coordenadas e interpretar los valores de los puntos de las coordenadas según el contexto. Representan problemas matemáticos y del mundo real al representar gráficamente puntos en el primer cuadrante del plano de coordenadas e interpretan los valores de los puntos de las coordenadas según el Contexto. 

            16-03: More Patterns and Graphing
            
               Develop the Concept: Visual
               
                  More Patterns and Graphing: Visual Learning
                    Curriculum Standards: Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Representar problemas matemáticos y de la vida diaria al graficar puntos en el primer cuadrante del plano de coordenadas e interpretar los valores de los puntos de las coordenadas según el contexto. Representan problemas matemáticos y del mundo real al representar gráficamente puntos en el primer cuadrante del plano de coordenadas e interpretan los valores de los puntos de las coordenadas según el Contexto. 

               Assess & Differentiate
               
                  16-03: Digital Quick Check
                    Curriculum Standards: Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Representar problemas matemáticos y de la vida diaria al graficar puntos en el primer cuadrante del plano de coordenadas e interpretar los valores de los puntos de las coordenadas según el contexto. Representan problemas matemáticos y del mundo real al representar gráficamente puntos en el primer cuadrante del plano de coordenadas e interpretan los valores de los puntos de las coordenadas según el Contexto. 

            16-04: Graphing Number Patterns
            
               Develop the Concept: Visual
               
                  Graphing Number Patterns: Visual Learning
                    Curriculum Standards: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule U1Add 3Ue and the starting number 0, and given the rule U1Add 6Ue and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule _Add 3? and the starting number 0, and given the rule _Add 6? and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule ñAdd 3î and the starting number 0, and given the rule ñAdd 6î and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generar dos patrones numéricos a partir de dos reglas dadas. Identificar la relación aparente entre los términos correspondientes. Formar pares ordenados con los términos correspondientes de ambos patrones y graficar los pares ordenados en un plano de coordenadas. Por ejemplo, dada la regla “Sumar 3” y el número 0 inicial, y dada la regla “Sumar 6” y el número 0 inicial, generar los términos en cada secuencia y observar que cada término de una secuencia es el doble que el término correspondiente en la otra secuencia. Explicar informalmente por qué esto es así. Generan dos patrones numéricos utilizando dos reglas dadas. Identifican la relación aparente entre términos correspondientes. Forman pares ordenados que consisten de los términos correspondientes de ambos patrones, y marcan los pares ordenados en un plano de coordenadas. Por ejemplo, dada la regla “Sumar 3” y el número inicial 0, y dada la regla “Sumar 6” y el número inicial 0, generan los términos en cada secuencia y observan que cada término de una secuencia, es el doble que el término correspondiente en la otra secuencia. Explican informalmente por qué esto es así. 

               Assess & Differentiate
               
                  16-04: Digital Quick Check
                    Curriculum Standards: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule U1Add 3Ue and the starting number 0, and given the rule U1Add 6Ue and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule _Add 3? and the starting number 0, and given the rule _Add 6? and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule ñAdd 3î and the starting number 0, and given the rule ñAdd 6î and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generar dos patrones numéricos a partir de dos reglas dadas. Identificar la relación aparente entre los términos correspondientes. Formar pares ordenados con los términos correspondientes de ambos patrones y graficar los pares ordenados en un plano de coordenadas. Por ejemplo, dada la regla “Sumar 3” y el número 0 inicial, y dada la regla “Sumar 6” y el número 0 inicial, generar los términos en cada secuencia y observar que cada término de una secuencia es el doble que el término correspondiente en la otra secuencia. Explicar informalmente por qué esto es así. Generan dos patrones numéricos utilizando dos reglas dadas. Identifican la relación aparente entre términos correspondientes. Forman pares ordenados que consisten de los términos correspondientes de ambos patrones, y marcan los pares ordenados en un plano de coordenadas. Por ejemplo, dada la regla “Sumar 3” y el número inicial 0, y dada la regla “Sumar 6” y el número inicial 0, generan los términos en cada secuencia y observan que cada término de una secuencia, es el doble que el término correspondiente en la otra secuencia. Explican informalmente por qué esto es así. 

            16-05: Problem Solving: Work Backward
            
               Develop the Concept: Visual
               
                  Problem Solving: Work Backward: Visual Learning
                    Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Utilizar un par de rectas numéricas perpendiculares, llamadas ejes, para definir un sistema de coordenadas, situando la intersección de las rectas (el origen) para que coincida con el 0 de cada recta y con un punto determinado en el plano que se pueda ubicar usando un par de números ordenados, llamados coordenadas. Entender que el primer número indica la distancia que se recorre desde el origen en dirección sobre un eje, y el segundo número indica la distancia que se recorre sobre el segundo eje, siguiendo la convención de que los nombre de los dos ejes y los de las coordenadas correspondan (por ej., el eje de las x y la coordenada x, el eje de las y la coordenada y). Utilizan un par de rectas numéricas perpendiculares, llamadas ejes, para definir un sistema de coordenadas, situando la intersección de las rectas (el origen) para que coincida con el 0 de cada recta y con un punto determinado en el plano que se pueda ubicar usando un par de números ordenados, llamados coordenadas. Entienden que el primer número indica la distancia que se recorre desde el origen en dirección sobre un eje, y el segundo número indica la distancia que se recorre sobre el segundo eje, siguiendo la convención de que los nombre de los dos ejes y los de las coordenadas correspondan (por ejemplo, el eje x con la coordenada x, el eje y con la coordenada y). 

               Assess & Differentiate
               
                  16-05: Digital Quick Check
                    Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Utilizar un par de rectas numéricas perpendiculares, llamadas ejes, para definir un sistema de coordenadas, situando la intersección de las rectas (el origen) para que coincida con el 0 de cada recta y con un punto determinado en el plano que se pueda ubicar usando un par de números ordenados, llamados coordenadas. Entender que el primer número indica la distancia que se recorre desde el origen en dirección sobre un eje, y el segundo número indica la distancia que se recorre sobre el segundo eje, siguiendo la convención de que los nombre de los dos ejes y los de las coordenadas correspondan (por ej., el eje de las x y la coordenada x, el eje de las y la coordenada y). Utilizan un par de rectas numéricas perpendiculares, llamadas ejes, para definir un sistema de coordenadas, situando la intersección de las rectas (el origen) para que coincida con el 0 de cada recta y con un punto determinado en el plano que se pueda ubicar usando un par de números ordenados, llamados coordenadas. Entienden que el primer número indica la distancia que se recorre desde el origen en dirección sobre un eje, y el segundo número indica la distancia que se recorre sobre el segundo eje, siguiendo la convención de que los nombre de los dos ejes y los de las coordenadas correspondan (por ejemplo, el eje x con la coordenada x, el eje y con la coordenada y). 

            Topic 16: Online Topic Test
              Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Utilizar un par de rectas numéricas perpendiculares, llamadas ejes, para definir un sistema de coordenadas, situando la intersección de las rectas (el origen) para que coincida con el 0 de cada recta y con un punto determinado en el plano que se pueda ubicar usando un par de números ordenados, llamados coordenadas. Entender que el primer número indica la distancia que se recorre desde el origen en dirección sobre un eje, y el segundo número indica la distancia que se recorre sobre el segundo eje, siguiendo la convención de que los nombre de los dos ejes y los de las coordenadas correspondan (por ej., el eje de las x y la coordenada x, el eje de las y la coordenada y). Utilizan un par de rectas numéricas perpendiculares, llamadas ejes, para definir un sistema de coordenadas, situando la intersección de las rectas (el origen) para que coincida con el 0 de cada recta y con un punto determinado en el plano que se pueda ubicar usando un par de números ordenados, llamados coordenadas. Entienden que el primer número indica la distancia que se recorre desde el origen en dirección sobre un eje, y el segundo número indica la distancia que se recorre sobre el segundo eje, siguiendo la convención de que los nombre de los dos ejes y los de las coordenadas correspondan (por ejemplo, el eje x con la coordenada x, el eje y con la coordenada y). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Representar problemas matemáticos y de la vida diaria al graficar puntos en el primer cuadrante del plano de coordenadas e interpretar los valores de los puntos de las coordenadas según el contexto. Representan problemas matemáticos y del mundo real al representar gráficamente puntos en el primer cuadrante del plano de coordenadas e interpretan los valores de los puntos de las coordenadas según el Contexto. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule U1Add 3Ue and the starting number 0, and given the rule U1Add 6Ue and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule _Add 3? and the starting number 0, and given the rule _Add 6? and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule ñAdd 3î and the starting number 0, and given the rule ñAdd 6î and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generar dos patrones numéricos a partir de dos reglas dadas. Identificar la relación aparente entre los términos correspondientes. Formar pares ordenados con los términos correspondientes de ambos patrones y graficar los pares ordenados en un plano de coordenadas. Por ejemplo, dada la regla “Sumar 3” y el número 0 inicial, y dada la regla “Sumar 6” y el número 0 inicial, generar los términos en cada secuencia y observar que cada término de una secuencia es el doble que el término correspondiente en la otra secuencia. Explicar informalmente por qué esto es así. Generan dos patrones numéricos utilizando dos reglas dadas. Identifican la relación aparente entre términos correspondientes. Forman pares ordenados que consisten de los términos correspondientes de ambos patrones, y marcan los pares ordenados en un plano de coordenadas. Por ejemplo, dada la regla “Sumar 3” y el número inicial 0, y dada la regla “Sumar 6” y el número inicial 0, generan los términos en cada secuencia y observan que cada término de una secuencia, es el doble que el término correspondiente en la otra secuencia. Explican informalmente por qué esto es así. Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution. Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate. Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution. Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate. 

            Alternate Test

            Digital Enhanced Topic Test

            Enhanced Topic Test

         Grade 5: Online Topics 13-16: Benchmark Test
           Curriculum Standards: Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convertir unidades de medida estándar de diferentes tamaños dentro de un sistema de medición determinado (por ej., convertir 5 cm a 0.05 m), y utilizar estas conversiones para resolver problemas de varios pasos de la vida diaria. Convierten unidades de medición estándar de diferentes tamaños dentro de un sistema de medición dado (por ejemplo, convierten 5 cm en 0.05 m), y utilizan estas conversiones en la solución de problemas de varios pasos y del mundo real. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Entender que los atributos que pertenecen a una categoría de figuras bidimensionales también pertenecen a todas las subcategorías de dicha categoría. Por ejemplo, todos los rectángulos tienen cuatro ángulos rectos y los cuadrados son rectángulos; por lo tanto, todos los cuadrados tienen cuatro ángulos rectos. Entienden que los atributos que pertenecen a una categoría de figuras bidimensionales también pertenecen a todas las subcategorías de dicha categoría. Por ejemplo, todos los rectángulos tienen cuatro ángulos rectos y los cuadrados son rectángulos; por lo tanto, todos los cuadrados tienen cuatro ángulos rectos. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Clasificar las figuras bidimensionales dentro de una jerarquía, según sus propiedades. Clasifican las figuras bidimensionales dentro de una jerarquía, según sus propiedades. Describe the key attributes of the coordinate plane, including perpendicular number lines (axes) where the intersection (origin) of the two lines coincides with zero on each number line and the given point (0, 0); the x-coordinate, the first number in an ordered pair, indicates movement parallel to the x-axis starting at the origin; and the y-coordinate, the second number, indicates movement parallel to the y-axis starting at the origin. Describe the process for graphing ordered pairs of numbers in the first quadrant of the coordinate plane. Describe the key attributes of the coordinate plane, including perpendicular number lines (axes) where the intersection (origin) of the two lines coincides with zero on each number line and the given point (0, 0); the x-coordinate, the first number in an ordered pair, indicates movement parallel to the x-axis starting at the origin; and the y-coordinate, the second number, indicates movement parallel to the y-axis starting at the origin. Describe the process for graphing ordered pairs of numbers in the first quadrant of the coordinate plane. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Representar problemas matemáticos y de la vida diaria al graficar puntos en el primer cuadrante del plano de coordenadas e interpretar los valores de los puntos de las coordenadas según el contexto. Representan problemas matemáticos y del mundo real al representar gráficamente puntos en el primer cuadrante del plano de coordenadas e interpretan los valores de los puntos de las coordenadas según el Contexto. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Utilizar un par de rectas numéricas perpendiculares, llamadas ejes, para definir un sistema de coordenadas, situando la intersección de las rectas (el origen) para que coincida con el 0 de cada recta y con un punto determinado en el plano que se pueda ubicar usando un par de números ordenados, llamados coordenadas. Entender que el primer número indica la distancia que se recorre desde el origen en dirección sobre un eje, y el segundo número indica la distancia que se recorre sobre el segundo eje, siguiendo la convención de que los nombre de los dos ejes y los de las coordenadas correspondan (por ej., el eje de las x y la coordenada x, el eje de las y la coordenada y). Utilizan un par de rectas numéricas perpendiculares, llamadas ejes, para definir un sistema de coordenadas, situando la intersección de las rectas (el origen) para que coincida con el 0 de cada recta y con un punto determinado en el plano que se pueda ubicar usando un par de números ordenados, llamados coordenadas. Entienden que el primer número indica la distancia que se recorre desde el origen en dirección sobre un eje, y el segundo número indica la distancia que se recorre sobre el segundo eje, siguiendo la convención de que los nombre de los dos ejes y los de las coordenadas correspondan (por ejemplo, el eje x con la coordenada x, el eje y con la coordenada y). Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8 ). Use operations on fractions for this grade to solve problems involving information presented in line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8 ). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8 ). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Hacer un diagrama de puntos para mostrar un conjunto de medidas en unidades fraccionarias (1/2, 1/4, 1/8). Efectuar operaciones con fracciones apropiadas a este grado, para resolver problemas relacionados con la información presentada en los diagramas de puntos. Por ejemplo, dadas diferentes medidas de líquido en vasos de laboratorio idénticos, hallar la cantidad de líquido que cada vaso contiene, si la cantidad total en todos los vasos fuera redistribuida igualmente. Hacen un diagrama de puntos para mostrar un conjunto de medidas en unidades fraccionarias (1/2, 1/4, 1/8). Efectúan operaciones con fracciones apropiadas a este grado, para resolver problemas relacionados con la información presentada en los diagramas de puntos. Solve problems by calculating conversions within a measurement system, customary or metric. Solve problems by calculating conversions within a measurement system, customary or metric. Classify two-dimensional figures in a hierarchy of sets and subsets using graphic organizers based on their attributes and properties. Classify two-dimensional figures in a hierarchy of sets and subsets using graphic organizers based on their attributes and properties. 

         Grade 5: Online End of Year Test
           Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ 1/5 , and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 x (1/5) = 4. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ 1/5 , and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 x (1/5) = 4. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 … 1/5 , and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 … (1/5 ) = 20 because 20 x (1/5 ) = 4. Aplicar y ampliar los conocimientos previos sobre la división para dividir fracciones unitarias por números enteros no negativos y números enteros no negativos por fracciones unitarias. Interpretar la división de un número entero no negativo por una fracción unitaria y calcular este tipo de cocientes. Por ejemplo, inventar un contexto para 4 ÷ (1/5), y utilizar un modelo visual de fracciones para expresar el cociente. Utilizar la relación entre la multiplicación y la división para explicar que 4 ÷ (1/5) =20 porque 20 ×(1/5)= 4. Interpretan la división de un número entero entre una fracción unitaria y calculan sus cocientes. Por ejemplo, crean en el contexto de un cuento 4 ÷ (1/5), y utilizan un modelo visual de fracciones para expresar el cociente. Utilizan la relación entre la multiplicación y la división para explicar que 4 ÷ (1/5) =20 porque 20 ×(1/5)= 4. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8 ). Use operations on fractions for this grade to solve problems involving information presented in line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8 ). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8 ). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Hacer un diagrama de puntos para mostrar un conjunto de medidas en unidades fraccionarias (1/2, 1/4, 1/8). Efectuar operaciones con fracciones apropiadas a este grado, para resolver problemas relacionados con la información presentada en los diagramas de puntos. Por ejemplo, dadas diferentes medidas de líquido en vasos de laboratorio idénticos, hallar la cantidad de líquido que cada vaso contiene, si la cantidad total en todos los vasos fuera redistribuida igualmente. Hacen un diagrama de puntos para mostrar un conjunto de medidas en unidades fraccionarias (1/2, 1/4, 1/8). Efectúan operaciones con fracciones apropiadas a este grado, para resolver problemas relacionados con la información presentada en los diagramas de puntos. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 , by observing that 3/7 < 1/2 . Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 , by observing that 3/7 < 1/2 . Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Resolver problemas verbales de suma y resta de fracciones que se refieran a un todo, incluyendo casos de denominadores distintos; por ejemplo, empleando modelos visuales de fracciones o ecuaciones para representar el problema. Utilizar las fracciones de referencia y el sentido numérico para hacer cálculos mentales y evaluar la lógica de las respuestas. Por ejemplo, reconocer como incorrecto el resultado 2/5 + 1/2 = 3/7, observando que 3/7 < 1/2. Resuelven problemas verbales de suma y resta de fracciones que se refieran a un entero, incluyendo casos de denominadores distintos, por ejemplo, al emplear modelos visuales de fracciones o ecuaciones para representar el problema. Utilizan las fracciones de referencia y el sentido numérico para hacer cálculos mentales y evaluar la lógica de las respuestas. Por ejemplo, reconocen como incorrecto el resultado 2/5 + 1/2 = 3/7, observando que 3/7 < 1/2. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Representar problemas matemáticos y de la vida diaria al graficar puntos en el primer cuadrante del plano de coordenadas e interpretar los valores de los puntos de las coordenadas según el contexto. Representan problemas matemáticos y del mundo real al representar gráficamente puntos en el primer cuadrante del plano de coordenadas e interpretan los valores de los puntos de las coordenadas según el Contexto. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Utilizar un par de rectas numéricas perpendiculares, llamadas ejes, para definir un sistema de coordenadas, situando la intersección de las rectas (el origen) para que coincida con el 0 de cada recta y con un punto determinado en el plano que se pueda ubicar usando un par de números ordenados, llamados coordenadas. Entender que el primer número indica la distancia que se recorre desde el origen en dirección sobre un eje, y el segundo número indica la distancia que se recorre sobre el segundo eje, siguiendo la convención de que los nombre de los dos ejes y los de las coordenadas correspondan (por ej., el eje de las x y la coordenada x, el eje de las y la coordenada y). Utilizan un par de rectas numéricas perpendiculares, llamadas ejes, para definir un sistema de coordenadas, situando la intersección de las rectas (el origen) para que coincida con el 0 de cada recta y con un punto determinado en el plano que se pueda ubicar usando un par de números ordenados, llamados coordenadas. Entienden que el primer número indica la distancia que se recorre desde el origen en dirección sobre un eje, y el segundo número indica la distancia que se recorre sobre el segundo eje, siguiendo la convención de que los nombre de los dos ejes y los de las coordenadas correspondan (por ejemplo, el eje x con la coordenada x, el eje y con la coordenada y). Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold wholenumber products as volumes, e.g., to represent the associative property of multiplication. Apply the formulas V = l x w x h and V = b x h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold wholenumber products as volumes, e.g., to represent the associative property of multiplication. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold wholenumber products as volumes, e.g., to represent the associative property of multiplication. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Apply the formulas V = l x w x h and V = b x h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. Relacionar el volumen con las operaciones de multiplicación y suma para resolver problemas matemáticos y de la vida diaria relativos al volumen. Hallar el volumen de un prisma rectangular recto con lados que se miden en números enteros no negativos, llenando el prisma con unidades cúbicas, y demostrar que el volumen es el mismo que se hallaría multiplicando la altura por el área de la base. Representar tres veces el producto de un número entero no negativo como un volumen, por ej., para representar la propiedad asociativa de la multiplicación. Relacionar el volumen con las operaciones de multiplicación y suma para resolver problemas matemáticos y de la vida diaria relativos al volumen. Aplicar las fórmulas V = l × a × h   y   V = b × h de los prismas rectangulares para hallar los volúmenes de prismas rectangulares rectos cuyos lados se miden en números enteros no negativos, en el contexto de resolver problemas matemáticos y de la vida diaria. Hallan el volumen de un prisma rectangular recto con lados que se miden en números enteros, llenando el prisma con unidades cúbicas, y demostrando que el volumen es el mismo que se hallaría multiplicando la altura por el área de la base. Representan tres veces el producto de un número entero como un volumen, por ejemplo, para representar la propiedad asociativa de la multiplicación. Aplican las fórmulas V = l × a × h y V = b × h de los prismas rectangulares para hallar los volúmenes de prismas rectangulares rectos cuyos lados se miden en números enteros, en el contexto de resolver problemas matemáticos y del mundo real. A cube with side length 1 unit, called a U1unit cube,Ue is said to have U1one cubic unitUe of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A cube with side length 1 unit, called a _unit cube,? is said to have _one cubic unit? of volume, and can be used to measure volume. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A cube with side length 1 unit, called a ñunit cube,î is said to have ñone cubic unitî of volume, and can be used to measure volume. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Reconocer el volumen como un atributo de las figuras sólidas y entender los conceptos de la medición del volumen. Se dice que un cubo con lados de 1 unidad, llamado “bloque de unidad”, tiene “una unidad cúbica” de volumen, y ésta se puede utilizar para medir el volumen. Reconocer el volumen como un atributo de las figuras sólidas y entender los conceptos de la medición del volumen. Se dice que una figura sólida que se puede rellenar con n bloques de unidad sin dejar espacios o superposiciones tiene un volumen de n unidades cúbicas. Se dice que un cubo con lados de 1 unidad, llamado “unidad cúbica”, tiene “una unidad cúbica” de volumen, y ésta se puede utilizar para medir el volumen. Se dice que una figura sólida que se puede rellenar con la unidad cúbica n sin dejar espacios o superposiciones tiene un volumen de n unidades cúbicas. Represent the value of the digit in decimals through the thousandths using expanded notation and numerals. Represent the value of the digit in decimals through the thousandths using expanded notation and numerals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Sumar, restar, multiplicar y dividir números decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionar la estrategia a algún método escrito y explicar el razonamiento empleado. Suman, restan, multiplican, y dividen decimales hasta las centésimas utilizando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la suma y la resta; relacionan la estrategia a algún método escrito y explican el razonamiento empleado. Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Utilizar la comprensión del valor de posición para redondear números decimales a cualquier lugar de redondeo. Utilizan el entendimiento del valor de posición para redondear decimales a cualquier lugar. Represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects and pictorial models and properties of operations. Represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects and pictorial models and properties of operations. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Hallar números enteros no negativos como cocientes de números enteros no negativos con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y la relación entre la multiplicación y la división. Ilustrar y explicar el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Hallan números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule U1Add 3Ue and the starting number 0, and given the rule U1Add 6Ue and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule _Add 3? and the starting number 0, and given the rule _Add 6? and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule ñAdd 3î and the starting number 0, and given the rule ñAdd 6î and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generar dos patrones numéricos a partir de dos reglas dadas. Identificar la relación aparente entre los términos correspondientes. Formar pares ordenados con los términos correspondientes de ambos patrones y graficar los pares ordenados en un plano de coordenadas. Por ejemplo, dada la regla “Sumar 3” y el número 0 inicial, y dada la regla “Sumar 6” y el número 0 inicial, generar los términos en cada secuencia y observar que cada término de una secuencia es el doble que el término correspondiente en la otra secuencia. Explicar informalmente por qué esto es así. Generan dos patrones numéricos utilizando dos reglas dadas. Identifican la relación aparente entre términos correspondientes. Forman pares ordenados que consisten de los términos correspondientes de ambos patrones, y marcan los pares ordenados en un plano de coordenadas. Por ejemplo, dada la regla “Sumar 3” y el número inicial 0, y dada la regla “Sumar 6” y el número inicial 0, generan los términos en cada secuencia y observan que cada término de una secuencia, es el doble que el término correspondiente en la otra secuencia. Explican informalmente por qué esto es así. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Explicar los patrones en la cantidad de ceros que tiene un producto cuando se multiplica un número por una potencia de 10, y explicar los patrones al mover el punto decimal cuando hay que multiplicar o dividir un número decimal por una potencia de 10. Utilizar números enteros no negativos como exponentes para denotar la potencia de 10. Explican los patrones en la cantidad de ceros que tiene un producto cuando se multiplica un número por una potencia de 10, y explican los patrones en la posición del punto decimal cuando hay que multiplicar o dividir un decimal por una potencia de 10. Utilizan número enteros como exponentes para denotar la potencia de 10. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Utilizar paréntesis, corchetes o llaves en las expresiones numéricas y evaluar las expresiones con estos símbolos. Utilizan paréntesis, corchetes o llaves en expresiones numéricas, y evaluan expresiones con estos símbolos. Classify two-dimensional figures in a hierarchy of sets and subsets using graphic organizers based on their attributes and properties. Classify two-dimensional figures in a hierarchy of sets and subsets using graphic organizers based on their attributes and properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Entender que los atributos que pertenecen a una categoría de figuras bidimensionales también pertenecen a todas las subcategorías de dicha categoría. Por ejemplo, todos los rectángulos tienen cuatro ángulos rectos y los cuadrados son rectángulos; por lo tanto, todos los cuadrados tienen cuatro ángulos rectos. Entienden que los atributos que pertenecen a una categoría de figuras bidimensionales también pertenecen a todas las subcategorías de dicha categoría. Por ejemplo, todos los rectángulos tienen cuatro ángulos rectos y los cuadrados son rectángulos; por lo tanto, todos los cuadrados tienen cuatro ángulos rectos. Add and subtract positive rational numbers fluently. Add and subtract positive rational numbers fluently. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convertir unidades de medida estándar de diferentes tamaños dentro de un sistema de medición determinado (por ej., convertir 5 cm a 0.05 m), y utilizar estas conversiones para resolver problemas de varios pasos de la vida diaria. Convierten unidades de medición estándar de diferentes tamaños dentro de un sistema de medición dado (por ejemplo, convierten 5 cm en 0.05 m), y utilizan estas conversiones en la solución de problemas de varios pasos y del mundo real. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Clasificar las figuras bidimensionales dentro de una jerarquía, según sus propiedades. Clasifican las figuras bidimensionales dentro de una jerarquía, según sus propiedades. Interpret the product (a/b) x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷ b. For example, use a visual fraction model to show (2/3) x 4 = 8/3 , and create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd.) Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷ b. For example, use a visual fraction model to show (2/3) x 4 = 8/3 , and create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd.) Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q … b. For example, use a visual fraction model to show (2/3) x 4 = 8/3 , and create a story context for this equation. Do the same with (2/3) x ( 4/5) = 8/15. (In general, (a/b) x (c/d ) = ac/bd.) Aplicar y ampliar los conocimientos previos sobre la multiplicación para multiplicar una fracción o un número entero por una fracción. Interpretar el producto (a/b) × q como a partes de la repartición de q en partes iguales de b; de manera equivalente, como el resultado de la secuencia de operaciones a × q ÷ b. Por ejemplo, emplear un modelo visual de fracciones para representar (2/3) × 4 = 8/3, e inventar un contexto para esta ecuación. Hacer lo mismo con (2/3) ×(4/5) = 8/15. (En general, (a/b) ×(c/d) = ac/bd). Interpretan el producto (a/b) × q como tantas partes a de la repartición de q en partes iguales de b; de manera equivalente, como el resultado de la secuencia de operaciones a × q ÷ b. Por ejemplo, al emplear un modelo visual de fracciones para representar (2/3) × 4 = 8/3, y crear un contexto para esta ecuación. Hacen lo mismo con (2/3) × (4/5) = 8/15. (En general, (a /b) × (c /d) = ac/bd). Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc/bd) . Sumar y restar fracciones con denominadores distintos (inclusive números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) /bd). Suman y restan fracciones con denominadores distintos (incluyendo números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) / bd) Solve problems by calculating conversions within a measurement system, customary or metric. Solve problems by calculating conversions within a measurement system, customary or metric. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100+ 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100_ + 2 x (1/1000). Read, write, and compare decimals to thousandths. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100+ 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100_ + 2 x (1/1000). Read, write, and compare decimals to thousandths. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100+ 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100_ + 2 x (1/1000). Leer, escribir y comparar números decimales hasta las milésimas. Leer, escribir y comparar números decimales hasta las milésimas usando números de base diez, números en palabras y la forma desarrollada; por ejemplo, 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1,000). Leen y escriben decimales hasta las milésimas usando números de base diez, los nombres de los números y su forma desarrollada; por ejemplo, 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiplicar números enteros no negativos de varios dígitos con fluidez, utilizando el algoritmo convencional. Multiplican números enteros de varios dígitos con fluidez, utilizando el algoritmo convencional. 

         Topic 17: Step Up to Grade 6
         
            17_01: Understanding Ratios
            
               Develop the Concept: Visual
               
                  Understanding Ratios: Visual Learning
                    Curriculum Standards: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. Entender el concepto de una razón y utilizar el lenguaje de las razones para describir una relación de razón entre dos cantidades. Por ejemplo, “La razón de alas a picos en una pajarera del zoológico era 2:1, porque por cada dos alas había un pico”. “Por cada voto que el candidato A recibió, el candidato C recibió casi tres votos”. Entender el concepto de una razón y utilizar el lenguaje de las razones para describir una relación de razón entre dos cantidades. Por ejemplo, “La razón de alas a picos en una pajarera del zoológico era 2:1, porque por cada dos alas había un pico”. “Por cada voto que el candidato A recibió, el candidato C recibió casi tres votos”. 

            17_02: Understanding Rates and Unit Rates
            
               Develop the Concept: Visual
               
                  Understanding Rates: Visual Learning
                    Curriculum Standards: Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. Understand the concept of a unit rate a/b associated with a ratio a:b with b _ 0, and use rate language in the context of a ratio relationship. Understand the concept of a unit rate a/b associated with a ratio a:b with b ­ 0, and use rate language in the context of a ratio relationship. Entender el concepto de una tasa por unidad a/b asociada con una razón a:b para b ? 0, y utilizar el lenguaje de las tasas en el contexto de una relación de razones. Por ejemplo, “Esta receta tiene una razón de 3 tazas de harina por 4 tazas de azúcar, por lo que hay 3/4 de taza de harina por cada taza de azúcar”. “Pagamos $75 por 15 hamburguesas, lo cual es una tasa de $5 por hamburguesa”. Entender el concepto de una tasa por unidad a/b asociada con una razón a:b para b ? 0, y utilizar el lenguaje de las tasas en el contexto de una relación de razones. Por ejemplo, “Esta receta tiene una razón de 3 tazas de harina por 4 tazas de azúcar, por lo que hay 3/4 de taza de harina por cada taza de azúcar”. “Pagamos $75 por 15 hamburguesas, lo cual es una tasa de $5 por hamburguesa”. 

            17_03: Equal Ratios and Proportions
            
               Develop the Concept: Visual
               
                  Equivalent Ratios: Visual Learning
                    Curriculum Standards: Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. Use ratio and rate reasoning to solve real world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. Use ratio and rate reasoning to solve real world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. Crean tablas de razones equivalentes relacionando cantidades a medidas de números enteros, hallan valores que faltan en las tablas, y marcan pares de valores en el plano de coordenadas. Utilizan tablas para comparar razones. Utilizar el razonamiento sobre las razones y tasas para resolver problemas matemáticos y de la vida diaria, por ej., pensando sobre tablas de razones equivalentes, diagramas de cintas, diagramas de rectas numéricas dobles o ecuaciones. Crear tablas de razones equivalentes relacionando cantidades a medidas de números enteros no negativos, hallar valores que faltan en las tablas y marcar pares de valores en el plano de coordenadas. Utilizar tablas para comparar razones. 

            17_04: Using Ratio Tables
            
               Develop the Concept: Visual
               
                  Using Ratio Tables: Visual Learning

            17_05: Comparing Rates
            
               Develop the Concept: Visual
               
                  Comparing Rates: Visual Learning
                    Curriculum Standards: Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Solve unit rate problems including those involving unit pricing and constant speed. Solve unit rate problems including those involving unit pricing and constant speed. Resuelven problemas sobre tasas de unidad, incluyendo aquellos problemas relacionados al precio por unidad y la velocidad constante. Por ejemplo, si toma 7 horas para cortar 4 céspedes, entonces, según esa tasa, ¿cuántos céspedes se podrían cortar en 35horas? ¿A qué tasa se cortarían los céspedes? Utilizar el razonamiento sobre las razones y tasas para resolver problemas matemáticos y de la vida diaria, por ej., pensando sobre tablas de razones equivalentes, diagramas de cintas, diagramas de rectas numéricas dobles o ecuaciones. Resolver problemas sobre tasas de unidad, incluyendo aquellos problemas relacionados al precio por unidad y la velocidad constante. Por ejemplo, si toma 7 horas podar 4 jardines, entonces, según esa tasa, ¿cuántos jardines podrían podarse en 35 horas? ¿A qué tasa se estaban podando los jardines? 

            17_06: Multiplying with Zeros in the Product
            
               Develop the Concept: Visual
               
                  Multiplying with Zeros in the Product: Visual Learning
                    Curriculum Standards: Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. Sumar, restar, multiplicar y dividir números decimales de múltiples dígitos utilizando el algoritmo convencional para cada operación. Sumar, restar, multiplicar y dividir números decimales de múltiples dígitos utilizando el algoritmo convencional para cada operación. 

            17_07: Greatest Common Factor
            
               Develop the Concept: Visual
               
                  Greatest Common Factor: Visual Learning
                    Curriculum Standards: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1?100 with a common factor as a multiple of a sum of two whole numbers with no common factor. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1_100 with a common factor as a multiple of a sum of two whole numbers with no common factor. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1Ð100 with a common factor as a multiple of a sum of two whole numbers with no common factor. Hallar el máximo común divisor de dos números enteros no negativos menores que o iguales a 100, y hallar el mínimo común múltiplo de dos números enteros no negativos menores que o iguales a 12. Utilizar la propiedad distributiva para expresar la suma de dos números enteros entre 1 y 100 que tienen un factor común como un múltiplo de la suma de dos números enteros que no tienen un factor común. Por ejemplo, expresar 36 + 8 como 4(9 +2). Hallar el máximo común divisor de dos números enteros no negativos menores que o iguales a 100, y hallar el mínimo común múltiplo de dos números enteros no negativos menores que o iguales a 12. Utilizar la propiedad distributiva para expresar la suma de dos números enteros entre 1 y 100 que tienen un factor común como un múltiplo de la suma de dos números enteros que no tienen un factor común. Por ejemplo, expresar 36 + 8 como 4(9 +2). 

            17_08: Using Expressions to Describe Patterns
            
               Develop the Concept: Visual
               
                  Using Expressions to Describe Patterns: Visual Learning
                    Curriculum Standards: Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y Write, read, and evaluate expressions in which letters stand for numbers. Write expressions that record operations with numbers and with letters standing for numbers. Write, read, and evaluate expressions in which letters stand for numbers. Write expressions that record operations with numbers and with letters standing for numbers. Escribir expresiones que representan operaciones mediante números y letras que simbolizan números. Por ejemplo, expresar el cálculo “Restar y de 5” como 5 - y. Escribir, leer y evaluar expresiones en las que las letras representan números. Escribir expresiones que representan operaciones mediante números y letras que simbolizan números. Por ejemplo, expresar el cálculo “Restar y de 5” como 5 - y. 

            17-09: Properties of Operations
            
               Develop the Concept: Visual
               
                  Properties of Operations: Visual Learning
                    Curriculum Standards: Apply the properties of operations to generate equivalent expressions. Apply the properties of operations to generate equivalent expressions. Apply the properties of operations to generate equivalent expressions. Aplicar las propiedades de las operaciones para generar expresiones equivalentes. Por ejemplo, aplicar la propiedad distributiva a la expresión 3 (2 + x) para obtener la expresión equivalente 6 + 3x; aplicar la propiedad distributiva a la expresión 24 x 18y para obtener la expresión equivalente 6(4x +3y); aplicar las propiedades de las operaciones a y +y +y para obtener la expresión equivalente 3y. Aplicar las propiedades de las operaciones para generar expresiones equivalentes. Por ejemplo, aplicar la propiedad distributiva a la expresión 3 (2 + x) para obtener la expresión equivalente 6 + 3x; aplicar la propiedad distributiva a la expresión 24 x 18y para obtener la expresión equivalente 6(4x +3y); aplicar las propiedades de las operaciones a y +y +y para obtener la expresión equivalente 3y. 

            17_10: Surface Area
            
               Develop the Concept: Visual
               
                  Surface Area of Prisms and Pyramids: Visual Learning
                    Curriculum Standards: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. Representar figuras tridimensionales utilizando modelos planos compuestos de rectángulos y triángulos, y utilizar los modelos planos para hallar el área total de estas figuras. Aplicar estas técnicas al contexto de la resolución de problemas de la vida diaria y problemas matemáticos. 

         Grade 5: Next Generation Assessment Practice Test

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              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            05-02: Printable Digital Quick Check
              Intended Role: Instructor

            05-02: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            05-03: Printable Digital Quick Check
              Intended Role: Instructor

            05-03: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            05-04: Printable Digital Quick Check
              Intended Role: Instructor

            05-04: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            05-05: Printable Digital Quick Check
              Intended Role: Instructor

            05-05: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            05-06: Printable Digital Quick Check
              Intended Role: Instructor

            05-06: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            05-07: Printable Digital Quick Check
              Intended Role: Instructor

            05-07: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            05-08: Printable Digital Quick Check
              Intended Role: Instructor

            05-08: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Topic Test
              Intended Role: Instructor

            Topic 05: Printable Online Topic Test
              Intended Role: Instructor

            Topic 05: Online Topic Test: Answer Key
              Intended Role: Instructor

            Topic 05: Digital Enhanced Topic Test Teacher Support
              Intended Role: Instructor

            Topic 05: Enhanced Topic Test Teacher Support
              Intended Role: Instructor

            Topic Readiness
              Intended Role: Instructor

            Topic 06: Printable Online Topic Readiness
              Intended Role: Instructor

            Topic 06: Online Topic Readiness: Answer Key
              Intended Role: Instructor

            Home-School Connection Letters
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            06-01: Printable Digital Quick Check
              Intended Role: Instructor

            06-01: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            06-02: Printable Digital Quick Check
              Intended Role: Instructor

            06-02: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            06-03: Printable Digital Quick Check
              Intended Role: Instructor

            06-03: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            06-04: Printable Digital Quick Check
              Intended Role: Instructor

            06-04: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            06-05: Printable Digital Quick Check
              Intended Role: Instructor

            06-05: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            06-06: Printable Digital Quick Check
              Intended Role: Instructor

            06-06: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            06-07: Printable Digital Quick Check
              Intended Role: Instructor

            06-07: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Topic Test
              Intended Role: Instructor

            Topic 06: Printable Online Topic Test
              Intended Role: Instructor

            Topic 06: Online Topic Test: Answer Key
              Intended Role: Instructor

            Topic 06: Digital Enhanced Topic Test Teacher Support
              Intended Role: Instructor

            Topic 06: Enhanced Topic Test Teacher Support
              Intended Role: Instructor

            Topic Readiness
              Intended Role: Instructor

            Topic 07: Printable Online Topic Readiness
              Intended Role: Instructor

            Topic 07: Online Topic Readiness: Answer Key
              Intended Role: Instructor

            Home-School Connection Letters
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            07-01: Printable Digital Quick Check
              Intended Role: Instructor

            07-01: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            07-02: Printable Digital Quick Check
              Intended Role: Instructor

            07-02: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            07-03: Printable Digital Quick Check
              Intended Role: Instructor

            07-03: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            07-04: Printable Digital Quick Check
              Intended Role: Instructor

            07-04: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            07-05: Printable Digital Quick Check
              Intended Role: Instructor

            07-05: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            07-06: Printable Digital Quick Check
              Intended Role: Instructor

            07-06: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            07-07: Printable Digital Quick Check
              Intended Role: Instructor

            07-07: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Topic Test
              Intended Role: Instructor

            Topic 07: Printable Online Topic Test
              Intended Role: Instructor

            Topic 07: Online Topic Test: Answer Key
              Intended Role: Instructor

            Topic 07: Digital Enhanced Topic Test Teacher Support
              Intended Role: Instructor

            Topic 07: Enhanced Topic Test Teacher Support
              Intended Role: Instructor

            Topic Readiness
              Intended Role: Instructor

            Topic 08: Printable Online Topic Readiness
              Intended Role: Instructor

            Topic 08: Online Topic Readiness: Answer Key
              Intended Role: Instructor

            Home-School Connection Letters
              Intended Role: Instructor

            Vocabulary Cards
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            08-01: Printable Digital Quick Check
              Intended Role: Instructor

            08-01: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            08-02: Printable Digital Quick Check
              Intended Role: Instructor

            08-02: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            08-03: Printable Digital Quick Check
              Intended Role: Instructor

            08-03: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            08-04: Printable Digital Quick Check
              Intended Role: Instructor

            08-04: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            08-05: Printable Digital Quick Check
              Intended Role: Instructor

            08-05: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            08-06: Printable Digital Quick Check
              Intended Role: Instructor

            08-06: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            08-07: Printable Digital Quick Check
              Intended Role: Instructor

            08-07: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Topic Test
              Intended Role: Instructor

            Topic 08: Printable Online Topic Test
              Intended Role: Instructor

            Topic 08: Online Topic Test: Answer Key
              Intended Role: Instructor

            Topic 08: Digital Enhanced Topic Test Teacher Support
              Intended Role: Instructor

            Topic 08: Enhanced Topic Test Teacher Support
              Intended Role: Instructor

            Grade 4: End of Year Test
              Intended Role: Instructor

            Printable Online Topics 05-08: Benchmark Test
              Intended Role: Instructor

            Online Topics 05-08: Benchmark Test: Answer Key
              Intended Role: Instructor

            Topic Readiness
              Intended Role: Instructor

            Topic 09: Printable Online Topic Readiness
              Intended Role: Instructor

            Topic 09: Online Topic Readiness: Answer Key
              Intended Role: Instructor

            Home-School Connection Letters
              Intended Role: Instructor

            Vocabulary Cards
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            09-01: Printable Digital Quick Check
              Intended Role: Instructor

            09-01: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            09-02: Printable Digital Quick Check
              Intended Role: Instructor

            09-02: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            09-03: Printable Digital Quick Check
              Intended Role: Instructor

            09-03: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            09-04: Printable Digital Quick Check
              Intended Role: Instructor

            09-04: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            09-05: Printable Digital Quick Check
              Intended Role: Instructor

            09-05: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            09-06: Printable Digital Quick Check
              Intended Role: Instructor

            09-06: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            09-07: Printable Digital Quick Check
              Intended Role: Instructor

            09-07: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Topic Test
              Intended Role: Instructor

            Topic 09: Printable Online Topic Test
              Intended Role: Instructor

            Topic 09: Online Topic Test: Answer Key
              Intended Role: Instructor

            Topic 09: Digital Enhanced Topic Test Teacher Support
              Intended Role: Instructor

            Topic 09: Enhanced Topic Test Teacher Support
              Intended Role: Instructor

            Topic Readiness
              Intended Role: Instructor

            Topic 10: Printable Online Topic Readiness
              Intended Role: Instructor

            Topic 10: Online Topic Readiness: Answer Key
              Intended Role: Instructor

            Home-School Connection Letters
              Intended Role: Instructor

            Vocabulary Cards
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            10-01: Printable Digital Quick Check
              Intended Role: Instructor

            10-01: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            10-02: Printable Digital Quick Check
              Intended Role: Instructor

            10-02: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            10-03: Printable Digital Quick Check
              Intended Role: Instructor

            10-03: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            10-04: Printable Digital Quick Check
              Intended Role: Instructor

            10-04: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            10-05: Printable Digital Quick Check
              Intended Role: Instructor

            10-05: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            10-06: Printable Digital Quick Check
              Intended Role: Instructor

            10-06: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Topic Test
              Intended Role: Instructor

            Topic 10: Printable Online Topic Test
              Intended Role: Instructor

            Topic 10: Online Topic Test: Answer Key
              Intended Role: Instructor

            Topic 10: Digital Enhanced Topic Test Teacher Support
              Intended Role: Instructor

            Topic 10: Enhanced Topic Test Teacher Support
              Intended Role: Instructor

            Topic Readiness
              Intended Role: Instructor

            Topic 11: Printable Online Topic Readiness
              Intended Role: Instructor

            Topic 11: Online Topic Readiness: Answer Key
              Intended Role: Instructor

            Home-School Connection Letters
              Intended Role: Instructor

            Vocabulary Cards
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            11-01: Printable Digital Quick Check
              Intended Role: Instructor

            11-01: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            11-02: Printable Digital Quick Check
              Intended Role: Instructor

            11-02: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            11-03: Printable Digital Quick Check
              Intended Role: Instructor

            11-03: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            11-04: Printable Digital Quick Check
              Intended Role: Instructor

            11-04: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            11-05: Printable Digital Quick Check
              Intended Role: Instructor

            11-05: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            11-06: Printable Digital Quick Check
              Intended Role: Instructor

            11-06: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            11-07: Printable Digital Quick Check
              Intended Role: Instructor

            11-07: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            11-08: Printable Digital Quick Check
              Intended Role: Instructor

            11-08: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            11-09: Printable Digital Quick Check
              Intended Role: Instructor

            11-09: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            11-10: Printable Digital Quick Check
              Intended Role: Instructor

            11-10: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            11-11: Printable Digital Quick Check
              Intended Role: Instructor

            11-11: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            11-12: Printable Digital Quick Check
              Intended Role: Instructor

            11-12: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Topic Test
              Intended Role: Instructor

            Topic 11: Printable Online Topic Test
              Intended Role: Instructor

            Topic 11: Online Topic Test: Answer Key
              Intended Role: Instructor

            Topic 11: Digital Enhanced Topic Test Teacher Support
              Intended Role: Instructor

            Topic 11: Enhanced Topic Test Teacher Support
              Intended Role: Instructor

            Topic Readiness
              Intended Role: Instructor

            Topic 12: Printable Online Topic Readiness
              Intended Role: Instructor

            Topic 12: Online Topic Readiness: Answer Key
              Intended Role: Instructor

            Home-School Connection Letters
              Intended Role: Instructor

            Vocabulary Cards
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            12-01: Printable Digital Quick Check
              Intended Role: Instructor

            12-01: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            12-02: Printable Digital Quick Check
              Intended Role: Instructor

            12-02: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            12-03: Printable Digital Quick Check
              Intended Role: Instructor

            12-03: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            12-04: Printable Digital Quick Check
              Intended Role: Instructor

            12-04: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Topic Test
              Intended Role: Instructor

            Topic 12: Printable Online Topic Test
              Intended Role: Instructor

            Topic 12: Online Topic Test: Answer Key
              Intended Role: Instructor

            Topic 12: Digital Enhanced Topic Test Teacher Support
              Intended Role: Instructor

            Topic 12: Enhanced Topic Test Teacher Support
              Intended Role: Instructor

            Grade 5: Topics 09-12: Benchmark Test
              Intended Role: Instructor

            Printable Online Topics 09-12: Benchmark Test
              Intended Role: Instructor

            Online Topics 09-12: Benchmark Test: Answer Key
              Intended Role: Instructor

            Topic Readiness
              Intended Role: Instructor

            Topic 13: Printable Online Topic Readiness
              Intended Role: Instructor

            Topic 13: Online Topic Readiness: Answer Key
              Intended Role: Instructor

            Home-School Connection Letters
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            13-01: Printable Digital Quick Check
              Intended Role: Instructor

            13-01: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            13-02: Printable Digital Quick Check
              Intended Role: Instructor

            13-02: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            13-03: Printable Digital Quick Check
              Intended Role: Instructor

            13-03: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            13-04: Printable Digital Quick Check
              Intended Role: Instructor

            13-04: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            13-05: Printable Digital Quick Check
              Intended Role: Instructor

            13-05: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            13-06: Printable Digital Quick Check
              Intended Role: Instructor

            13-06: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            13-07: Printable Digital Quick Check
              Intended Role: Instructor

            13-07: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Topic Test
              Intended Role: Instructor

            Topic 13: Printable Online Topic Test
              Intended Role: Instructor

            Topic 13: Online Topic Test: Answer Key
              Intended Role: Instructor

            Topic 13: Digital Enhanced Topic Test Teacher Support
              Intended Role: Instructor

            Topic 13: Enhanced Topic Test Teacher Support
              Intended Role: Instructor

            Topic Readiness
              Intended Role: Instructor

            Topic 14: Printable Online Topic Readiness
              Intended Role: Instructor

            Topic 14: Online Topic Readiness: Answer Key
              Intended Role: Instructor

            Home-School Connection Letters
              Intended Role: Instructor

            Vocabulary Cards
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            14-01: Printable Digital Quick Check
              Intended Role: Instructor

            14-01: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            14-02: Printable Digital Quick Check
              Intended Role: Instructor

            14-02: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            14-03: Printable Digital Quick Check
              Intended Role: Instructor

            14-03: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            14-04: Printable Digital Quick Check
              Intended Role: Instructor

            14-04: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            14-05: Printable Digital Quick Check
              Intended Role: Instructor

            14-05: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Topic Test
              Intended Role: Instructor

            Topic 14: Printable Online Topic Test
              Intended Role: Instructor

            Topic 14: Online Topic Test: Answer Key
              Intended Role: Instructor

            Topic 14: Digital Enhanced Topic Test Teacher Support
              Intended Role: Instructor

            Topic 14: Enhanced Topic Test Teacher Support
              Intended Role: Instructor

            Topic Readiness
              Intended Role: Instructor

            Topic 15: Printable Online Topic Readiness
              Intended Role: Instructor

            Topic 15: Online Topic Readiness: Answer Key
              Intended Role: Instructor

            Home-School Connection Letters
              Intended Role: Instructor

            Vocabulary Cards
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            15-01: Printable Digital Quick Check
              Intended Role: Instructor

            15-01: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            15-02: Printable Digital Quick Check
              Intended Role: Instructor

            15-02: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            15-03: Printable Digital Quick Check
              Intended Role: Instructor

            15-03: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            15-04: Printable Digital Quick Check
              Intended Role: Instructor

            15-04: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            15-05: Printable Digital Quick Check
              Intended Role: Instructor

            15-05: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            15-06: Printable Digital Quick Check
              Intended Role: Instructor

            15-06: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Topic Test
              Intended Role: Instructor

            Topic 15: Printable Online Topic Test
              Intended Role: Instructor

            Topic 15: Online Topic Test: Answer Key
              Intended Role: Instructor

            Topic 15: Digital Enhanced Topic Test Teacher Support
              Intended Role: Instructor

            Topic 15: Enhanced Topic Test Teacher Support
              Intended Role: Instructor

            Topic Readiness
              Intended Role: Instructor

            Topic 16: Printable Online Topic Readiness
              Intended Role: Instructor

            Topic 16: Online Topic Readiness: Answer Key
              Intended Role: Instructor

            Home-School Connection Letters
              Intended Role: Instructor

            Vocabulary Cards
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            16-01: Printable Digital Quick Check
              Intended Role: Instructor

            16-01: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            16-02: Printable Digital Quick Check
              Intended Role: Instructor

            16-02: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            16-03: Printable Digital Quick Check
              Intended Role: Instructor

            16-03: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            16-04: Printable Digital Quick Check
              Intended Role: Instructor

            16-04: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Daily Common Core Review
              Intended Role: Instructor

            Listen and Look For
              Intended Role: Instructor

            Quick Check Remediation
              Intended Role: Instructor

            16-05: Printable Digital Quick Check
              Intended Role: Instructor

            16-05: Digital Quick Check: Answer Key
              Intended Role: Instructor

            Quick Check
              Intended Role: Instructor

            Practice
              Intended Role: Instructor

            Center Activity *
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Center Activity **
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Topic Test
              Intended Role: Instructor

            Topic 16: Printable Online Topic Test
              Intended Role: Instructor

            Topic 16: Online Topic Test: Answer Key
              Intended Role: Instructor

            Topic 16: Digital Enhanced Topic Test Teacher Support
              Intended Role: Instructor

            Topic 16: Enhanced Topic Test Teacher Support
              Intended Role: Instructor

            Grade 4: Topics 05-08: Benchmark Test
              Intended Role: Instructor

            Printable Online Topics 13-16: Benchmark Test
              Intended Role: Instructor

            Online Topics 13-16: Benchmark Test: Answer Key
              Intended Role: Instructor

            Printable Online End of Year Test
              Intended Role: Instructor

            Online End of Year Test: Answer Key
              Intended Role: Instructor

            Math Diagnosis and Intervention System 2.0
              Intended Role: Instructor

            Online 3/4-Year Practice Performance Tasks
              Intended Role: Instructor

            Grade 5: Printable Next Generation Assessment Practice Test
              Intended Role: Instructor

            Grade 5: Next Generation Assessment Practice Test: Answer Key
              Intended Role: Instructor

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            Teacher Edition: Grade 5

            Student Edition: Grade 5