# Bridges Grade 5 Supplement Sets Correlations to Common Core State Standards

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1 Bridges Grade 5 Supplement Sets Correlations to Common Core State s By Set Set A4 Set A6 Set A9 Number & Operations: Long Division...2 Number & Operations: Fraction Concepts...2 Number & Operations: Multiplying Fractions...2 Set A10 Number and Operations: Integers...3 Dividing Decimals...3 Whole Numbers...4 Set B1 Set C1 Set D2 Algebra: Diagrams & Equations...4 Geometry: Triangles & Quadrilaterals...4 Measurement: Volume...5 By 5.OA Operations and Algebraic Thinking NBT Number and Operations in Base Ten MD Measurement and Data G Geometry...9 Bridges supplements not correlated to the Common Core State s are not listed here. CCSS standards not addressed by any supplements are not shown. The Math Learning Center 1

2 Bridges Grade 5 Supplement Sets CCSS Correlations by Set Set A4 Number & Operations: Long Division 5.NBT Number and Operations in Base Ten 5.NBT.6 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. 1 2 Set A6 Number & Operations: Fraction Concepts 5.NF.1 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, = = (In general, a b + c d = (ad + bc) bd.) Set A9 Number & Operations: Multiplying Fractions NF.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 = 3 7, by observing that 3 7 < NF.3 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. Between what two whole numbers does your answer lie? 5.NF.4a Interpret the product ( a b) q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a q b. For example, use a visual fraction model to show ( 2 3) 4 = 8 3, and create a story context for this equation. Do the same with ( 2 3) ( 4 5) = (In general, ( a b) ( c d) = ac bd.) 5.NF.4b 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.5b [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 a) (n b) to the effect of multiplying a b by 1. 5.NF.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. 2 The Math Learning Center

3 Bridges Grade 5 Supplement Sets CCSS Correlations by Set Set A10 Number and Operations: Integers 5.G Geometry 5.G.1 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.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 Set A11 Number & Operations: Multiplying & Dividing Decimals NBT Number and Operations in Base Ten 5.NBT.1 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.2a 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 NBT.2b Use whole-number exponents to denote powers of NBT.4 Use place value understanding to round decimals to any place. 5.NBT.6 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.7a Add and subtract 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.7b 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.NF.4b 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.5a [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. 1 Extension 3 The Math Learning Center 3

4 Bridges Grade 5 Supplement Sets CCSS Correlations by Set Set A12 Number & Operations: Dividing Fractions & Whole Numbers NF.3 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. Between what two whole numbers does your answer lie? 5.NF.4a Interpret the product ( a b) q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a q b. For example, use a visual fraction model to show ( 2 3) 4 = 8 3, and create a story context for this equation. Do the same with ( 2 3) ( 4 5) = (In general, ( a b) ( c d) = ac bd.) 5.NF.4b 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.7a 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) 4 = NF.7b 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 ( 1 5) = 4. 5.NF.7c 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 2lb of chocolate equally? How many 1 3-cup servings are in 2 cups of raisins? Set B1 Algebra: Diagrams & Equations 5.OA Operations and Algebraic Thinking 5.OA.2 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 (8 + 7). Recognize that 3 ( ) is three times as large as , without having to calculate the indicated sum or product Set C1 Geometry: Triangles & Quadrilaterals 5.G Geometry 5.G.3 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 G.4 Classify two-dimensional figures in a hierarchy based on properties. 4 The Math Learning Center

6 Bridges Grade 5 Supplement Sets CCSS Correlations by 5.OA Operations and Algebraic Thinking Write and interpret numerical expressions. 5.OA.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. 5.OA.2 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 (8 + 7). Recognize that 3 ( ) is three times as large as , without having to calculate the indicated sum or product. Bridges Practice Book, pp 11, 12, 121, 122, 124 Set B1 Algebra: Diagrams & Equations, Activity 1 & Ind. 1, 2 Bridges Practice Book, pp 1, 31, 125, 126, 128 Analyze patterns and relationships. 5.OA.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 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. Bridges Practice Book, pp 6, 7, 8, 33 5.NBT Number and Operations in Base Ten Understand the place value system. 5.NBT.1 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.2a 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 NBT.2b Use whole-number exponents to denote powers of NBT.3a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., = ( 1 10) + 9 ( 1 100) + 2 ( ). Dividing Decimals, 1, 2 & Ind. 1, 2 Bridges Practice Book, pp 111, 112, 113, 130 Dividing Decimals, 1, 2, 4 Bridges Practice Book, pp 22, 23 Dividing Decimals, Activity 2 (Extension 3) Bridges Practice Book, pp 111, 112, 113, 130 Understand the place value system. 5.NBT.4 Use place value understanding to round decimals to any place. Dividing Decimals, Ind. Worksheet 1 Bridges Practice Book, p 14 Perform operations with multi-digit whole numbers and with decimals to hundredths. 5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm. Bridges Practice Book, pp 25, 26, 28, 29, 30, 81 5.NBT.6 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. Set A4 Number & Operations: Long Division, 1 & 2 Dividing Decimals, 1 8 & Ind. 1 7 Bridges Practice Book, pp 1, 5, 9, 21, 22, 30, 32, 35 39, 61, 63, 64, 66 68, 70, 79, 81 83, 85, 90, 92, 99, 100, 131 Perform operations with multi-digit whole numbers and with decimals to hundredths. 5.NBT.7a Add and subtract 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. Dividing Decimals, Activity 4 Bridges Practice Book, pp 112, 113, 114, 115, 116, 120, 130, 137, The Math Learning Center

8 Bridges Grade 5 Supplement Sets CCSS Correlations by 5.NF.5 Interpret multiplication as scaling (resizing) by: 5.NF.5a 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.5b 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 a) (n b) to the effect of multiplying a b by 1. Dividing Decimals, 1, 2, 4 2, 3, 4 Practice Book, pp 103, 104, 106, 127, 129 Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 5.NF.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. 2 7 & Ind. 1 5 Set D2 Measurement: Volume, 4, 5 & Ind. 4, 5 5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (Note: Division of a fraction by a fraction is not a requirement at this grade.) 5.NF.7a 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) 4 = NF.7b 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 ( 1 5) = 4. 5.NF.7c 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 2lb of chocolate equally? How many 1 3-cup servings are in 2 cups of raisins? Whole Numbers 2 7 Whole Numbers 2 7 Whole Numbers MD Measurement and Data Convert like measurement units within a given measurement system. 5.MD.1 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. Set D2 Measurement: Volume, 4, 5 & Ind. 4, 5 Bridges Practice Book, pp 17, 27, 28, 54, 72, 74, 86, 91 Represent and interpret data. 5.MD.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. 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. Set D2 Measurement: Volume, 4, 5 & Ind. 4, 5 Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. 8 The Math Learning Center

9 Bridges Grade 5 Supplement Sets CCSS Correlations by 5.MD Measurement and Data 5.MD.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement. 5.MD.3a 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. 5.MD.3b A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. 5.MD.4 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Set D2 Measurement: Volume, 1 3 Set D2 Measurement: Volume, 1 3 Set D2 Measurement: Volume, 1 3 Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. 5.MD.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. 5.MD.5a 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 whole-number products as volumes, e.g., to represent the associative property of multiplication. 5.MD.5b Apply the formulas V = l w h and V = b 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.5c 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. Set D2 Measurement: Volume, 1 3 Set D2 Measurement: Volume, 1 3 Bridges Practice Book, pp 57, 59, 60, 65, 69 Set D2 Measurement: Volume, 3 5 & Ind G Geometry Graph points on the coordinate plane to solve real-world and mathematical problems. 5.G.1 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.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. Set A10 Number & Operations: Integers, Activity 3 & Ind. 2, 3 Set A10 Number & Operations: Integers, Activity 3 & Ind. 2, 3 Bridges Practice Book, pp 55, 98 Classify two-dimensional figures into categories based on their properties. 5.G.3 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 arerectangles, so all squares have four right angles. 5.G.4 Classify two-dimensional figures in a hierarchy based on properties. Set C1 Geometry: Triangles & Quadrilaterals, 1, 2 & Ind. 1 4 Bridges Practice Book, pp 41, 43, 44, 97, 140 Set C1 Geometry: Triangles & Quadrilaterals, 1, 2 & Ind. 1 4 The Math Learning Center 9

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