# Smarter Balanced Assessment Consortium Claims, Targets, and Standard Alignment for Math

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1 Smarter Balanced Assessment Consortium Claims, Targets, and Standard Alignment for Math The Smarter Balanced Assessment Consortium (SBAC) has created a hierarchy comprised of claims and targets that together can be used to make statements about student achievement. The claim is a broad statement that will outline the outcomes achieved with mastery of the standards within it. Within each claim are a variety of assessment targets that further clarify the knowledge and specific skills that cross over a cluster of standards. The following tables layout the claims and targets for claims 1-4. Each target may feature a standard or a variety of standards that make up the skill(s) of the target. Each target also features a Depth of Knowledge level(s) and item type(s) in which the target may be assessed. Item Types: MC Multiple Choice, Single Correct Response MS Multiple Choice, Multiple Correct Response EQ Equation/Numeric MA Matching Tables TI Fill-in tables DD Drag and Drop HS Hot Spot G Graphing GI Graphing Interaction ST Short Text Depth of Knowledge: 1 - Recall 2 - Skill/Concept 3 - Strategic Thinking 4 - Extended Thinking Work: Not all content in a given grade is emphasized equally in the standards. Some clusters require greater emphasis than others based on the depth of ideas, the time they take to master, and/or their importance to future mathematics or the demands of college and career readiness. The following tables identify the additional and supporting work for the grade by shading. If no shading is included, all standards listed are part of the major work for that level. Prepared for the Riverside County Office of Education by Key Data Systems.

2 Claim Target DOK Standards Item Types 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 A: Write and interpret 1, 2 numbers, and interpret numerical expressions without evaluating them. numerical expressions. For example, express the calculation add 8 and 7, then multiply by 2 MC, EQ as 2 (8 + 7). Recognize that 3 ( ) is three times as large as , without having to calculate the indicated sum or product. 1: Concepts and Procedures: Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency. B: Analyze patterns and relationships. C: Understand the place value system. 2 1, 2 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. 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.2: 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 NBT.3: Read, write, and compare decimals to thousandths. 5.NBT.4: Use place value understanding to round decimals to any place. MC, G, HS EQ, MC, MA Prepared for the Riverside County Office of Education by Key Data Systems. Page 1

3 Claim Target DOK Standards Item Types 5.NBT.5: Fluently multiply multi digit whole numbers using the standard algorithm. 5.NBT.6: Find whole number quotients of whole numbers with up to four digit dividends and two digit divisors, using strategies based on D: Perform operations with place value, the properties of operations, and/or the relationship multi digit whole numbers between multiplication and division. Illustrate and explain the 1, 2 and with decimals to calculation by using equations, rectangular arrays, and/or area models. MC, EQ hundredths. 5.NBT.7: 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. 1: Concepts and Procedures: Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency. E: Use equivalent fractions as a strategy to add and subtract fractions. 1, 2 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, 2/3 + 5/4 = 8/ /12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) 5.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 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. MC, EQ Prepared for the Riverside County Office of Education by Key Data Systems. Page 2

4 Claim Target DOK Standards Item Types 5.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. 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? 1: Concepts and Procedures: Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency. F: Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 1, 2 5.NF.4: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. 5.NF.5: Interpret multiplication as scaling (resizing), by: a. 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. b. 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. 5.NF.7: Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. MC, EQ Prepared for the Riverside County Office of Education by Key Data Systems. Page 3

5 Claim Target DOK Standards Item Types G: Convert like 5.MD.1: Convert among different sized standard measurement units measurement units within within a given measurement system (e.g., convert 5 cm to 0.05 m), and 1, 2 a given measurement use these conversions in solving multi step, real world problems. EQ system. 1: Concepts and Procedures: Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency. H: Represent and interpret data. I: Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. J: Graph points on the coordinate plane to solve real world and mathematical problems. 2 1, 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. 5.MD.3: Recognize volume as an attribute of solid figures and understand concepts of volume measurement. 5.MD.4: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 5.MD.5: Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. 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. HS, MC, EQ MA, EQ MC, HS, G, DD Prepared for the Riverside County Office of Education by Key Data Systems. Page 4

6 Claim Target DOK Standards Item Types 5.G.3: Understand that attributes belonging to a category of twodimensional 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. 1: Concepts and Procedures: Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency. K: Classify two dimensional figures into categories based on their properties. 2 5.G.4: Classify two dimensional figures in a hierarchy based on properties. MA Prepared for the Riverside County Office of Education by Key Data Systems. Page 5

7 5.NBT.5: Fluently multiply multi digit whole numbers using the A: Apply mathematics to solve standard algorithm. well posed problems in pure mathematics and rising in everyday life, society, and the workplace. (2, 3) 2: Problem Solving: Students can solve a range of well posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies. B: Select and use appropriate tools strategically. (1, 2) C: Interpret results in the context of a situation. (2) D: Identify important quantities in a practical situation and map their relationships (e.g., using diagrams, two way tables, graphs, flowcharts, or formulas). (1, 2, 3) 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.7: 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.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, 2/3 + 5/4 = 8/ /12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) 5.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 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. TI Prepared for the Riverside County Office of Education by Key Data Systems. Page 6

8 5.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 A: Apply mathematics to solve numbers, e.g., by using visual fraction models or equations to represent well posed problems in pure the problem. For example, interpret 3/4 as the result of dividing 3 by 4, mathematics and rising in noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are everyday life, society, and the shared equally among 4 people each person has a share of size 3/4. If 9 workplace. (2, 3) 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? 2: Problem Solving: Students can solve a range of well posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies. B: Select and use appropriate tools strategically. (1, 2) C: Interpret results in the context of a situation. (2) D: Identify important quantities in a practical situation and map their relationships (e.g., using diagrams, two way tables, graphs, flowcharts, or formulas). (1, 2, 3) 5.NF.4: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. 5.NF.5: Interpret multiplication as scaling (resizing), by: a. 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. b. 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. 5.NF.7: Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. TI Prepared for the Riverside County Office of Education by Key Data Systems. Page 7

9 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 A: Apply mathematics to solve well posed problems in pure mathematics and rising in everyday life, society, and the workplace. (2, 3) 5.MD.3: Recognize volume as an attribute of solid figures and understand concepts of volume measurement. 5.MD.4: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 2: Problem Solving: Students can solve a range of well posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies. B: Select and use appropriate tools strategically. (1, 2) C: Interpret results in the context of a situation. (2) D: Identify important quantities in a practical situation and map their relationships (e.g., using diagrams, two way tables, graphs, flowcharts, or formulas). (1, 2, 3) 5.MD.5: Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. 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. TI Prepared for the Riverside County Office of Education by Key Data Systems. Page 8

10 A: Test propositions or 5.NBT.2: Explain patterns in the number of zeros of the product when conjectures with specific multiplying a number by powers of 10, and explain patterns in the examples. (2) 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 3: Communicating Reasoning: Students clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of other. B. Construct, autonomously, chains of reasoning that will justify or refute propositions or conjectures. (3, 4) C. State logical assumptions being used. (2, 3) D. Use the technique of breaking an argument into cases. (2, 3) E. Distinguish correct logic or reasoning from that which is flawed and if there is a flaw in the argument explain what it is. (2, 3, 4) F. Base arguments on concrete references such as objects, drawings, diagrams, and actions. (2, 3) 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.7: 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.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, 2/3 + 5/4 = 8/ /12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) 5.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 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. TI, ST 1 Prepared for the Riverside County Office of Education by Key Data Systems. Page 9

11 A: Test propositions or conjectures with specific examples. (2) 3: Communicating Reasoning: Students clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of other. B. Construct, autonomously, chains of reasoning that will justify or refute propositions or conjectures. (3, 4) C. State logical assumptions being used. (2, 3) D. Use the technique of breaking an argument into cases. (2, 3) E. Distinguish correct logic or reasoning from that which is flawed and if there is a flaw in the argument explain what it is. (2, 3, 4) 5.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. 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? 5.NF.4: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. 5.NF.5: Interpret multiplication as scaling (resizing), by: a. 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. b. 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. TI, ST 1 F. Base arguments on concrete references such as objects, drawings, diagrams, and actions. (2, 3) 5.NF.7: Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Prepared for the Riverside County Office of Education by Key Data Systems. Page 10

12 A: Test propositions or 5.NF.7a: Interpret division of a unit fraction by a non zero whole conjectures with specific number, and compute such quotients. For example, create a story examples. (2) context for (1/3) 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to 3: Communicating Reasoning: Students clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of other. B. Construct, autonomously, chains of reasoning that will justify or refute propositions or conjectures. (3, 4) C. State logical assumptions being used. (2, 3) D. Use the technique of breaking an argument into cases. (2, 3) E. Distinguish correct logic or reasoning from that which is flawed and if there is a flaw in the argument explain what it is. (2, 3, 4) F. Base arguments on concrete references such as objects, drawings, diagrams, and actions. (2, 3) explain that (1/3) 4 = 1/12 because (1/12) 4 = 1/3. 5.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.MD.3: Recognize volume as an attribute of solid figures and understand concepts of volume measurement. 5.MD.4: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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 wholenumber 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. TI, ST 1 Prepared for the Riverside County Office of Education by Key Data Systems. Page 11

13 A: Test propositions or 5.MD.5b: Apply the formulas V = l w h and V = b h for rectangular conjectures with specific prisms to find volumes of right rectangular prisms with whole number examples. (2) edge lengths in the context of solving real world and mathematical problems. B. Construct, autonomously, chains of reasoning that will justify or refute propositions or conjectures. (3, 4) 5.G.3: Understand that attributes belonging to a category of twodimensional 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. 3: Communicating Reasoning: Students clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of other. C. State logical assumptions being used. (2, 3) D. Use the technique of breaking an argument into cases. (2, 3) E. Distinguish correct logic or reasoning from that which is flawed and if there is a flaw in the argument explain what it is. (2, 3, 4) 5.G.4: Classify two dimensional figures in a hierarchy based on properties. TI, ST 1 F. Base arguments on concrete references such as objects, drawings, diagrams, and actions. (2, 3) Prepared for the Riverside County Office of Education by Key Data Systems. Page 12

14 A: Apply mathematics to solve 5.NBT.5: Fluently multiply multi digit whole numbers using the problems arising in everyday life, standard algorithm. society, and the workplace. (2, 3) 4: Modeling and Data Analysis: Students can analyze complex, real world scenarios and can construct and use mathematical models to interpret and solve problems. B: Construct, autonomously, chains of reasoning to justify mathematical models used, interpretations made, and solutions proposed for a complex problem. (2, 3, 4) C: State logical assumptions being used. (1, 2) D: Interpret results in the context of a situation. (2, 3) E: Analyze the adequacy of and make improvements to an existing model or develop a mathematical model of a real phenomenon. (3, 4) F: Identify important quantities I a practical situation and map their relationships (e.g., using diagrams, two way tables, graphs, flowcharts, or formulas). (1, 2, 3) G*: Identify, analyze, and synthesize relevant external resources to pose or solve problems. (3, 4) 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.7: 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.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, 2/3 + 5/4 = 8/ /12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) 5.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 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. TI Prepared for the Riverside County Office of Education by Key Data Systems. Page 13

15 A: Apply mathematics to solve problems arising in everyday life, society, and the workplace. (2, 3) 4: Modeling and Data Analysis: Students can analyze complex, real world scenarios and can construct and use mathematical models to interpret and solve problems. B: Construct, autonomously, chains of reasoning to justify mathematical models used, interpretations made, and solutions proposed for a complex problem. (2, 3, 4) C: State logical assumptions being used. (1, 2) D: Interpret results in the context of a situation. (2, 3) E: Analyze the adequacy of and make improvements to an existing model or develop a mathematical model of a real phenomenon. (3, 4) F: Identify important quantities I a practical situation and map their relationships (e.g., using diagrams, two way tables, graphs, flowcharts, or formulas). (1, 2, 3) G*: Identify, analyze, and synthesize relevant external resources to pose or solve problems. (3, 4) 5.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. 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? 5.NF.4: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. 5.NF.5: Interpret multiplication as scaling (resizing), by: a. 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. b. 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. 5.NF.7: Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. TI Prepared for the Riverside County Office of Education by Key Data Systems. Page 14

16 5.MD.1: Convert among different sized standard measurement units A: Apply mathematics to solve within a given measurement system (e.g., convert 5 cm to 0.05 m), and problems arising in everyday life, use these conversions in solving multi step, real world problems. society, and the workplace. (2, 3) 4: Modeling and Data Analysis: Students can analyze complex, real world scenarios and can construct and use mathematical models to interpret and solve problems. B: Construct, autonomously, chains of reasoning to justify mathematical models used, interpretations made, and solutions proposed for a complex problem. (2, 3, 4) C: State logical assumptions being used. (1, 2) D: Interpret results in the context of a situation. (2, 3) E: Analyze the adequacy of and make improvements to an existing model or develop a mathematical model of a real phenomenon. (3, 4) F: Identify important quantities I a practical situation and map their relationships (e.g., using diagrams, two way tables, graphs, flowcharts, or formulas). (1, 2, 3) G*: Identify, analyze, and synthesize relevant external resources to pose or solve problems. (3, 4) 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. 5.MD.3: Recognize volume as an attribute of solid figures and understand concepts of volume measurement. 5.MD.4: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 5.MD.5: Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. 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. TI Prepared for the Riverside County Office of Education by Key Data Systems. Page 15

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