Addition and Subtraction of Fractions, Standards:
Standard 1:Number Sense, Properties, and Operations
GLE3: Formulate, represent, and use algorithms to add and subtract fractions with flexibility, accuracy, and efficiency
EOa:Use equivalent fractions as a strategyto add and subtract fractions. (CCSS: 5.NF)
EOa.i:Use benchmark fractions and number sense of fractions to estimate mentallyand assess the reasonableness of answers. (CCSS: 5.NF.2)
EOa.ii:Add and subtract fractions with unlike denominators (including mixed numbers) byreplacing given fractions with equivalent fractions with like denominators. (CCSS: 5.NF.1)
EOa.iii: Solve word problems involving addition and subtraction of fractions referring to the same whole. (CCSS: 5.NF.2)
Standard MP: Mathematical Practices
GLE1:Developing mathematical practices are processes and proficiencies necessaryto flexiblyuse skills and concepts in multiple contexts.
EO1: Make sense of problems and persevere in solving them.
EO4: Model with mathematics.
EO6:Attend to precision
Addition and Subtraction with Decimals:
Standard 1:Number Sense, Properties, andOperations
GLE1: The decimal number system describes place value patterns and relationships that are repeated in large and small numbers and forms the foundation for efficient algorithms
EOa: Explain 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 ofwhat it represents in the place to its left. (CCSS: 5.NBT.1)
EOb:Read,write, and compare decimals to thousandths. (CCSS: 5.NBT.3)
EOb.i:Read and write decimals to thousandths using base-ten numerals, number names, and expanded form. (CCSS: 5.NBT.3a)
EOb.ii:Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. (CCSS: 5.NBT.3b)
EOc:Use place value understanding to round decimals to anyplace. (CCSS: 5.NBT.4)
EOd.ii:Use measurement conversions in solving multi-step, real world problems. (CCSS: 5.MD.1)
GLE2: Formulate, represent, and use algorithms with multi-digitwhole numbers and decimals with flexibility, accuracy, and efficiency
EOc:Add, subtract, multiply, and divide decimals to hundredths. (CCSS: 5.NBT.7)
EOc.i:Use concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. (CCSS: 5.NBT.7)
EOc.ii:Relate strategies to a written method and explain the reasoning used. (CCSS: 5.NBT.7)
Standard MP: Mathematical Practices
GLE1:Developing mathematical practices are processes and proficiencies necessaryto flexiblyuse skills and concepts in multiple contexts.
EO4: Model with mathematics.
EO6:Attend to precision
EO7: Look for and make use of structure
Multiplication and Division of Fractions Standards:
Standard 1:Number Sense, Properties, andOperations
GLE3: Formulate, represent, and use algorithms to add and subtract fractions with flexibility, accuracy, and efficiency
EOa.i:Use benchmark fractions and number sense of fractions to estimate mentallyand assess the reasonableness of answers. (CCSS: 5.NF.2)
GLE4: The concepts of multiplication and division can be applied to multiplyand divide fractions (CCSS: 5.NF)
EOa: Interpret a fraction as division of the numerator bythe denominator (a/b = a � b). (CCSS: 5.NF.3)
EOb: Solve word problems involving division ofwhole numbers leading to answers in the form of fractions or mixed numbers. (CCSS: 5.NF.3)
EOc: 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. In general, (a/b) � (c/d) = ac/bd. (CCSS: 5.NF.4a)
EOd.i: Multiplyfractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. (CCSS: 5.NF.4b)
EOe: Interpret multiplication as scaling (resizing). (CCSS: 5.NF.5)
EOe.i:Compare 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. (CCSS: 5.NF.5a)
EOe.ii:Applythe principle of fraction equivalence a/b = (n � a)/(n � b) to the effect of multiplying a/b by1. (CCSS: 5.NF.5b)
EOf: Solve real world problems involving multiplication of fractions and mixed numbers. (CCSS: 5.NF.6)
EOg: Interpret division of a unit fraction bya non-zero whole number, and compute such quotients. (CCSS: 5.NF.7a)
EOh: Interpret division of a whole number bya unit fraction, and compute such quotients. (CCSS: 5.NF.7b)
EOi: Solve real world problems involving division of unit fractions bynon-zero whole numbers and division ofwhole numbers byunit fractions. (CCSS: 5.NF.7c)
Standard MP: Mathematical Practices
GLE1:Developing mathematical practices are processes and proficiencies necessaryto flexiblyuse skills and concepts in multiple contexts.
EO2:Reason abstractlyand quantitatively.
Multiplication with Whole Numbers and Decimals Standards:
Standard 1:Number Sense, Properties, andOperations
GLE1: The decimal number system describes place value patterns and relationships that are repeated in large and small numbers and forms the foundation for efficient algorithms
EOa: Explain 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 ofwhat it represents in the place to its left. (CCSS: 5.NBT.1)
EOa.i: Explain patterns in the number of zeros of the productwhen multiplying a number bypowers of 10. (CCSS: 5.NBT.2)
EOa.ii: Explain patterns in the placement of the decimal pointwhen a decimal is multiplied or divided bya power of 10. (CCSS: 5.NBT.2)
EOa.iii:Use whole-number exponents to denote powers of 10. (CCSS: 5.NBT.2)
EOb:Read,write, and compare decimals to thousandths. (CCSS: 5.NBT.3)
EOb.ii:Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. (CCSS: 5.NBT.3b)
EOc:Use place value understanding to round decimals to anyplace. (CCSS: 5.NBT.4)
GLE2: Formulate, represent, and use algorithms with multi-digitwhole numbers and decimals with flexibility, accuracy, and efficiency
EOa: Fluentlymultiplymulti-digitwhole numbers using standard algorithms. (CCSS: 5.NBT.5)
EOc:Add, subtract, multiply, and divide decimals to hundredths. (CCSS: 5.NBT.7)
EOc.i:Use concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. (CCSS: 5.NBT.7)
EOc.ii:Relate strategies to a written method and explain the reasoning used. (CCSS: 5.NBT.7)
GLE4: The concepts of multiplication and division can be applied to multiplyand divide fractions (CCSS: 5.NF)
EOe: Interpret multiplication as scaling (resizing). (CCSS: 5.NF.5)
EOe.i:Compare 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. (CCSS: 5.NF.5a)
EOe.ii:Applythe principle of fraction equivalence a/b = (n � a)/(n � b) to the effect of multiplying a/b by1. (CCSS: 5.NF.5b)
Standard MP: Mathematical Practices
GLE1:Developing mathematical practices are processes and proficiencies necessaryto flexiblyuse skills and concepts in multiple contexts.
EO4: Model with mathematics.
EO6:Attend to precision
EO7: Look for and make use of structure
Division with Whole Numbers and Decimals Standards:
Standard 1:Number Sense, Properties, andOperations
GLE1: The decimal number system describes place value patterns and relationships that are repeated in large and small numbers and forms the foundation for efficient algorithms
EOa.i: Explain patterns in the number of zeros of the productwhen multiplying a number bypowers of 10. (CCSS: 5.NBT.2)
EOa.ii: Explain patterns in the placement of the decimal pointwhen a decimal is multiplied or divided bya power of 10. (CCSS: 5.NBT.2)
EOa.iii:Use whole-number exponents to denote powers of 10. (CCSS: 5.NBT.2)
EOb.ii:Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. (CCSS: 5.NBT.3b)
GLE2: Formulate, represent, and use algorithms with multi-digitwhole numbers and decimals with flexibility, accuracy, and efficiency
EOa: Fluentlymultiplymulti-digitwhole numbers using standard algorithms. (CCSS: 5.NBT.5)
EOb: Find whole-number quotients ofwhole numbers. (CCSS: 5.NBT.6)
EOb.i:Use strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. (CCSS: 5.NBT.6)
EOb.ii: Illustrate and explain calculations byusing equations, rectangular arrays, and/or area models. (CCSS: 5.NBT.6)
EOc:Add, subtract, multiply, and divide decimals to hundredths. (CCSS: 5.NBT.7)
EOc.i:Use concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. (CCSS: 5.NBT.7)
EOc.ii:Relate strategies to a written method and explain the reasoning used. (CCSS: 5.NBT.7)
GLE4: The concepts of multiplication and division can be applied to multiplyand divide fractions (CCSS: 5.NF)
EOe: Interpret multiplication as scaling (resizing). (CCSS: 5.NF.5)
EOe.i:Compare 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. (CCSS: 5.NF.5a)
Standard MP: Mathematical Practices
GLE1:Developing mathematical practices are processes and proficiencies necessaryto flexiblyuse skills and concepts in multiple contexts.
EO1: Make sense of problems and persevere in solving them.
EO3:Construct viable arguments and critique the reasoning of others.
EO8: Look for and express regularityin repeated reasoning.
Operations and Word Problems Standards:
Standard 1:Number Sense, Properties, andOperations
GLE1: The decimal number system describes place value patterns and relationships that are repeated in large and small numbers and forms the foundation for efficient algorithms
EOc:Use place value understanding to round decimals to anyplace. (CCSS: 5.NBT.4)
GLE2: Formulate, represent, and use algorithms with multi-digitwhole numbers and decimals with flexibility, accuracy, and efficiency
EOa: Fluentlymultiplymulti-digitwhole numbers using standard algorithms. (CCSS: 5.NBT.5)
EOb: Find whole-number quotients ofwhole numbers. (CCSS: 5.NBT.6)
EOb.i:Use strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. (CCSS: 5.NBT.6)
EOb.ii: Illustrate and explain calculations byusing equations, rectangular arrays, and/or area models. (CCSS: 5.NBT.6)
EOc:Add, subtract, multiply, and divide decimals to hundredths. (CCSS: 5.NBT.7)
EOc.i:Use concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. (CCSS: 5.NBT.7)
EOc.ii:Relate strategies to a written method and explain the reasoning used. (CCSS: 5.NBT.7)
EOd: Write and interpret numerical expressions. (CCSS: 5.OA)
EOd.i:Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. (CCSS: 5.OA.1)
GLE3: Formulate, represent, and use algorithms to add and subtract fractions with flexibility, accuracy, and efficiency
EOa.i:Use benchmark fractions and number sense of fractions to estimate mentallyand assess the reasonableness of answers. (CCSS: 5.NF.2)
EOa.ii:Add and subtract fractions with unlike denominators (including mixed numbersbyreplacing given fractions with equivalent fractions with like denominators. (CCSS: 5.NF.1)
EOa.iii: Solve word problems involving addition and subtraction of fractions referring to the same whole. (CCSS: 5.NF.2)
GLE4: The concepts of multiplication and division can be applied to multiplyand divide fractions (CCSS: 5.NF)
EOa: Interpret a fraction as division of the numerator bythe denominator (a/b = a � b). (CCSS: 5.NF.3)
EOb: Solve word problems involving division ofwhole numbers leading to answers in the form of fractions or mixed numbers. (CCSS: 5.NF.3)
EOc: 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. In general, (a/b) � (c/d) = ac/bd. (CCSS: 5.NF.4a)
EOd: Find the area of a rectangle with fractional side lengths bytiling itwith unit squares of the appropriate unit fraction side lengths, and showthat the area is the same as would be ) found bymultiplying the side lengths. (CCSS:
5.NF.4b)
EOd.i: Multiplyfractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. (CCSS: 5.NF.4b)
EOe: Interpret multiplication as scaling (resizing). (CCSS: 5.NF.5)
EOe.i:Compare 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. (CCSS: 5.NF.5a)
EOe.ii:Applythe principle of fraction equivalence a/b = (n � a)/(n � b) to the effect of multiplying a/b by1. (CCSS: 5.NF.5b)
EOf: Solve real world problems involving multiplication of fractions and mixed numbers. (CCSS: 5.NF.6)
EOg: Interpret division of a unit fraction bya non-zero whole number, and compute such quotients. (CCSS: 5.NF.7a)
EOh: Interpret division of a whole number bya unit fraction, and compute such quotients. (CCSS: 5.NF.7b)
EOi: Solve real world problems involving division of unit fractions bynon-zero whole numbers and division ofwhole numbers byunit fractions. (CCSS: 5.NF.7c)
Algebra, Patterns, and Coordinate Graphs Standards:
Standard 1:Number Sense, Properties, andOperations
GLE2: Formulate, represent, and use algorithms with multi-digitwhole numbers and decimals with flexibility, accuracy, and efficiency
EOd: Write and interpret numerical expressions. (CCSS: 5.OA)
EOd.i:Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. (CCSS: 5.OA.1)
EOd.ii: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. (CCSS: 5.OA.2)
Standard 2: Patterns, Functions, andAlgebraic Structures
GLE1:Number patterns are based on operations and relationships
EOa:Generate two numerical patterns using given rules. (CCSS: 5.OA.3)
EOb: Identifyapparent relationships between corresponding terms. (CCSS: 5.OA.3)
EOc: Form ordered pairs consisting of corresponding terms from the two patterns, and graphs the ordered pairs on a coordinate plane. (CCSS: 5.OA.3)
EOd: Explain informallyrelationships between corresponding terms in the patterns. (CCSS: 5.OA.3)
EOe:Use patterns to solve problems including those involving saving and checking accounts. (PFL)
EOf: Explain, extend, and use patterns and relationships in solving problems, including those involving saving and checking accounts such as understanding that spending more means saving less (PFL)
Standard 4: Shape,Dimension, andGeometricRelationships
GLE2:Geometric figures can be described bytheir attributes and specific locations in the plane
EOa:Graph points on the coordinate plane to solve real-world and mathematical problems. (CCSS: 5.G)
EOb:Represent real world and mathematical problems bygraphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. (CCSS: 5.G.2)
Standard MP: Mathematical Practices
GLE1:Developing mathematical practices are processes and proficiencies necessaryto flexiblyuse skills and concepts in multiple contexts.
EO2:Reason abstractlyand quantitatively.
EO7: Look for and make use of structure
EO8: Look for and express regularityin repeated reasoning.
Measurement and Geometry Standards:
Standard 1:Number Sense, Properties, andOperations
GLE1: The decimal number system describes place value patterns and relationships that are repeated in large and small numbers and forms the foundation for efficient algorithms
EOd:Convert like measurement units within a given measurement system. (CCSS: 5.MD)
EOd.i:Convert among different-sized standard measurement units within a given measurement system. (CCSS: 5.MD.1)
EOd.ii:Use measurement conversions in solving multi-step, real world problems. (CCSS: 5.MD.1)
Standard 3:DataAnalysis, Statistics, and Probability
GLE1: Visual displays are used to interpret data
EOa:Represent and interpret data. (CCSS: 5.MD)
EOa.i: Make a line plot to displaya data set of measurements in fractions of a unit (1/2, 1/4, 1/8). (CCSS: 5.MD.2)
EOa.ii:Use operations on fractions for this grade to solve problems involving information presented in line plots. (CCSS: 5.MD.2)
Standard 4: Shape,Dimension, andGeometricRelationships
GLE2:Geometric figures can be described bytheir attributes and specific locations in the plane
EOc:Classifytwo-dimensional figures into categories based on their properties. (CCSS: 5.G)
EOc.i: Explain that attributes belonging to a categoryof two-dimensional figures also belong to all subcategories of that category. (CCSS: 5.G.3)
EOc.ii:Classifytwo-dimensional figures in a hierarchybased on properties. (CCSS: 5.G.4)
Standard MP: Mathematical Practices
GLE1:Developing mathematical practices are processes and proficiencies necessaryto flexiblyuse skills and concepts in multiple contexts.
EO3:Construct viable arguments and critique the reasoning of others.
EO5:Use appropriate tools strategically
EO6:Attend to precision
EO7: Look for and make use of structure
