In our class we learn through a "Math Workshop" model. After their math lessons and working on practice problems together, students rotate through workshops meeting with the teacher, technology, hands-on games, and math skills practice.

Below are the math standards and example math projects for the 4th graders. They learn from the FIFTH grade Math Expressions curriculum. 5th graders will be learning from the SIXTH grade Math Expressions curriculum. 

When time allows, we do both a large "Road-Trip: Planning a Math Vacation" project as well as extension projects throughout the year for students needing more challenge. Below are a few examples of the "Road-Trip" project.

First Unit

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

Second Unit

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

Third Unit:

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.

Fourth Unit:

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

Fifth Unit:

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.

Sixth Unit:

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)

Seventh Unit:

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.

Eighth Unit:

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