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6th Grade – Expressions and Equations includes ten activities that help students develop mastery of the mathematical practices within the content area of expressions and equations. For educators for whom the Common Core Standards are important, each activity is referenced to the sixth grade expressions and equations standards. The description of each standard follows:

6.EE.A.1. Write and evaluate numerical expressions involving whole-number exponents.

6.EE.A.2. Write, read, and evaluate expressions in which letters stand for numbers.

6.EE.A.2.a. 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.2.b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.

6.EE.A.2.c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2.

6.EE.A.3. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

6.EE.A.4. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.

6.EE.B.5. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

6.EE.B.6. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

6.EE.B.7. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

6.EE.B.8. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

6.EE.C.9. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.

6.EE.A.1 is addressed in Activity 1

6.EE.A.2 is addressed in Activities 2, 6, 7

6.EE.A.2.a. is addressed in Activity 2

6.EE.A.2.b. is addressed in Activity 2

6.EE.A.2.c. is addressed in Activities 3

6.EE.A.3. is addressed in Activities 4

6.EE.A.4. is addressed in Activities 4

6.EE.B.5. is addressed in Activities 5

6.EE.B.6. is addressed in Activities 5, 6, 7, 8

6.EE.B.7. is addressed in Activities 6, 7

6.EE.B.8. is addressed in Activities 8

6.EE.C.9. is addressed in Activities 9

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The Make It Real Learning Middle Grades Math Series is a collection of 20 workbooks that address the mathematical content standards of Grades 5, 6, 7, and 8. Each workbook contains ten standards-aligned activities that develop mathematical thinking. Interesting real world contexts are integrated into many of the activities.

Fifth Grade Mathematics Workbooks

• 5th Grade Operations and Algebraic Thinking

• 5th Grade Numbers and Operations in Base 10

• 5th Grade Numbers and Operations – Fractions

• 5th Grade Measurement and Data

• 5th Grade Geometry

Sixth Grade Mathematics Workbooks

• 6th Grade Ratios and Proportional Relationships

• 6th Grade The Number System

• 6th Grade Expressions and Equations

• 6th Grade Geometry

• 6th Grade Statistics and Probability

Seventh Grade Mathematics Workbooks

• 7th Grade Ratios and Proportional Relationships

• 7th Grade The Number System

• 7th Grade Expressions and Equations

• 7th Grade Geometry

• 7th Grade Statistics and Probability

Eighth Grade Mathematics Workbooks

• 8th Grade The Number System

• 8th Grade Expressions and Equations

• 8th Grade Functions

• 8th Grade Geometry

• 8th Grade Statistics and Probability

6.EE.A.1. Write and evaluate numerical expressions involving whole-number exponents.

6.EE.A.2. Write, read, and evaluate expressions in which letters stand for numbers.

6.EE.A.2.a. 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.2.b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.

6.EE.A.2.c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2.

6.EE.A.3. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

6.EE.A.4. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.

6.EE.B.5. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

6.EE.B.6. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

6.EE.B.7. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

6.EE.B.8. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

6.EE.C.9. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.

6.EE.A.1 is addressed in Activity 1

6.EE.A.2 is addressed in Activities 2, 6, 7

6.EE.A.2.a. is addressed in Activity 2

6.EE.A.2.b. is addressed in Activity 2

6.EE.A.2.c. is addressed in Activities 3

6.EE.A.3. is addressed in Activities 4

6.EE.A.4. is addressed in Activities 4

6.EE.B.5. is addressed in Activities 5

6.EE.B.6. is addressed in Activities 5, 6, 7, 8

6.EE.B.7. is addressed in Activities 6, 7

6.EE.B.8. is addressed in Activities 8

6.EE.C.9. is addressed in Activities 9

---------------------------------------------

The Make It Real Learning Middle Grades Math Series is a collection of 20 workbooks that address the mathematical content standards of Grades 5, 6, 7, and 8. Each workbook contains ten standards-aligned activities that develop mathematical thinking. Interesting real world contexts are integrated into many of the activities.

Fifth Grade Mathematics Workbooks

• 5th Grade Operations and Algebraic Thinking

• 5th Grade Numbers and Operations in Base 10

• 5th Grade Numbers and Operations – Fractions

• 5th Grade Measurement and Data

• 5th Grade Geometry

Sixth Grade Mathematics Workbooks

• 6th Grade Ratios and Proportional Relationships

• 6th Grade The Number System

• 6th Grade Expressions and Equations

• 6th Grade Geometry

• 6th Grade Statistics and Probability

Seventh Grade Mathematics Workbooks

• 7th Grade Ratios and Proportional Relationships

• 7th Grade The Number System

• 7th Grade Expressions and Equations

• 7th Grade Geometry

• 7th Grade Statistics and Probability

Eighth Grade Mathematics Workbooks

• 8th Grade The Number System

• 8th Grade Expressions and Equations

• 8th Grade Functions

• 8th Grade Geometry

• 8th Grade Statistics and Probability

Total Pages

46 pages

Answer Key

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Teaching Duration

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