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

6.NS.A.1. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.

6.NS.B.2. Fluently divide multi-digit numbers using the standard algorithm.

6.NS.B.3. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

6.NS.B.4. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4(9+2).

6.NS.C.5. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

6.NS.C.6. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

6.NS.C.7. Understand ordering and absolute value of rational numbers.

6.NS.C.8. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

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

6.NS.B.2 is addressed in Activity 2.

6.NS.B.3 is addressed in Activity 3.

6.NS.B.4 is addressed in Activity 4.

6.NS.C.5 is addressed in Activities 5, 9, and 10.

6.NS.C.6 is addressed in Activities 6, 8, 9, and 10.

6.NS.C.7 is addressed in Activities 7 and 9.

6.NS.C.8 is addressed in Activities 6, 8, and 10.

Worked out solutions for each activity are provided at the end of the workbook.

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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.NS.A.1. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.

6.NS.B.2. Fluently divide multi-digit numbers using the standard algorithm.

6.NS.B.3. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

6.NS.B.4. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4(9+2).

6.NS.C.5. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

6.NS.C.6. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

6.NS.C.7. Understand ordering and absolute value of rational numbers.

6.NS.C.8. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

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

6.NS.B.2 is addressed in Activity 2.

6.NS.B.3 is addressed in Activity 3.

6.NS.B.4 is addressed in Activity 4.

6.NS.C.5 is addressed in Activities 5, 9, and 10.

6.NS.C.6 is addressed in Activities 6, 8, 9, and 10.

6.NS.C.7 is addressed in Activities 7 and 9.

6.NS.C.8 is addressed in Activities 6, 8, and 10.

Worked out solutions for each activity are provided at the end of the workbook.

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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

Total Pages

45 pages

Answer Key

Included

Teaching Duration

N/A

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