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Middle Grades Math

The Number System

In this unit, students will explore different representations of rational numbers, such as fractions, decimals (with finite or repeating digits) and percents. Students will extend addition, subtraction, multiplication and division to all rational numbers. Students will use rational approximations of irrational numbers to estimate their values, compare sizes and approximate their locations on a number line.

This unit was developed from the Common Core State Standards. For more information download the unit guide (on the right) where the specific content standard is identified. There may be other CCSS that align to the activities as well that are not referenced on the guide.

Middle Grades Math: The Number System Activities

Title Type

Addition and Subtraction of Rational Numbers: Part 1

This lesson involves using pattern blocks to model addition and subtraction of positive mixed numbers for randomly generated numeric expressions.

Alignments  Standards  |  Textbook  
  • 3687

Addition and Subtraction of Rational Numbers: Part 2

This lesson involves representing addition and subtraction of signed mixed numbers on a number line for a randomly generated target sum or difference.

Alignments  Standards  |  Textbook  
  • 2692

Multiplication and Division of Rational Numbers

This lesson involves using an interactive area model to solve multiplication and division problems with positive decimals and mixed numbers.

Alignments  Standards  |  Textbook  
  • 2612

Bathroom Flooring

This lesson involves students tiling the floors of three bathrooms with provided tiles and determining the cost of the floor based on the unit price of each tile.

Alignments  Standards  |  Textbook  
  • 2594

Repeating Decimals and Fractions

This lesson involves students exploring patterns in repeating decimals that represent fractions with denominators 9, 99, and 999.

Alignments  Standards  |  Textbook  
  • 2476

What is Root 2?

This lesson involves estimating the values of two irrational numbers using a number line with increasing precision of scale.

Alignments  Standards  |  Textbook  
  • 2363

Comparing Pi's and Roots

This lesson involves manipulating the radius of a circle and the sides of a right triangle in an attempt to set the circumference of the circle equal to the hypotenuse of the right triangle

Alignments  Standards  |  Textbook  
  • 2237
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