# Math Building Blocks: Chapter 6Inverses and Fractions

6-1     Building the Whole Numbers and Natural Numbers

Tasks: Describe the mathematical meaning of each image. Compare them.
Learning goals: Understand and compare how whole numbers are generated using addition vs. multiplication.

6-2     Additive and Multiplicative Inverses

Tasks: Describe the mathematical meaning of each image. Predict the value of the "X"d white block. Compare the images.
Learning goals: Understand the general concept of an inverse. Compare and contrast additive and multiplicative inverses.

6-3     The Inverse of a Product

Tasks: Describe the mathematical meaning of each image. Create your own examples.
Learning goals: Explore and find patterns related to multiplicative inverses of products.

6-4     Building the Positive Rational Numbers

Tasks: Describe the mathematical meaning of each image. Create your own examples.
Learning goals: Use the Math Building Blocks to represent positive rational numbers.

6-5     Simplification

Tasks: Describe the mathematical meaning of each image. Create your own examples.
Learning goals: Compare unsimplified and simplified diagrams for multiplications and addition. Use the Math Building Blocks to represent and simplify fractions.

6-6     Reciprocals of Fractions

Tasks: Describe the mathematical meaning of each image, Create your own examples.
Learning goals: Use Math Building Blocks to represent reciprocals of positive rational numbers. Understand reciprocals are multiplicative inverses.

6-7     A New Multiplication Magic Square

Tasks: Describe the mathematical meaning of each image, Compare and contrast the images. Create your own examples.
Learning goals: Continue to explore multiplicative inverses by analyzing diagrams of multiplication magic squares.