**Introduction**

*Learn what the Math Building Blocks representation is and how to use it in the classroom. Become familiar with the strengths and limitations of the model.*

**Chapter 1: Prime Factorizations**

*Use colored blocks to visualize prime factorizations. Explore beautiful patterns. Reason about relationships. Solve challenging puzzles.*

**Chapter 2: Multiplication, Division, and Exponents**

*Visualize properties of multiplication, division and exponents. Understand why they make sense.*

**Chapter 3: Factors**

*Visualize factors easily. Discover new ways to find them. Create a formula for counting them.*

**Chapter 4: GCFs and LCMs**

* Develop new strategies for finding GCFs and LCMs. Discover and visualize a powerful relationship between the GCF and LCM.*

**Chapter 5: Squares, Cubes, and Radicals**

*Discover connections between exponents and radicals. Use prime factorizations to recognize and work with with powers and roots. Use properties of exponents and radicals to name expressions in many equivalent ways.*

**Chapter 6: Inverses and Fractions**

*Use "anti-blocks" to represent reciprocals and fractions. Make connections to addition and subtraction. Explore properties of reciprocals.*

**Chapter 7: Multiplying and Dividing Fractions**

*Use the Math Building Blocks to discover and apply rules for simplifying, multiplying, and dividing fractions.*

**Chapter 8: Algebra**

*Use the Math Building Blocks to represent variables in order to generalize concepts from the first seven chapters.*

**Chapter 9: The Worlds of Addition and Multiplication**

*Use the Math Building Blocks recognize, explore, and analyze parallels between objects and properties belonging to the worlds of addition and multiplication. (currently being written)*

**Chapter 10: Putting Radicals, Inverses, Fractions, and Algebra Together**

*Synthesize and extend learning from chapters 5 through 9. (currently being written)*

**Chapter 11: General Properties and Theorems**

*Use the Math Building Blocks to explore abstract properties of divisibility and to visualize famous proofs such as the infinitude of primes and the irrationality of the square root of 2. (currently being written)*

**More Resources**

*Learn about alternate ways to introduce the Math Building Blocks to students. Download a version of the building blocks grid that uses symbols instead of colors. Watch slide shows that use the blocks to illustrate a modified version of the Sieve of Eratosthenes. Play a prime factorization game on the computer. Explore a huge prime factorization grid that shows the block diagrams for all natural numbers from 1 through 1024. *

**Table of Contents** Intro** ** 1 2 3 4 5 6 7 8 9 10 11 More Resources