1. Cuisenaire Rods

2. Piaget • Concrete • A manipulative • Something I can move around and investigate things with • Semi-concrete • A picture of the things I have been moving around • If I have never moved it around before this becomes semi-abstract for me

3. Piaget • Semi-abstract • Symbols or alternate representations for my semi-concrete models • Good time to use algebraic thinking with students • Abstract • Using numbers to represent all parts of the original concrete model

4. Integer Rods • White 1 cm x 1 cm W • Red 2 cm x 1 cm R • Lime 3 cm x 1 cm L • Purple 4 cm x 1 cm P • Yellow 5 cm x 1 cm Y • Green 6 cm x 1 cm G • Black 7 cm x 1 cm K • Brown 8 cm x 1 cm N • Blue 9 cm x 1 cm B • Orange 10 cm x 1 cm E

5. Integer Rods • Equivalents / Combinations • Number of Equivalents = 2n-1

6. Integer Rods • Equivalent Fractions • ½ • 1/3 • ¼ • Etc.