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 White1 cm x 1 cmW Red2 cm x 1 cmR Lime3 cm x 1 cmL Purple4 cm x 1 cmP Yellow5 cm x 1 cmY Green6 cm x 1 cmG Black7 cm x 1 cmK Brown8 cm x 1 cmN Blue9 cm x 1 cmB Orange 10 cm x 1 cmE

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

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