ALTA Education
Cuisenaire Task Library
Odds and Evens
Your turn — Can you prove it?
Work with a partner. Choose one statement:
- Odd + Even is always Odd
- Odd + Odd is always Even
Then:
- Test the statement using rods.
- Find another example.
- Rearrange the rods to show why it works.
- Record your argument on your Show Me board.
- Explain why it must work for every possible example, not just the ones you tested.
Be ready to convince the rest of us.
Answers
Odd + Even: odd is two equivalent parts plus one white; even is two equivalent parts. Together they can be rearranged into two equivalent trains plus one white, so the result is odd.
Odd + Odd: each odd length is two equivalent parts plus one white. Together there are two of every part and two whites, which can be rearranged into two identical trains, so the result is even.