Tonight I gave the kids the choice of doing more partitions, or something else. They chose something else. In the book Math Tricks, Puzzles & Games by Raymond Blum I found this problem:
Try to connect each rectangle with the triangle that has the same number. Lines cannot cross or go outside the diagram.
When I showed the problem to the kids, A was very upset and said that she didn’t know how to do it because she had never learned. She threw a fit and started drawing a picture instead of working on it. B immediatly started working on it. He worked for about 20 minutes, drawing lines, erasing, drawing more lines. He eventually got frustrated, saying that it was impossible. In spite of A’s protests I brought her over next to B and had him explain what he had tried, and why it was impossible. B connected rectangle 1 to triangle 1, then connected rectangle 2 to triangle 2, but at that point rectangle 3 was completely cut off from triangle 3. Then A took a pencil and a copy of the puzzle and without pausing connected rectangle 1 to triangle 1 and rectangle 3 to triangle 3. Just as B was saying that she wouldn’t be able to connect the last pair, she did!
Getting A to look at a problem is 95% of the battle. I reminded her that it was B’s work on the problem that helped her to her solution.