Interactive Mathematics Program (IMP)
EXAMPLE: This unit follows the following progression:
1. Students are introduced to the unit question by playing games of Pig and thinking about strategy.
2. The first section detours from the unit question to help students "define" probability. There are investigations about gambler's fallacy, experimental versus theoretical probability, and measuring probability between 0 and 1.
3. The second section introduces "rug diagrams" as a way to represent probability. There are some investigations about this and the end of the section ties rug diagrams back to coin and dice games.
4. The third section looks at how things play out "in the long run." It involves investigations about the law of large numbers and expected value.
5. The last section looks at a simplified version of the game of Pig before returning to the original unit question.
EXAMPLE: Here are some problems, in sequence, from the Year 1 Exeter problem set:
Clearly, there are advantages and disadvantages to both approaches. What are they? Do you prefer one over the other? Why? In short, "What's the Difference?!?"