Dice in a Corner
Why I like this problem: This it the perfect example of a low-floor and high ceiling problem. Anyone who can count to 18 can access this problem, but through questioning, teachers can bring it to a very high level. The manipulation part of the task is great for tactile learners, and student who struggle with focus or sitting still.
Observations from class: Students must have access to dice for this one, and I found it helpful to give them a strip of card stock which they folded into a corner. Some students wanted to stop after finding one solution, and asking questions really helped them dig in and think more deeply.
Follow-up questions I asked:
1. What were the touching values on your dice? Can you find a solution with different sides touching?
2. Can you find any patterns with the solutions?
3. What strategy are you using to figure out your solutions?
4. How will using a different number of dice affect your solutions?
5. How many solutions can you find with 4 dice? With 5 dice?
Required skills / content: Counting to 18.