Taking an idea from Ariane, I modified the activity to multiplying beads rather than adding beads. I did this simply to relate to what we are doing in class. So most of the class was working with multiplication. However, I did have a group that did the addition as written up. The questions were posted and I added a few questions:

What patterns do you notice?

If you used only odd (or only even numbers) could you make a prediction about the ones digit in the next answer?

If you used odd and even numbers could you make a prediction about the ones digit in the next answer?

All of the students enjoyed the activity. The higher students, who tend to be bored during regular math instruction and need to be challenged, enjoyed looking for patterns and relationships. The students who tend to struggle enjoyed that they had an entry point.

The answers to the questions were not as thoughtful and deep as one would hope. That was to be expected due to the age of the students and the lack of exposure of problem solving and justifying or proving their reasoning.

I also did a quick poll as to whether the students would like to do this activity again, never again, or if I made them. The class was pretty much divided.

Great additions Dave. I loved Ariane's and you comments about how this approach, and this problem, keep students on both ends of the performance spectrum engaged! It's going to be interesting after time to see whether we can't have a better understanding of your split vote. It reminds me of another teacher I knew who, as part of her Masters research, surveyed her students on whether they liked to help others. Over half said "no"! She later found out that these kids rarely felt able to help others, and she implemented ways to help them help.

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