Even seemingly simple problems can offer opportunities for deep mathematical thinking and justifications. Over the last week, for instance, mathematicians in Room 123 have explored partners of numbers through 10. As they worked, their challenge was to find all the possible partners for a given total.

When students shared out their solutions after finding partners for five, one student had a question: Will there be the same number of partners for other numbers or more? As they continued their work finding partners for larger numbers, they noticed a pattern and then used the pattern to make predictions.

Then I challenged the class to explain the pattern.

After talking in pairs, students offered some conjectures, but were not yet able to fully explain why the pattern worked.

I told the class we would return to this question over the next few days, fully expecting that it would take that long to arrive at an answer. But just before lunch, another student came to me and said, “Mrs. Mooney, I’ve been thinking about the question and I think I know the answer!”

After lunch and specials, the student shared her claim. She justified her thinking and convinced the class!