My Teaching Journey

through the intersection of math and middle school

The Tough Girl Theorem

I taught a new lesson a few weeks ago, one that I did not teach last year. The goal of the lesson was for students to understand that there are patterns (useful patterns!) when calculating the standard form of a number from the exponential from. The table they completed is below. Students are sitting in groups of 3 or 4, so I assigned each group two columns to complete. Groups shared their findings with the rest of the class before they answered questions based on the patterns.

One student, a bright girl who acts tough and spends more time socializing than learning during class looked at the completed table and observed that the even bases have all even numbers in standard form and the off bases have all odd numbers in standard form. The students had already told me that they could use the patterns to help confirm their multiplication when finding standard from without a calculator, but another student got excited and explained how Tough Girl’s idea could be more useful since it did not change with different bases like the patterns do.

I named the idea after [Tough Girl] on the spot. Now, my second period can refer to [Tough Girl]’s Theorem to help prove or disprove their work. [Tough Girl] was so proud of herself, and for good reason. I was proud of her too.

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