Algebra is starting exponents. Yet again, I pulled an opening activity from Dan. This time it came from a video.

Here is a quick rundown

**Ask students to break 25 down into as many pieces as they want.**
**Multiply those pieces.**
**Talk to a neighbor, compare.**
**Who has the largest?**

This took a good 15-20 minutes till students were satisfied and convinced their number was the largest. Almost every period settled on a different number. I am not going to push them to reach one magical number.

It got tiring and time consuming to write **2(2)(2)(2)(2)(2)(2)(2)(2)(2)(2)(2)(2)(2)(2)(2)(2)(2)(2)(2)(2)(2)(2)(2)(1) **into the calculator and on papers so eventually the idea of 2¹²(1) came up instead writing all those 2s. This lead really well into talk about exponents.

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Nice opener, by the way!

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But why not raise the the eleventh and multiply by 3?

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Interesting… none of my students thought of that. It was only in one period that a student came up with 2.5 raised to the tenth. I see a lot of potential in discussing how 25 can be broken into bases of two and three. i.e. two to the power of 8 multiplied by 3 to the power of three.

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