# Powers of Ten and Place Value

My resident and I are pulling our hair out over our Honors Algebra 1 class. They’re happy to work, but they don’t want to think. If they don’t know what comes next, the majority of the class just shuts down. Seriously?!? I’m guessing part of this comes from their backgrounds–they got into the Honors program here in high school, but they’re in Algebra–the top kids passed the Chicago Algebra Exam and are taking Geometry as freshmen instead. That means they have a complex and aren’t usually the very top–just close to it. So they really, really don’t want to be wrong–they’d rather just not try it. I’ll win this one eventually but man am I frustrated right now. Particularly since I think the best way to get what I want is to give a little right now to get them working for me (even if it isn’t really thinking for me) so that they get in the habit of trying things my way for the future.

Anyhow.

We wanted to do some early work around estimation, especially in terms of using powers of ten (both for estimating with operations and for place value/number sense understanding). They can all name their place values and identify numbers, but don’t seem to have a strong concept of equivalence–its all procedural.

So we came up with pyramids.

The basic idea is pretty straightforward–find the product of the numbers on the left side and fill in the pyramid (this is the part they found easy). Down the right side, we gave them similar products, but changed the number on the left as well, so for instance 3.2*10000 or 320*10. The back side has only one number each and they had to find all of their own products using different powers of 10.

We ended up also making a matching chain to practice the powers of 10 for in class, which gave us a good idea of where they struggle (anything with a decimal). If anyone is interested, I’d be happy to share it.

(This document was made by my awesome resident Mrs. D after we brainstormed the idea together.)