# Exponential Representations

Algebra 1B is working on exponential equations. We introduced the unit with the idea of paper folding to the moon. This is a well used example, but I used the TedEd lesson here for inspiration. I didn’t show the video or anything, we just started to compare our numbers to real life objects so they could conceptualize the numbers.

Students folded paper in half to create a number of folds vs layer chart and make predictions about folds they couldn’t complete. Since the model only work for awhile, we talked about how to move from a model using the pattern. I also challenged them to break the world record , but no luck there.

After discussing how the record holder managed to get to 12, I slid this in my “also try with geometry” file since it seems like a lot of deep math to explore with similarity and different sized papers versus folding ability.

I asked the students come up with there own patterns that followed a similar rule.  They drew boxes on graph paper and nicely color coded the information we saw repeated in the pattern, table and graph. I “accidentally” read a students paper backwards and my graph decayed! So they all made new decaying patterns too. Spent some time discussing the surprise that some students felt with the shape of the graph and how quickly it was off the paper. This was also a good spot to revisit scales on graphs.

Anyhow, a few examples:

Note for Self (or Others): Since we didn’t do any transformations, the reflection/write ups seemed to implied an exponential could never cross the x-axis as opposed to the actual idea about their being a limit. We talked about limits, and we’ll revisit when I we start doing the transformations, but I wished I had challenged their reflections right there. Even without going into a transformation, I should have pushed them to explain it not as “can’t cross” but instead the idea of the value approaching zero and why it is the case.