Function transformations: Desmos rocks it

In Algeba 2, we’ve got our growing list of parent functions, and we know how to slide, flip, and stretch them. Some students have developed a pretty deep understanding of the transformation formulas – that is, they know why they work – and I believe they will be able to recall and use them far into the future. Others are able to use the formulas correctly (some more often than others) but maybe don’t really get exactly how they do what they do. These kids may memorize the formulas for the test, and then forget them.

Today I projected a bunch of  graphs of transformed functions, and kids sought to write an equation for each. It’s a classic Algebra 2 lesson, developing more fluency between the algebraic and graphical contexts. When I handed out the iPads and sent kids to, things really got going.

Desmos is so much better than a graphing calculator for this purpose. It provides instant feedback, and you see the equation and graph at the same time. The graph changes while you edit the equation. Or, you can make a copy of an equation and edit that, then compare. I got some great “What would happen if…” and “Why” questions, which I love. In both sections we had a detailed discussion of why translating then dilating a half-circle would yield a different result than dilating then translating.

The lower-achieving kids seemed to do well with this lesson. It was nice to be able to try something, see what happens, then adjust. And because everyone was engaged, I got to spend some more time working directly with them.

Downsides of Desmos: On an iPad it’s pretty easy to lose your work by deleting or navigating away. Also, the parentheses take some getting used to. The downsides were totally outweighed by how immersed the kids were in the algebra-graph environment, and how much they liked it.


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We are all born into this world, and at some point we will die and that will be that. In the meantime, let’s enjoy our minds and the wonderful and ridiculous things we can do with them. I don’t know about you, but I’m here to have FUN.
-Paul Lockhart

In theory, theory and practice are the same. In practice, they are not.

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