My 8th Grade students need a lot of practice with some of the basic moves of algebra. But I’m not finding practice resources that organize things along the lines that I feel they need.

A lot of the existing practice resources categorize equations in big amorphous clumps like “one-step” or “two-step” equations — but there is a whole world of variety between different types of “one-step” equations!

I think this is a confusing way of asking kids to practice equations. It groups equations based on how the equations *look.* It would be better to group practice along the lines of *how you can think* about them.

What I really want — what I think my students need — is practice that focuses on moves, and that includes chances to use those moves on situations that look very different from each other.

Here’s something I whipped up for class today. I haven’t tried it yet, but this is the sort of thing I’m thinking of:

Questions:

- Do you think this is a useful way to organize practice (example/targeted practice/mixed)?
- Do you agree that this (adding to both sides) is a useful chunk of a skill to teach? (I know that, for my students, it is, because I’d found that kids very easily see opportunities to remove something from both sides but not to add.)
- What other moves in algebra do you think would be useful to practice in this way? (Next up for my students, I think, would be super-focusing on equations/inequalities that come down to Ax = B.)

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A game I liked to play with college students who struggle with fluency in Symbolic Algebra is to decouple strategy (about what to do) vs mechanics of carrying out the move. I usually start with them making decisions about what operations they’d like me to carry out to both sides. I don’t let them say things like “cancel, move, cross multiply”. Whatever they tell me to do, I faithfully and correctly carry it out. Then we look at what effect that had, and whether or not that had the effect they wanted. After some

time we switch roles, with me telling them an operation I’d like to try, and they carry out the mechanics. I’ll often show them how to use Desmos to check their mechanics. Not all, but part of what I’m doing feels similar, and I imagine their is someway to scale up from my one-on-one coaching to peer instruction and/or individual practice.

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