Saturday, October 15, 2011

Algebra Scales Worksheets and Longer-Term Grade 7 Vision

I've been taking a pretty holistic, integrated approach to my Grade 7 curriculum. Our last test looked something like this and it covered some mental percentage arithmetic, some patterns and writing of equations, and then some basic word problems. The class did fair on the exam; most kids got most things correct, except for the setting up of the (rather complicated) word problem. It showed me that we're going to have to come back to practice that skill before the next go-around on an exam, but that as a class we're ready to move on to a new topic -- proportions, but in an integrated fashion still, while looping in all the things we already know.

So far, in terms of actually solving equations, the kids have not progressed to formal symbols and algebra yet. Since I promised them that every Friday is going to be something "fun", I made up yesterday a sheet of algebra scales problems for them to do. (Normally, I'd do this kind of thing on the computer, but for reasons that are not easy to explain, I couldn't get easy access to the computers at the school. I figured doing it on paper is almost as good.) Here was the file I used, and the kids were a bit nuts about it while working loudly but enthusiastically in groups! The problems are scaffolded up to letting the kids see when there are no solutions or there are infinite solutions, and then on the back side they needed to draw their own scales from a given equation, in order to solve for x. I used different levels of the scale to show why we might have something like 5x + 3x + 2 = ... and why that's equivalent to 8x + 2 = ... In a few weeks, once the kids have internalized this visualization method (including negative coefficients and negative integers), we'll go over how it translates formally to algebraic symbols. As always, I am a firm believer that symbols need to be introduced only after the visualization of the operations becomes second-nature to the kids.

It's probably nothing new, but I think if you don't already have a worksheet like this, you may find my scaffolding helpful, so here it is: Positive things on scales and Negative things on scales.

Isn't algebra fun?? :) My hope is that by the end of the first semester, my kids will: be comfortable with the idea of predicting linear patterns forwards/backwards and reading/making graphs; understand intuitively what proportions are, when to use them, and how they are tied to linear patterns; have great number sense and be able to quickly compare quantities that involve calculating fractions or percents; be able to set up and solve linear equations given a word problem. I think the list is ambitious, but definitely doable. That would leave us time in the second semester to do some probability/basic geometry and to begin tackling a "harder" algebra topic such as quadratics.

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