I’ve really been pushing multiple representations with my Algebra 1 students. As we’ve started solving linear equations, we’ve been using verbal representations and symbolic representations and translating between them. Problem represented verbally have often proved more accessible to them than ones presented symbolically, at least as first. For instance,

Andrew picks a number.

He adds five to it.

He doubles the result.

Then he adds five more.

He ends up with 39.

can give students a foothold where 2(x+5)+5=39 would leave them not sure where to start. I’ve had students rewrite symbolic problems as verbal problems in order to solve them.

On Thursday, I introduced the idea of using a graphical representation to solve linear equations. The photo above gave the graphical solution to the following “number twirl”–an idea I got from Don Steward. (Don’s site is an amazing resource.) The idea is to find a number that you can put into the twirl so that after it goes once around, it stays the same.

We wrote out the equation suggested by the twirl and then graphed the two resulting expressions. The graph found the solution for us! I talked up the graph as a paper calculator—we set things up, and then the answer pops out. Pretty smart for a bit of paper!

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