Predict: What responses to this prompt would you expect from my Algebra 1 students? (Prior to this problem my kids had mostly worked with integer arithmetic, solving linear equations in one-variable and graphing scenarios and equations.)

problem1

Study: What do you notice in this (small) class set of responses? Note anything that surprises you.

Kid 1:

kid1

Kid 2

kid2

Kid 3

kid3

Kid 4

kid4

Kid 5

kid5

 

 

Kid 6

kid6

Kid 7

kid7

Kid 8

kid8

Kid 9

kid9

Wrap Up

How did your predictions hold up? What surprised you the most? What’s something you wish you knew more about?

Here are 7 mistakes. There represent all of the variety of mistakes from a selection of 36 students. The first two mistakes were repeated by several students, but the last 5 were unique in the sample.

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Which of these mistakes would you predict? Which ones surprise you? Can you make sense of them all?

Clearly the kid doesn’t have a deep conceptual understanding of how to solve equations or simplify expressions. True, the kid probably learned some stuff proceduraly as opposed to conceptually. (Though, I can confirm, that in this classroom nobody ever said anything, like, “When you have an equation you need to add something to each side to isolate the x.” The balanced-scale model was used at first.)

There’s still two interesting, deeper questions, to consider. (Possibly more: bring it up in the comments.)

a) Would this kiddo always make this mistake, when presented with an expression to simplify?

b) If not, then what exactly is it about this problem that prompts the kid to employ a basic move from equations?