Noticing Subtleties

This just happened…

I walked into an 8th grade classroom finishing up writing and solving systems of equations given word problems.  They began this learning last week.

I overheard the teacher and a student having a discussion about drawing pictures to represent the problem versus trying to write the equations.  This told me that the weekend was too big of a gap from the examples that they had done last Thursday (they had a sub on Friday).

Here is a problem from the set that they were working on:

I briefly walked over to a different student and noticed that she only had one equation to represent this cars and motorcycles problem. She defined the variables correctly, but had written a single equation that mixed the information about the number of wheels and the total number of vehicles.  She hadn’t made sense of what her equation actually meant.

But, I thought that maybe it goes further than that.

I think the students need to see the difference between problems that require a one-variable equation, a two-variable equation, and a system of equations side by side. Here is what I came up with:

It’s nothing fancy or mind-blowing…I just want to see if this gives them a structure to look for when they are deciding how best to represent a given scenario.  I want them to see that there are two unknowns in the third case, and that they need to create an algebraic representation for Eli’s savings and for Lucas’ savings.

I’m wondering if we should ask them to notice and wonder???  Or simply ask…what is the same and what is different…

I’m also wondering if I should remove the headings from the table before we ask them to notice and wonder???

We’re going to try this tomorrow…so I’ll let you know how it goes.