Noticing Subtleties…Reflection

So I wrote this post yesterday, and today we tried it out.

The purpose was to give students an opportunity to notice the subtleties in the language associated with three different mathematical scenarios they may need to represent.

We read each scenario out loud and then asked the students to compare and contrast each problem type with their table partner.

Some students began by discussing the similarities and differences of the contexts…noticing subtleties 1

Others began by making a list of what they noticed on the back…You can see that this student paid attention to more of the mathy parts~understanding what was meant by a one-variable versus a two variable equation.

noticing subtleties 2

 

And then you’ll see below where students were able to make sense of each scenario and the math required.  However, the first student used an equation in two variables for the first scenario and created a table to find the solution.

We didn’t get to the whole class conversation part of this lesson…I want to talk about each problem type and how to recognize the differences.  Notice that two of the students above wrote the equation for the two variable scenario, but the third student created a table.  I think we need to talk about why that is.  Also, I think I may want to do three more scenarios that would produce equations in standard form, to see if they would recognize the differences then.

I definitely think that this was a useful exercise and would do it again.

One little shout out…one student pulled out their phone because they wanted to check out the equations for the third scenario on their Desmos app!!!

 

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:

motorcycles and cars

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:

one var vs two var vs system

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.