Believe it or not, playground equity is something my students have talked a lot about. At my school, we have a “Primary” playground and a “Junior” playground. The Primary students think the junior side is better, and the junior students agree, but sometimes wish they could go back to the Primary side to play. I mention this because the context of a community playground and having equal play space is something I know they could relate to. This week’s problem can be found in detail here.

Trying to solve this problem reminded me how much I still struggle to see and draw a model of my thinking. I really didn’t have any trouble with those rectangular subs! But 3/4 of 2/5 and 2/5 of 3/4 sort of messed with my mind. I wanted to work it out with some manipulatives at school today. I was going to use colour tiles. Unfortunately, I have this thing called a “full time job” that tends to interfere with my blogging life and I didn’t get to it. Add to that the fact that we are right at the beginning of the “Measuring for the Art Show” unit and any spare time I have to work things out for my own understanding is being devoted to that right now. (I’m going to blog about that unit at the end of the week! Or I’m going to work on report cards. Or maybe both.)

I was able to work this one out with the numbers though. This is my first attempt at drawing a model:

I was confusing myself, so I went back to numbers. After, tried to model it again (on the top sheet.)

Working this problem took me right back to school. I was forever answering the question I thought was being asked instead of making sure I understood the problem. Time and again I would have a test returned to, read a problem to see if I could figure out what I had done incorrectly, and discover I simply hadn’t answered the right question. With age comes wisdom and this time I went back and listened to the teacher set up the problem a second time before I tried to solve it. The first time I thought I was to find 3/4 of the whole and 2/5 of the whole and compare to see if the playground and pavement were equal. Now I know what I have to ask myself if the question makes sense, and this one did not. After listening the second time I knew I was to find 2/5 of 3/4, and 3/4 of 2/5 and compare which is a different question!

Without going into too much detail, I’ll tell you that this turns out to be a common concern amongst my colleagues. Students answer the question (in reading, in writing, in math, on the provincial assessment) they think was asked, not the question that was asked. I love the way putting the problem in an understandable context, and presenting it in a way that encourages students to really discuss the problem until they understand what they need to figure out, helps us make sure we are really assessing what the students know about math, not about following directions. And I also love that the conferring process can focus on straightening out misconceptions so the student can go forward with a set of skills that help them make sense of problems, not just find answers.

And I love that if I was actually going to teach this unit (I won’t because I don’t teach the grades these units are recommended for) there are some models modelled in the books and I could learn how to draw them before I teach the unit to my class.