## Sunday, July 29, 2012

### Draw a Picture, You Idiot!

I'd like to make my lesson on writing algebraic expressions more concrete for students. My hope is that students' understanding of simple expressions will lead to better interpretation of equation word problems. I was inspired by Steve Leinwand's book, Accessible Mathematics, where he argues that diagrams should be drawn as much as possible to help students conceptualize material. Here is an excerpt:

"Without question, one of the most common responses I have when sitting in the back of a mathematics class is screaming under my breath, 'Draw a picture!' or 'Use a number line!' or 'Ask them what it looks like!'" (page something or other...I don't know, it's on my Kindle app, how am I supposed to cite these things?)

I think he really meant to say, "Draw a picture, you idiot!" (hence, my post title). So I figured, why not apply it to this lesson:
What does everyone think about teaching this way? Will this help students gain a better understanding of variables and operations? Should I preface this with diagramming of numerical expressions first? What about expressions that don't lend themselves well to a diagram (such as 5 divided by n)? Any suggestions?

Nathan Kraft

#### 7 comments:

1. I can just see Steve exclaiming, "Draw a picture, you idiot!" Anyway, I'm going to encourage my students to draw (sketch) more this year, granted we make the time. As for 5/n, draw a picture for 1/n + 1/n + 1/n + 1/n + 1/n. How's that?

1. But what does 1/n look like?

2. 1/n looks like 1/n. I think I will use this as a review activity with my 6th graders now that I remember this post. Lately, I've really been into rectangles to illustrate some concepts.

2. I am going to try to have my kids have the "Draw Something" app be part of their notes this year. I am going tomorrow to a PD on Accessible Mathematics. I must say when I was reading the book, the solving systems by drawing pictures blew my mind!! So I have decided this year to change up the student summary portion every now and again. Most kids know of the "Draw Something" app, so I hope they will like the idea. We will see.

1. I guess I didn't get that far in the book yet. I'm interested to see what the systems drawing-solution looks like.
I think giving the kids more interesting tools to draw with will certainly help. My district does have iPads, though they probably wouldn't let me install "Draw Something". (No games allowed!) But I'll be using small 12"x12" whiteboards. Probably similar degree of fun.

3. I think I'm kinda known in my circle of workshop teachers as the "rectangle queen" because I DRAW RECTANGLES TO SOLVE EVERYTHING!! Of course not everything, but that's where my mind always goes first. This habit of mind (HOM) comes from the best class I've ever taken called "Visual Math for Middle School Teachers." I mean how can one not sign up for a class with that title, right? That class planted a big robust seed to my love for problem solving. For 5/n, I'd just start with 5 discrete equal sized items (like rectangles!) and leave them be because you're ready to split them up but you don't know into how many pieces yet.

4. Late to the party...

I started using this method for multiplying and dividing polynomials last semester. The graphical representation helped a ton of students. It is also makes factoring quadratics easier.