A few weeks ago, I agreed to teach a lesson on domain and range in a Math 10C class. I told the teacher I’d make it interesting and engaging. Shortly after making that promise, I realized I had no idea at all how to make it interesting and engaging. I did what I always do in those situations. I begged for help on Twitter.

It turns out I wasn’t alone in looking for ways to teach Domain and Range. Marshall Thompson admitted he was also interested in finding something. Don’t worry, Marshall, I’m about to hook you up.

Dan Meyer jumped in and was, as advertised, not all that helpful. And he spelled cheques wrong.

I had given up hope. I was about to plan a typical boring lesson. Then Peter Vandermeulen came through.

Peter’s link was to this file. It’s really all you need. It’s a nice, fun, compelling and engaging way to get at Domain and Range. Peter tells me he got the idea from a workshop in his district. I made some additions and modifications, and I’ll explain the lesson below. I’ll present it how I would do it if I ever did it again. I learned a few things.

**Domain and Range Lesson (2 Classes)**

**Introduction and Hook – Pictionary**

Run off the documents below. They contain some blank grids and lots of different types of graphs. Cut them out. The idea is that one student will be given a graph and have to describe it to a partner, who will draw it without looking at it. You make it tougher if you don’t let the describor see what the describee is drawing until the graph is done.

There are two ways you can go from here. Peter’s lesson plan suggests pairing students off and giving them each one graph and one blank. Partner 1 describes his graph, while partner 2 draws. Then they switch. I’d put a time limit of 1 minute on each drawing. When the time is up, they can look at the original and the drawing and see how accurately the drawer was able to replicate the graph based only on the verbal description of the partner.

I tried to make this competitive, like pictionary. I put them in teams of 2 and had them compete against another pair. I photocopied the completed graphs on card stock and gave each group of 4 the whole set, shuffled and face down. Each student was given the sheet with the blank graphs on it. Then the students took turns pulling the top card, and describing it to their partner. The pair sitting out in a round had to judge and decide if the pair doing the drawing did well enough to earn a point. I tried my best to make sure that the person describing the graph couldn’t see what his partner was drawing. It’s much more challenging that way. We played 12 rounds of 1 minute each, so that each student got to describe 3 times and draw 3 times. The competition was fun, but the noise level got pretty high in the room. Peter’s way might be simpler, quieter, faster, and every bit as engaging.

Graph Templates

- Word document so you can modify my graphs if you want.
- PDF file in case my graphs look terrible when you open them with your version of Word.

**The Lesson**

After the game, have a class discussion about what kind of words they were using to describe the graphs to their partners. Students will throw out words like *arrow, axis, quadrant, stops, keeps going, points, curves, straight, ends, begins, lowest, highest, farthest right, farthest left* and more. Their language leads nicely into domain and range.

Give every student two different coloured pencil crayons for the domain and range lesson. Walk them through several graphs from the game, and show the set notation appropriate to the various types (set of points, between two values, going on forever in one or both directions). All I did was make a quick notebook file with screen shots of some of the graphs from the game. What I tried that was new to me, was using the coloured pencil crayons. I asked students to identify the farthest left and right points, mark them, and then colour the *x*-axis in that same colour. Then I had them switch colours, find the highest and lowest points, and colour the *y*-axis in that colour. It really made the domain and range pop out for them.

**Formative Assessment**

After the brief lesson, give them a short sheet with 3 questions. In a 60 minute class, this will pretty much be an exit slip, which is what I called it. In an 90 minute class, you’ll have time for the next part. Use the exit slip to see who understood the lesson, and who needs more help. As students hand them in, you can sort them pretty quickly. I sort them into three piles – “Got It”, “Mostly Got It”, and “Didn’t Get It”.

**Day 2**

**Practice Time** (I use this instead of assigning homework) Group the kids according to how they did on the exit slip. Those in the “Got It” pile are given some higher level questions to practice. Normally, I just pull these right out of the student resource. Those in the “Mostly Got It” pile are given some basic practice questions, as well as some higher level practice questions. Those in the “Didn’t Get It” pile work with me. We will go over some more examples together before I turn them loose.

**Closing Activity**

Peter’s materials contained a set of cards that I used for a closing activity. Half the cards have domains and ranges on them, and the other half have corresponding graphs on them. I didn’t modify these at all, and used them as-is. Peter’s lesson plan suggests giving each student one card, and having them match up with the person who has the corresponding card.

I went a slightly different way. I copied these cards on coloured card stock and separated the kids into groups of 4-5. I gave them an entire set of cards and had them pair them all off, working as a group.

Closing Activity Materials

**My Thoughts**

Thanks to Twitter, I think I delivered a way better lesson than I used to do on this topic way back when I was in the classroom. I’d like to try this lesson once more, exactly as described here. It is ready to go. If you try it, let me know how it goes for you.

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