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

- Word Document of the cards
- PDF File of the cards

**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.

on October 26, 2012 at 3:46 pm |Derek Hatch (Hatcherelli)Hi John,

This is a brilliant lesson! Thanks so much for sharing it. I shared it with the Math teachers in my school as well as our district consultant.

on October 26, 2012 at 5:13 pm |susan russoI played an “Inverse Pictionary” game last year with an algebra 2 class – very fun. The goal was to use math terms (increasing, decreasing, relative min/max, intercepts, etc.) I played 2 kids at the board against each other with the winner being the kid who drew the correct graph first.

As for domain and range, I’ve found that starting with a real-world graph gets the kids understanding the concept before we go to very mathy graphs. I use gapminder and we have wonderful discussions about functions (life expectancy vs. GDP – NOT a function; life expectancy vs time – function.) Life expectancy in the US over time D: {x|1800 < x < 2009}, R: {y| 40 < y < 78}. We talk about some good math words, too – if we look at child mortality, do we expect the graph to decrease or increase over time? What caused the number of children per women to sharply decrease after the 1950s? Good stuff. They actually pick their heads up off the desk for the first time in math class during the domain/range lesson, which is weird.

on November 2, 2012 at 6:48 pm |mathheadinc (@mathheadinc)That is and excellent exercise. Here is an similar, interactive exercise. Press the rest icon and get a new problem each time. http://media.lanecc.edu/users/gettyst/Geogebra/domrang.html

on November 19, 2012 at 9:32 am |Dan Allen (@AllenMath)Check out http://www.desmos.com. There are lots of interesting creations that were created using domain/range restrictions.

on July 23, 2013 at 3:15 am |www.fandompost.comI’m not that much of a online reader to be honest but your sites really nice, keep it up!

I’ll go ahead and bookmark your site to come back later. Many thanks

on July 24, 2013 at 1:01 am |HeatherLove it! Thank you for taking the time to link the documents, love the sharing attitude. I super appreciate you! :-)

on October 24, 2013 at 11:41 am |Suzanne MilkowichI really loved this lesson! I used it this week in my Algebra 2 class and they really enjoyed it. I will be using it again!

on November 5, 2013 at 1:36 pm |mathybeagleI remembered this activity from a while back but I didn’t remember where I saved it. I googled “domain and range cool” and there it was! Lucky me!

on November 5, 2013 at 2:42 pm |John ScammellWhat did we do before Google?

on December 1, 2013 at 8:39 am |Relevant Mathematics | Math I – Unit 1: Problem Solving[…] http://thescamdog.wordpress.com/2012/10/26/domain-and-range-lesson/ […]

on January 6, 2014 at 6:54 pm |MikeTried this today when I found your site last minute. The only change I made was that I did not print out the picture cards. I only printed out the graphs. I put the class into groups of two with one students back to the smartboard. I then projected a card for everyone to describe and the other to draw. I thought it was really fun and nice that they were all working on the same card. I was going to schedule my observation for this lesson but I chickened out. Thanks again.

on January 7, 2014 at 1:38 pm |John ScammellGlad it worked. I like the modification you made. I like to be observed when I’m trying something new and/or strange. That way I show that I’m willing to try that kind of stuff, and if it goes badly we can have a conversation about why that was and what I could have done differently.