# Composition of Functions Activities & Games

Instructor: Clio Stearns

Clio has taught education courses at the college level and has a Ph.D. in curriculum and instruction.

Helping students understand the composition of functions is not an easy task. This lesson offers you some activities and games that will help you make this aspect of math learning more interesting for yourself and you students.

## The Right Activity Makes All the Difference

As a math teacher, sometimes you have to work with material that your students do not immediately find engaging. This makes your responsibility especially complicated. Not only are you responsible for communicating the material to your students, but you also have to help get your students motivated to learn and practice.

One thing that can make a huge difference is incorporating games and activities into your instruction. When you choose the right activity, you help students consolidate their understanding, and you also help them see that math can be relevant and fun. This lesson offers some activities and games oriented toward teaching your students about the composition of functions.

## Composition of Functions Games

The games in this section are designed to give students practice with composition of functions while also having fun.

### Match Them Up

This game will help your students think quickly about how to compose functions. You can create the cards for playing this game yourself, or you can have more advanced students create the cards. You should make one set of cards that show functions in terms of f(x), as well as an answer for a value of x. A separate set of cards should show functions in terms of g(x). Students must work to match up their cards so that the g(x) creates the answer found on the f(x) card. They should work as quickly as possible, then go back and check their matching work. Students can work alone or as partners.

### I Do F, You Do G

This is another game that students can play in partnerships. Give your students worksheets with a set of functions that correspond. For instance, they might see the following pair: f(x) = 3x + 7 and g(x) = 20 - x2. The worksheet should then have at least ten different possible values for x. One student should take responsibility for determining f(x) for each value of x, and the other should take responsibility for g(x). Then, they should go back over their lists. The first student should figure out all of the f(g(x)), and the second student should determine g(f(x)) for each of the given values and functions. They should then compare answers and think about how the different orders of composition compare and contrast. A student could also do this independently, racing against herself instead of a partner.

## Composition of Functions Activities

These activities allow students to think about composition of functions using different learning styles.

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