# Transformations of Functions Card Game

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## Objective

Students will be able to graph transformations on absolute value, polynomial, square root, rational, exponential, logarithmic, and trigonometric functions.

#### Big Idea

Go fish! Students describe transformations of functions to get pairs of cards and win.

## Warm Up

5 minutes

I include Warm ups with a Rubric as part of my daily routine. My goal is to allow students to work on Math Practice 3 each day. Grouping students into homogeneous pairs provides an opportunity for appropriately differentiated math conversations.  This lesson’s Warm Up- Transformations of Functions Review, asks students to describe the transformations on a square root function.  This is a perfect lead in to the day's activity where they will be describing the transformations on many different functions.

## Card Game

45 minutes

I am excited about this game.  I think this is a great way for students to get an opportunity to review every type of function that we looked at this year.  They get multiple opportunities to verbally describe a large variety of functions as well as evaluate the accuracy of their peer's descriptions (Math Practice 3).

I begin by giving the students a sheet of Parent Functions.  This will provide an extra layer of scaffolding to help those that don't remember the shape of all of the functions that were studied over the year.  I found this sheet of parent functions on a great blog called Scholars on Mayhew.

Before they begin playing, it is important to encourage and model the appropriate way to describe a graph or equation.  The warm up is where I start.  I ask for a volunteer to share their description.  The class then evaluates this description and we add or subtract to it until it is clear, concise and accurate.  I then put the problem f(x) = ½ (x+2)4-3 on the board and ask the students to describe this to each other.  We then finalize a good description as a class.

This game is played in groups of three to four students.  Each group  receives a card set of 24 graphs and matching equations.  It is best to copy these onto card stock.  The cards should be shuffled and seven dealt to each student.  The remaining cards go to the center.

This game is played like Go Fish.  On their turn, the student will ask one other student if they have a specific graph or equation by describing the function and its transformations (Math Practice 2).  For example if a students has f(x) = 2x3 + 5 and wants its matching graph, they may say, "Bob, do you have a cubic function that translates up five and is stretched two times as tall?"  If the student does have the graph or equation, they will hand it over and the students whose turn it is gets to go again.  If they ask for something that the other student doesn't have, the other students says "Go Fish", they draw a card, and their turn is over.  The game is played until all pairs are used.  If a student runs out of cards, they draw one out of the pile.  The student with the most pairs is the winner.  Please watch my Video Narrative for information on differentiating this lesson.

The website donnayoung.org is a great resource for blank playing cards in a variety of sizes.  This is where I got the template for my cards.

My problems were created using Kuta Software.  This is an amazing resource that I would recommend to any secondary math teacher.