Comparing Functions

Resources for Comparing Functions that have been developed for the Algebra for All project are provided below. Use the comments area at the bottom of page to discuss these resources or share additional online resources related to Comparing Functions.

Student Access:

You do not need to go to the AfA Social Network to access these activities. Students and teachers can access these resources directly by going straight to the urls provided. Simply copy and paste the links given below and provide those links to your students. Click here for more detailed instructions.

The Shapes of Algebra

Description: In the shapes of Algebra, groups of students graph 4 different functions and identify which function is not like the others. In the process they explore features of tables and graphs of various function families. The activity concludes with a practice section in which students use a variety of representations to identify function families. The online version of the activity includes several automated practice applets to support graphing and identifying function families.

Graphing Applets: These applets each contain tables for graphing 4 different functions and a graphing tool that creates a graph of each function for comparison.

Other Groups: Group 1 | Group 2 | Group 3 | Group 4 | Group 5

Practice Applet 1: In this applet students identify which function is not like the others by looking at their equations.

Practice Applet 2: In this applet students match function rules (equations) to their corresponding table of values.

Practice Applet 3: In this applet students select the appropriate function rule for a given graph.

Practice Applet 4: In this applet students sketch the shape of a function given it's equation.

Teacher Video: The Shapes of Algebra: Introduction

Teacher Video: The Shapes of Algebra: Wrap-up

Describing Graphs

Description: In this activity students write the story of a race between four sisters, given a graph of the race. Students also have the opportunity for interactive practice with drawing and interpreting graphs. Finally, there is a practice section in which students identify appropriate graphs for given scenarios.

Two Brothers Race Applet: In this applet students interact with a graph of 2 brothers racing cars. Students can draw graphs based on stories, develop stories based on graphs, and experiment with graphs in a "free play" mode.

Teacher Video: The Four Sisters Race: Introduction

Teacher Video: The Four Sisters Race: Extensions

Teacher Video: Graphs and Scenarios: Introduction

Teacher Video: Graphs and Scenarios: Extensions


Description: This activity provides an introduction to recursive notation. It includes instruction, as well as interactive practice

Recursion Practice 1: Practice identifying patterns and writing recursive notation using frames and arrows.

Recursion Practice 2: Practice identifying patterns and writing recursive notation using next-now and recursive notation.

Teacher Video: Recursion

Lilly's Mussels

Description: Apply a linear and exponential model to a small data set in order to explore the differences in growth pattern, depending on which model is selected.

Teacher Video: Lilly's Mussels: Introduction

Teacher Video: Lilly's Mussels: Wrap-Up

Comparing Linear and Exponential Models

Description: In this activity students compare linear and exponential models by listing their characteristics side-by-side in a table.

Teacher Video: Comparing Linear And Exponential Functions: Examples

Make Me Rich

Description: In this activity, students explore a variety of functions through four different payment plans. They must select the best payment plan for different conditions.

Teacher Video: Make Me Rich: Introduction

Categorizing Patterns

Description: In this activity students explore the characteristics of various function families by comparing the patterns in six different tables of values and identify which type of relationship is shown in each one.

Teacher Video: Categorizing Patterns: Introduction

General Translations

Description: In this activity students learn about and practice how to translate functions, and identify translations from equations of functions.

General Translations Applet: In this applet students practice translating functions by creating graphs of translated functions, or writing functions from given graphs.

Teacher Video: General Translations

Teacher Video: Function Aerobics

Please provide comments on the resources provided on this page, or links to similar resources using the comments feature below.


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Comment by Kelly Kroft on August 11, 2010 at 9:05am
Hey, I'm a little late in trying this applet out. Did anyone try printing at the end? does it give you your results for the entire tutorial? It would be nice to have students complete this at home for homework and bring in their results.
Comment by David Young on July 11, 2010 at 12:08am
When you click on the story or draw tabs it says "Ryan's red car" in the instructions.
Comment by Lisa Anne Jacobs on July 10, 2010 at 1:26pm
the two brothers race doesn't identify WHICH red/blue is RYAN.
Comment by Tonya Raye-Clark on June 29, 2010 at 10:56am
Great job Dave. Thanks. This is so much easier and user friendly.

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