What's My Rule? Simple Linear Functions

Students investigate simple linear functions by trying to guess a function rule from inputs and outputs. They then write the function rule in algebraic form. This lesson uses a resource of Shodor Education Foundation, Inc. Permission has been granted for the use of the materials as part of the workshop "Interactivate Your Bored Math Students."

A lesson plan for grade 7 Mathematics

By Bev Koester

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Learning outcomes

Students will:

• understand the concept of function.
• relate functions to everyday situations.
• look for patterns and use problem-solving skills to identify simple linear equations based on a sets of ordered pairs.

Teacher planning

Time required for lesson

90 minutes

Materials/resources

Pen and regular notebook paper for each student.

A copy of Function Machine Investigations for each student.

Technology resources

A computer lab or at least a one-computer classroom with an LCD projector, in order to project the screen of the one computer onto a screen in the classroom.

A web browser, such as Internet Explorer or Netscape.

Pre-activities

Students should know how to compute with integers.

Before beginning the lesson, the teacher should become familiar with the internet activity called Function Machine at the web address http://www.shodor.org/interactivate/activities/fm/index.html

Activities

This lesson may take about 60 minutes to complete, either in one long period or two shorter periods. A suggested break is after the free exploration period.

Introduction (about 20 minutes)
Demonstrate to students how the Function Machine activity works. Call on different students to suggest inputs for the machine. Model for students how to keep track of inputs and outputs by using a table.

During this introduction, allow students to keep inputting numbers until most students in the class think that they know the rule. Students who identify the rule quickly can demonstrate their understanding by naming the output before the computer does its calculation.

Now ask a volunteer to explain the rule in words. Ask: “Can anyone think of a different way to express the same rule?”

Show students how to write a formula of the function, and show them how to enter the formula in the computer game.

Finally, ask students to make up a story about how this machine may be used in a real-life application.
Example: y = x * 4 may be used to describe the perimeter of a square when the length of one side is known.

Play one more game with the whole class, and then invite students to explore independently.

Free Exploration (about 10 minutes)
Invite students to “play” with the Function Machine, either independently or by taking turns with a partner. Encourage students to record inputs and outputs and to jot down any discoveries that they make.

Circulate among students, watching for strategies. (See assessment section.)

Structured Investigation (About 30 minutes)
Give each student a copy of the paper called “Function Machine Activities.”

Encourage students to work independently as they write about their strategies to identify rules.

Assessment

Assess student understanding of concepts by reviewing written work. Interview students who may have difficulty expressing ideas in writing.

Consider the following questions:

• After some practice, is the student able to identify a function rule based on only a few inputs? A student who consistently identifies a rule using only two inputs shows excellent understanding.
• Does the student make use of strategies such as entering the numbers 0 or 1?
• Can the student describe a general strategy that can apply to any situation?
• Is the student able to relate an abstract function to a situation in real life?

Supplemental information

None

Related websites

The Function Machine activity in the Shodor Foundation website:

http://www.shodor.org/interactivate/activities/fm/index.html

Comments

Extension:
When students have mastered the Function Machine, they may be ready to explore the Linear Function Machine at the web address:

http://www.shodor.org/interactivate/activities/lfm/index.html

This function machine generates functions in the form y = mx + b, where m and b are integers in the range from -10 to 10.