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# From Patterns of Input and Output to Algebraic Equations

### Collection Developed by:

Collection Credits

### Collection Funded by:

Funding for the VITAL/Ready to Teach collection was secured through the United States Department of Education under the Ready to Teach Program.

## Resources for this Lesson:

Connections

Everyday Math (2004)
Teacher Lesson Guide: pp. 105, 462, 920
Teacher Reference Manual: pp. 145-148
Student Reference Book: pp. 69

Standards

to:

Not yet reviewed.

### Overview

In this Cyberchase activity, students watch a video clip in which Hacker creates a cyberfrog with numeric buttons that produce different numbers of hops. The relationship between input and output values is used to teach students how to use algebraic expressions and, subsequently, equations.

### Why is this an important concept?

To anticipate the idea of functions, students learn to discern patterns based on input and output values and they see that the same input consistently produces the same output. They learn to describe the patterns in both words and symbols.

4-8

1 hour

### Media Resources

Frog Hops, Part 1 QuickTime Video
Frog Hops, Part 2 QuickTime Video

### Part I: Learning Activity

1. Read the following to your students: "Hacker once again attempts to infiltrate Motherboard, this time by creating a cyberfrog with numeric buttons that produce certain patterns of hops. As you watch the video clips you will see two different patterns. On a piece of paper write down a sentence that describes the relationship between the input and the output for each of the two patterns."

2. Play Frog Hops, Part 1 QuickTime Video and Frog Hops, Part 2 QuickTime Video.

3. Discuss students' descriptions of the patterns demonstrated in the two video segments.

4. Distribute Handout: Algebraic Expressions and Equations.

5. Ask students to complete the handout.

6. Discuss student answers to the handout.

### Part II: Assessment

Assessment: Level A (proficiency): Students are asked to translate written phrases to algebraic expressions and equations. Students then use their algebraic equation to extrapolate for a large input value.

Assessment: Level B (above proficiency): Students are asked to solve new algebraic relationships in which the input values are not consecutive integers.