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## Using Two Variables to Express Algebraic Relationships

Students are introduced to algebraic expressions that use more than one variable and have multiple solutions. They figure out combinations of two items at different costs, with each combination adding up to 100.

### Overview

Students are introduced to simple algebraic expressions that have multiple solutions and use more than one variable. Students are asked to figure out combinations of two items at different costs, with each combination adding up to 100. This CYBERCHASE activity is motivated by an episode in which Harry has a fixed budget for clothing, and figures out what combination of jackets and pants he can buy with his \$100.

4-7

1 hour

### Media Resources

Finding the Right Combination of Clothes QuickTime Video

### Part I: Learning Activity

1. Distribute Handout 1: What Clothes to Buy? .

2. Ask students to work handout.

3. Tell the students that they will watch a video clip in which Harry goes shopping for new clothes. Ask students to make a list of clothes they would like to buy. Ask them if their list matches Harry's list of clothing.

4. Show the Finding the Right Combination of Clothes QuickTime Video .

5. Discuss the variety of solutions.

Note to the teacher: The term variable has two related meanings as an unknown and as a quantity that varies. In this episode, the equation is written as 3J + 4P = 100 (where J represents the cost per jacket and P is the cost per pair of pants). One could argue that in this instance J and P are not unknowns nor are they really quantities that vary. Be attuned to see if anyone writes the equation 20J + 10P = 100, in which J and P are the number of jackets and number of pants. Remind students of the importance of carefully labeling their variables.

### Part II: Assessment

Assessment: Level A (proficiency): Students are asked to figure out combinations of jackets and pants that cost less than Harry's full budget.

Assessment: Level B (above proficiency): Students are asked to figure out combinations of three items that cost \$100.

## Educational Standards

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