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5-8

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## Exponential Growth Introduced

Harry and his friend make a wager on a game of chess.

### Overview

In this Cyberchase activity, students are introduced to a problem that gives them a sense of how quickly exponential growth accrues in the classic problem about a chess board and grains of rice. The context is extended to consider applications using money growth and chain letters. They are introduced to the algebraic representation for exponential growth.

5-8

### Suggested Time

60 minutes

### Media Resources

Chess Wager QuickTime Video

### Materials

Exponential Growth Handout

Assessment: Level A

Assessment: Level B

### Part I: Learning Activity

1. Read the following to your students: "If someone offered to place a bet with you, and you had your choice of \$100 or a set of pennies, which would you choose? Before you decide, keep in mind that the number of pennies would be determined by the following rule: one penny is placed on a corner square of a chess board. Two pennies are placed in the square next to it. Four pennies are placed in the square next to it. The pennies are doubled again for the next square. This procedure is repeated until all squares on the chessboard have pennies in them." Consider providing a model of a chessboard for the students.

2. Ask students to vote which they would choose, the \$100 or the pennies, by raising their hands. Record the vote on the board. Discuss students' reasons for their choices.

3. Read the following to your students: "You will watch a video clip in which Harry and a young friend are playing chess and they discuss this very problem. Watch the video clip to see how the two of them chose their wager."

4. Show the video Chess Wager.

5. Distribute the Exponential Growth Handout.

6. Ask the students to complete the entire handout.

7. Discuss the handout. (Note: Because the relation starts with 1grain of rice on the first square and two grains of rice on the second square, and four grains of rice on the third square, the relationship is y = 2x-1. You may either teach the students why 20 = 1 or limit the domain to x = 2.)

### Part II: Assessment

Assessment: Level A (proficiency): Students are asked to predict how much money they have in their account after one year if a bank doubles their balance everymonth.

Assessment: Level B (above proficiency): Students apply their knowledge of exponential growth to the context of chain letters.

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