# Lesson 15

Changing the Score

- Let’s keep increasing or decreasing an amount by a percentage.

### 15.1: Math Talk: Rewriting Expressions

Express each percent change using an expression that only uses multiplication.

\(x\) increased by 5%

\(y\) decreased by 10%

\(z\) increased by 25%

\(w\) decreased by 2.5%

### 15.2: Your New Score

Round 1: Your starting score is 50. Roll your number cube 10 times. If you are in group

- A, your score increases by 5% every time you roll a 4, 5, or 6 (and stays the same otherwise).
- B, your score increases by 10% every time you roll a 5 or a 6 (and stays the same otherwise).
- C, your score increases by 20% every time you roll a 6 (and stays the same otherwise). Compute your new score after each roll.

roll | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|---|

calculation | |||||||||||

new score | 50 |

Round 2: Your starting score is the result from Round 1. Roll your number cube 10 times. If you are in group

- A, your score decreases by 5% every time you roll a 6 (and stays the same otherwise).
- B, your score decreases by 10% every time you roll a 5 or a 6 (and stays the same otherwise).
- C, your score decreases by 20% every time you roll a 4, 5, or 6 (and stays the same otherwise). Compute your new score after each roll.

roll | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|---|

calculation | |||||||||||

new score |

### 15.3: Bad Assumptions

- Mai started with 100 which increased by 10% for each successful roll. She had 2 successful rolls.
- Mai thinks her score is 120. Explain why this is incorrect.
- What is Mai’s score, really?

- Han started with 100 points and lost 10% for each successful roll. He had 2 successful rolls.
- Han thinks his score is 80. Explain why this is incorrect.
- What is Han’s score, really?

- Suppose you have 100 points. Would you rather be in a group that gets a 5% increase per successful roll and makes 4 successful rolls, or in a group that gets a 10% increase per successful roll but makes 2 successful rolls?