Module 1 lesson 8
- 1. Module 1 Lesson 8.notebook 1 September 18, 2014 Lesson 7 Homework Review
- 2. Module 1 Lesson 8.notebook 2 September 18, 2014 Module 1 Ratios and Unit Rates Topic A: Representing and Reasoning About Ratios Lesson 8: Equivalent Ratios Defined Through the Value of a Ratio
- 3. Module 1 Lesson 8.notebook 3 September 18, 2014 Classwork Exercise 1 Circle any equivalent ratios from the list below. Ratio: 1:2 Ratio: 5:10 Ratio: 6:16 Ratio: 12:32 Find the value of the following ratios, leaving your answer as a fraction, but re‐write the fraction using the largest possible unit. Ratio: 1:2 Value of the Ratio: Ratio: 5:10 Value of the Ratio: Ratio: 6:16 Value of the Ratio: Ratio: 12:32 Value of the Ratio: What do you notice about the value of the equivalent ratios? The value of the ratio is the same for equivalent ratios.
- 4. Module 1 Lesson 8.notebook 4 September 18, 2014 Note that 1:2 is not the same ratio as 5:10, so we do not say they are equal. The ratios are not the same, but their values are equal. Would this always be the case? Would the values of equivalent ratios always be equal? Exercise 2 Here is a theorem:(a theorem is a statement that is always true) If two ratios are equivalent, then they have the same value. Can you provide any counter‐examples to the theorem above?
- 5. Module 1 Lesson 8.notebook 5 September 18, 2014 Exercise 3 Taivon is training for a duathlon, which is a race that consists of running and cycling. The cycling leg is longer than the running leg of the race, so while Taivon trains, he rides his bike more than he runs. During training, Taivon runs 4 miles for every 14 miles he rides his bike. a. Identify the ratio associated with this problem and find its value.
- 6. Module 1 Lesson 8.notebook 6 September 18, 2014 Use the value of each ratio to solve the following. b. When Taivon completed all of his training for the duathlon, the ratio of total number of miles he ran to total number of miles he cycled was 80:280. Is this possible according to Taivon’s training schedule? Explain why or why not. This is possible because the ratio of the number of miles he ran to the number of miles he biked, 80:280, has the value of which is the same value as the ratio 4:14 27
- 7. Module 1 Lesson 8.notebook 7 September 18, 2014 c. In one training session Taivon ran 4 miles and cycled 7 miles. Did this training session represent an equivalent ratio of the distance he ran to the distance he cycled? Explain why or why not. The training session does not represent an equivalent ratio of the distance he ran to the distance he cycled because the value of the ratio in this instance is which is not equal to 47 27
- 8. Module 1 Lesson 8.notebook 8 September 18, 2014 Closing How is the value of a ratio related to the ratio? Please take out your exit ticket for Lesson 1, close your binder, and complete the exit ticket. This will be collected.