Topic A: Proportional Relationships

1. Topic A: Proportional Relationships Lesson 4 Identifying Proportional and Non-Proportional Relationships in Table

2. Topic A Overview Lesson 1: An Experience in Relationships as Measuring Rate Lesson 2: Proportional Relationships Lessons 3-4: Identifying Proportional and Non-Proportional Relationships in Tables Lessons 5-6: Identifying Proportional and Non-Proportional Relationships in Graphs

4. Review Key Vocabulary • Proportional – when two quantities simplify to the same ratio. • Constant – a quantity having a value that does not change or vary. • Constant of Proportionality- a constant value of the ratio of two proportional quantities.

5. Warm-Up: Which Team Will Win the Race? You have decided to run in a long distance race. There are two teams that you can join. Team A runs at a constant rate of 2.5 miles per hour. Team B runs 4 miles the first hour and then 2 miles per hour after that. Task: Create a table for each team showing the distances that would be run for times of 1-6 hours.

6. MODEL: Finding the Constant of Proportionality Team A runs at a constant rate of 2.5 miles per hour.

7. MODEL: Finding the Constant of Proportionality Team B runs 4 miles the first hour and then 2 miles per hour after that.

8. Proportional or Non-Proportional? • For which team is distance proportional to time? Explain your reasoning. • Explain how you know the distance for the other team is not proportional to time?

9. Extension • If the race were 2.5 miles long, which team would win? Explain. • If the race were 3.5 miles long, which team would win? Explain. • If the race were 4.5 miles long, which team would win? Explain.

10. Exit Ticket The table below shows the relationship between the side lengths of a regular octagon and its perimeter. Complete the table. If Gabby wants to make an octagon with a side length of 20 inches using wire, how much wire does she need? Justify your reasoning with an explanation of whether perimeter is proportional to the side length.

12. Warm-Up: Day 2 Does the table show that y is proportional to x? Explain.

13. Review Key Vocabulary • Proportional – when two quantities simplify to the same ratio. • Constant – a quantity having a value that does not change or vary. • Constant of Proportionality- a constant value of the ratio of two proportional quantities.

14. Review: Which Team Will Win the Race? You have decided to run in a long distance race. There are two teams that you can join. Team A runs at a constant rate of 2.5 miles per hour. Team B runs 4 miles the first hour and then 2 miles per hour after that. Task: Create a table for each team showing the distances that would be run for times of 1-6 hours.

15. Discussion • For what length race would it be better to be on Team B than Team A? Explain. • Using the relationship, if the members on the team ran for 10 hours, how far would each member run on each team? • Will there always be a winning team, no matter what length of the course? Why or why not?

16. Discussion Continued… • If the race were 12 miles long, which team should you choose to be on if you wish to win? Why would you choose this team? • How much sooner would you finish on that team compared to the other team?

17. Lesson 4 – Problem Set

18. Lesson 4 – Quiz