1. Grade 6 Module 1 Lesson 14

2. Exercise 1 Create a table to show the time it will take Kelli and her team to travel from Yonkers to each town listed in the schedule assuming that the ratio of the amount of time traveled to the distance traveled is the same for each city. Then, extend the table to include the cumulative time it will take to reach each destination on the ride home.

3. Exercise 1 Hours Miles

4. Exercise 1 Hours Miles 2100

5. Exercise 1 Hours Miles 2100 4200

6. Exercise 1 Hours Miles 2100 4200 6300

7. Exercise 1 Hours Miles 2100 4200 6300 8400 10500 12600 14700 16800

8. Exercise 2 Create a double number line diagram to show the time it will take Kelli and her team to travel from Yonkers to each town listed in the schedule. Then, extend the double number line diagram to include the cumulative time it will take to reach each destination on the ride home. Represent the ratio of the distance traveled on the round trip to the amount of time taken with an equation.

9. Exercise 2 Hours ___________________________________ Miles

10. Exercise 2 Hours 0 2 4 6 8 10 12 14 16 ___________________________________ 0 100 200 300 400 500 600 700 800 Miles

11. Exercise 2 Using the information from the double number line diagram, how many miles would be traveled in one hour?

12. Exercise 2 Using the information from the double number line diagram, how many miles would be traveled in one hour? 50 miles in one hour How do you know?

13. Exercise 2 Using the information from the double number line diagram, how many miles would be traveled in one hour? 50 miles in one hour How do you know? If the train is moving at a constant speed, half of 2 is 1, and half of 100 is 50.

14. Example 1 Dinner service starts once the train is 250 miles away from Yonkers. What is the minimum time the team will have to wait before they can have their meal?

15. Example 1 2100(2,100) 4 6 8 10 12 14 16 Hours Miles Ordered Pair

16. Example 1 2100(2,100) 4200(4,200) 6300(6,300) 8400(8,400) 10500(10,500) 12600(12,600) 14700(14,700) 16800(16,800) Hours Miles Ordered Pair

17. Time and Distance of Travel Hours Miles

18. Discussion How do we label this axis?

19. Discussion How do we label the horizontal axis? Hours Which quantity will we measure using the vertical axis, time or distance?

20. Discussion How do we label the horizontal axis? Hours Which quantity will we measure using the vertical axis, time or distance? Distance

21. Discussion How do we label the horizontal axis? Hours Which quantity will we measure using the vertical axis, time or distance? Distance How should we label the vertical axis?

22. Discussion How do we label the horizontal axis? Hours Which quantity will we measure using the vertical axis, time or distance? Distance How should we label the vertical axis? Miles

23. Discussion Locate the ordered pair (4,200) on the coordinate plane. What does this point represent in the context of distance and time?

24. Discussion Locate the ordered pair (4,200) on the coordinate plane. What does this point represent in the context of distance and time? The train traveled 200 miles in 4 hours.

25. Discussion Locate the ordered pair (10,500) on the coordinate plane. How far did the train travel in 10 hours?

26. Discussion Locate the ordered pair (10,500) on the coordinate plane. How far did the train travel in 10 hours? The train traveled 500 miles in 10 hours.

27. Discussion Locate the ordered pair (14,700) on the coordinate plane. How many hours does it take the train to travel 700 miles?

28. Discussion Locate the ordered pair (14,700) on the coordinate plane. How many hours does it take the train to travel 700 miles? The train has traveled 700 miles in 14 hours.

29. Discussion What do you notice about the arrangement of the points on the coordinate plane?

30. Discussion What do you notice about the arrangement of the points on the coordinate plane? They appear to be in a line. What do you think having an ordered paid of (0,0) mean since we drew the line to the origin?

31. Discussion What do you notice about the arrangement of the points on the coordinate plane? They appear to be in a line. What do you think having an ordered paid of (0,0) mean since we drew the line to the origin? Zero hours after the trip began the train has traveled zero miles.

32. Discussion Using this graph, we can determine how many hours the team will have to wait before being served dinner. What information do we know?

33. Discussion Using this graph, we can determine how many hours the team will have to wait before being served dinner. What information do we know? Dinner is served at mile 250.

34. Discussion Where can we find 250 miles on our graphs?

35. Closing Why would you choose to use a graph to represent a ratio?

36. Closing Why would you choose to use a graph to represent a ratio? Reading a graph can be more efficient than creating a table to determine missing values.

37. Lesson Summary A ratio table, equation, or double number line diagram can be used to create ordered pairs. These ordered pairs can then be graphed on a coordinate plane as a representation of the ratio.

38. Lesson Summary Example: Equation: Y = 3x Ordered Pairs (x,y) (0,0) (1,3) (2,6) (3,9) XY 00 13 26 39

39. Lesson Summary