1. Grade 6 Module 1 Lesson 3

2. Equivalent Ratios Understanding of equivalent ratios. Use tape diagrams Formalize a definition of equivalent ratios

3. Exercise 1 Write a one-sentence story problem about a ratio.

4. Sample The ratio of the number of sunny days to the number of cloudy days in this city is 3:1.

5. Exercise 1 Write the ratio in two different forms

6. Answers 3:1 3 to 1

7. Exercise 2 Shanni and Mel are using ribbon to decorate a project in their art class. The ratio of the length of Shanni’s ribbon to the length of Mel’s ribbon is 7:3. Draw a tape diagram to represent this ratio.

8. Represent ratio in a table Shanni’s RibbonMel’s Ribbon 73

9. Represent ratio in a table Shanni’s RibbonMel’s Ribbon 73 146

10. Represent ratio in a table Shanni’s RibbonMel’s Ribbon 73 146 219

11. Tape Diagram Shanni Mel

12. Tape Diagram What does each unit on the tape diagram represent?

13. Tape Diagram What if each unit on the tape diagrams represent 1 inch? What are the lengths of the ribbons? What is the ratio of the lengths of the ribbons?

14. Tape Diagram What if each unit on the tape diagrams represents 2 meters? What are the lengths of the ribbons? How did you find that?

15. Tape Diagram What is the ratio of the lengths of Shanni’s ribbon to the length of Mel’s ribbon now? What if each unit represents 3 inches? What are the lengths of the ribbons? Record

16. Tape Diagram If each of the units represents 3 inches, what is the ratio of the length of Shanni’s ribbon to the length of Mel’s ribbon?

17. Tape Diagrams We just explored three different possibilities for the length of the ribbon; did the number of units in our tape diagrams ever change? What did these 3 ratios, 7:3, 14:6, 21:9, all have in common?

18. Tape Diagram Mathematicians call these ratios equivalent. What ratios can we say are equivalent to 7:3?

19. Tape Diagram Draw a tape diagram to represent this ratio: 7:3 7 inches to 3 inches 14:6 14 meters to 6 meters 21:921 inches to 9 inches

20. Tape Diagram 1 in Shanni Mel 7 inches to 3 inches 7:3

21. Tape Diagram 2 m Shanni Mel 14 meters to 6 meters 14:6

22. Tape Diagram 3 in Shanni Mel 21 inches to 9 inches 21:9

23. Exercise 3 (a) Mason Laney

24. Exercise 3 (a) Mason Laney = 4 miles = ? miles

25. Exercise 3 (a) 2 mi Mason Laney = 4 miles = 6 miles

26. Exercise 3 (b) Mason Laney = ? m = 930 m

27. Exercise 3 (b) 310m Mason Laney = 620 m = 930 m

28. Exercise 3(c) What ratios can we say are equivalent to 2:3?

29. Exercise 3(c) 4:6 and 620:930

30. Exercise 4(a) Wrong Right = 8 = ?

31. Exercise 4(a) rr rrrrrrrr Wrong Right = 8 = 36

32. Exercise 4(b) Wrong Right = 20 = ?

33. Exercise 4(b) Wrong Right = 20 = 90

34. Exercise 4(d) Wrong Right = = ?

35. 4(f) 2:3 and 4:6 are equivalent because they represent the same value. The diagram never changed, only the value of each unit in the diagram.

36. Closing Two ratios A:B and C:D are equivalent ratios if there is a positive number, c, such that C = c  A and D = c  B. Ratios are equivalent if there is a positive number that can be multiplied by both quantities in one ratio to equal the corresponding quantities in the second ratio.