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Grade 6 Module 1. Lesson 3. Equivalent Ratios. Understanding of equivalent ratios. Use tape diagrams Formalize a definition of equivalent ratios. Exercise 1. Write a one-sentence story problem about a ratio. Sample.

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## Grade 6 Module 1

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**Grade 6 Module 1**Lesson 3**Equivalent Ratios**• Understanding of equivalent ratios. • Use tape diagrams • Formalize a definition of equivalent ratios**Exercise 1**• Write a one-sentence story problem about a ratio.**Sample**The ratio of the number of sunny days to the number of cloudy days in this city is 3:1.**Exercise 1**Write the ratio in two different forms**Answers**• 3:1 3 to 1**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.**Tape Diagram**Shanni Mel**Tape Diagram**What does each unit on the tape diagram represent?**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?**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?**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**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?**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?**Tape Diagram**Mathematicians call these ratios equivalent. What ratios can we say are equivalent to 7:3?**Tape Diagram**Draw a tape diagram to represent this ratio: 7:3 7 inches to 3 inches 14:6 14 meters to 6 meters 21:9 21 inches to 9 inches**Tape Diagram**Shanni Mel 7 inches to 3 inches 7:3**Tape Diagram**Shanni Mel 14 inches to 6 inches 14:6**Tape Diagram**Shanni Mel 21 inches to 9 inches 21:9**Exercise 3 (a)**Mason Laney**Exercise 3 (a)**Mason = 4 miles Laney = 6 miles**Exercise 3 (a)**Mason = 4 miles Laney = 6 miles**Exercise 3 (b)**Mason = 620 m Laney = 930 m**Exercise 3 (b)**Mason = 620 m Laney = 930 m**Exercise 3(c)**What ratios can we say are equivalent to 2:3?**Exercise 3(c)**4:6 and 620:930**Exercise 4(a)**Wrong = 8 Right = ?**Exercise 4(a)**Wrong = 8 Right = 36**Exercise 4(b)**Wrong = 20 Right = ?**Exercise 4(b)**Wrong = 20 Right = 90**Exercise 4(d)**Wrong = Right = ?**Closing**Two ratios A:B and C:D are equivalent ratios if there is a positive number, c, such that C = cA and D = cB. 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.

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