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Lesson 3 Target I will develop an intuitive understanding of equivalent ratios by using tape diagrams to solve problems when the part-to-part ratio is given and the value of one of the quantities is given. I will formalize a definition of equivalent ratios.
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Classwork Exercise 1: 5 minutes Lesson 3 Share your sentences with each other in pairs or trios. Then I will ask a few of you to share with the whole class.
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Read the problem then describe in detail what the problem is about.
Classwork Exercise 2: 15 minutes Lesson 3 Read the problem then describe in detail what the problem is about.
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Let’s represent this ratio in a table!
Classwork Exercise 2: 15 minutes Lesson 3 Shanni’s Ribbon Mel’s Ribbon 7 3 14 6 21 9 Let’s represent this ratio in a table!
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Classwork Exercise 2: 15 minutes Lesson 3 We can use a tape diagram to represent the ratio of the lengths of ribbon. Let’s create one together. Shanni’s Ribbon Mel’s Ribbon 7 3 14 6 21 9
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What does each unit on the tape diagram represent?
Classwork Exercise 2: 15 minutes Lesson 3 Shanni Mel Shanni’s Ribbon Mel’s Ribbon 7 3 14 6 21 9
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Classwork Exercise 2: 15 minutes Lesson 3 We don’t know yet, but each unit represents some unit that is a length.
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What if each unit on the tape diagrams represents 1 inch
What if each unit on the tape diagrams represents 1 inch? What are the lengths of the ribbons? Classwork Exercise 2: 15 minutes Lesson 3 Shanni Mel Shanni’s Ribbon Mel’s Ribbon 7 3 14 6 21 9
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Shanni’s ribbon is 7 inches; Mel’s ribbon is 3 inches.
Classwork Exercise 2: 15 minutes Lesson 3 Shanni’s ribbon is 7 inches; Mel’s ribbon is 3 inches.
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What is the ratio of the lengths of the ribbons?
Classwork Exercise 2: 15 minutes Lesson 3 Shanni Mel Shanni’s Ribbon Mel’s Ribbon 7 3 14 6 21 9
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7:3 and I don’t need to add units!
Classwork Exercise 2: 15 minutes Lesson 3
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What if each unit on the tape diagrams represents 2 meters
What if each unit on the tape diagrams represents 2 meters? What are the lengths of the ribbons? Classwork Exercise 2: 15 minutes Lesson 3 Shanni Mel Shanni’s Ribbon Mel’s Ribbon 7 3 14 6 21 9
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Shanni’s ribbon is 14 meters; Mel’s ribbon is 6 meters.
Classwork Exercise 2: 15 minutes Lesson 3 Shanni’s ribbon is 14 meters; Mel’s ribbon is 6 meters.
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What is the ratio of the length of Shanni’s ribbon to the length of Mel’s ribbon now if each unit represents 2 meters? Classwork Exercise 2: 15 minutes Lesson 3 Shanni Mel Shanni’s Ribbon Mel’s Ribbon 7 3 14 6 21 9
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You are so wrong! It is 7:3. It is 14:6. Classwork Lesson 3
Exercise 2: 15 minutes Lesson 3 You are so wrong! It is 7:3. It is 14:6.
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Classwork Exercise 2: 15 minutes Lesson 3 Who is right?
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What if each unit represents 3 inches
What if each unit represents 3 inches? What are the lengths of the ribbons? Classwork Exercise 2: 15 minutes Lesson 3 Shanni Shanni’s is 21 inches. Mel Shanni’s Ribbon Mel’s Ribbon 7 3 14 6 21 9 Mel’s is 9 inches.
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7 times 3 equals 21; 3 times 3 equals 9.
Classwork Exercise 2: 15 minutes Lesson 3 7 times 3 equals 21; 3 times 3 equals 9. How do you know?
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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? Classwork Exercise 2: 15 minutes Lesson 3 Shanni Mel 21:9 Shanni’s Ribbon Mel’s Ribbon 7 3 14 6 21 9
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We just explored three different possibilities for the length of the ribbon; did the number of units in our tape diagrams ever change? Classwork Exercise 2: 15 minutes Lesson 3 Shanni Mel Shanni’s Ribbon Mel’s Ribbon 7 3 14 6 21 9
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Mathematicians call these ratios equivalent. Classwork Lesson 3
Exercise 2: 15 minutes Lesson 3 Shanni’s Ribbon Mel’s Ribbon 7 3 14 6 21 9
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2m 2m Shanni Mel Shanni Draw a tape diagram to represent this ratio:
Classwork Exercise 2: 15 minutes Lesson 3 7 inches 3 inches 7:3 Shanni Mel 14 meters 6 meters 14:6 Shanni 2m Draw a tape diagram to represent this ratio: Mel 2m 21 inches 9 inches 21:9 Shanni 3 in Draw a tape diagram to represent this ratio: Mel 3 in
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Classwork Exercise 3: 7 minutes Lesson 3
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Classwork Exercise 3: 7 minutes Lesson 3
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Classwork Exercise 3: 7 minutes Lesson 3 4:6 and 620:930
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Classwork Exercise 4: 7 minutes Lesson 3
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Classwork Exercise 4: 7 minutes Lesson 3
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Classwork Exercise 4: 7 minutes Lesson 3 8:36 and 20:90
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Classwork Exercise 4: 7 minutes Lesson 3
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Classwork Exercise 4: 7 minutes Lesson 3
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Classwork Exercise 4: 7 minutes Lesson 3
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Lesson 3
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Lesson 3 Exit Ticket Lesson 1
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Lesson 3 Exit Ticket Lesson 1 2:5
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Lesson 3 Exit Ticket Lesson 1 20 x 5 = 100 dollars
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Lesson 3 Exit Ticket Lesson 1 40:100 20 x 5 = 100 dollars
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Lesson 3 Exit Ticket Lesson 1 4:10, 8:20, etc.
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Problem Set
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2:2, 50:50, etc. 6:22, 9:33, etc.
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9 4
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72 mm wide and 32 mm high.
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2:3
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Jasmine drank 𝟒 cups of milk, and Brenda drank 𝟔 cups of milk
Jasmine drank 𝟒 cups of milk, and Brenda drank 𝟔 cups of milk. Since each pint represents 𝟐 cups, I multiplied Jasmine’s 𝟐 pints by 𝟐 and multiplied Brenda’s 𝟑 pints by 𝟐.
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4:6
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𝟐: 𝟑 and 𝟒: 𝟔 are equivalent because they represent the same value
𝟐: 𝟑 and 𝟒: 𝟔 are equivalent because they represent the same value. The diagrams never changed, only the value of each unit in the diagram.
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