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NYS Core Curriculum lesson 3 Equivalent Ratios Write a one-sentence story problem about ratios. The ratio of sunny days to cloudy days in Montgomery is 3:1. Write the ratio in two different forms. 3:1 3 to 1 When prompted by your teacher, share your sentences and ratios with your table partner. You will have 2 minutes. Lesson 3 Exercise 2 We can use a tape diagram to represent the ratio of the lengths of ribbon. Let us create one together. How many units should we draw for Shanni’s portion of the ratio? How many units should we draw for Mel’s portion of the ratio? Let’s represent this ratio in a table. Shanni’s Ribbon Mel’s Ribbon 7 3 14 6 21 9 Lesson 3 Exercise 2 Continued • Shanni and Mel are using ribbon to decorate a project in their art class. The ratio of the length of Shanni’s ribbon to Mel’s ribbon is 7:3. • Draw a tape diagram to represent this ratio: • Shanni (7) • Mel (3) • What does each unit on the tape diagram represent? (Students discuss….) • (some unit that is a length) • What if each unit on the tape diagram represents 1 inch? Shanni’s 7 inches and Mel’s 3 inches? • What is the ratio of the lengths of the ribbons? 7:3 • What if each unit on the tape diagram represents 2 meters? What are the lengths of the ribbons? Shanni= 14 meters; Mel = 6 meters • How did you determine that amount? • What is the length of Shanni’s and Mel’s ribbons now? (Go back to prior slide with equiv. chart) Lesson 3 continued • We just explored 3 different possibilities for the length of the ribbon; did the number of units in our tape ever diagram ever change? No • What did these 3 ratios, 7:3, 14:6, and 21:9, all have in common? • Mathematicians call these ratios equivalent. What ratios can we say are equivalent to 7:3? Lesson 3 continued • Shanni and Mel are using ribbon to decorate a project in their art class. The ratio of the length of Shanni’s ribbon to Mel’s ribbon is 7:3. • Draw a tape diagram to represent this ratio. • • • • • • Shanni Mel Shanni Mel Shanni Mel 2 2 2 2 2 2 2 2 2 3 3 3 3 2 3 3 3 3 3 3 7 inches 3 inches 7:3 14 meters 6 meters 14:6 21 inches 9 inches 21:9 Exercise 3 Lesson 3 • Mason and Laney ran laps to train for the long distance running team. The ratio of laps Mason ran to the number of laps Laney ran was 2 to 3. • • A. If Mason ran 4 miles, how far did Laney run? Draw a tape diagram to demonstrate how you found the answer. Mason (2) 2 2 • Laney(3) • B. If Laney ran 930 meters, how far did Mason run? Draw a tape diagram to determine how you found the answer. • • Mason (2) 620 meters 310 310 • • Laney (3) 930 meters 310 310 • C. What ratios can we say are equivalent to 2:3? 4:6 , 620:930 2 2 2 310 Exercise 4 Lesson 3 • Josie took a long multiple-choice, end of year vocabulary test. The ratio of the number of problems Josie got incorrect to the number of problems she got correct is 2:9. • A. If Josie missed 8 questions, how many did she get right? Draw a tape diagram to demonstrate how you found the answer. • Wrong 4 4 • Right 4 4 4 4 4 4 4 4 4 • B. If Josie missed 20, how many did she get right? Draw a tape diagram how you found the answer. • Wrong 10 10 • Right 10 10 10 10 10 10 10 10 10 10 Exercise 4 continued • C. Based on the tape diagram on the previous slide, what ratios can we say are equivalent to 2:9? • 8:36 and 20 :90 • D. Come up with another possible ratio of the number Josie got wrong to the number she got right. • Wrong 5 x2 = 10 5 • Right • • • • 5 ?X9= How do you find these missing numbers? Multiply 2x5 and 9x5 Describe how to create equivalent ratios. Multiply both numbers of the ratio by the same number, be sure to use the same number on the top and the bottom! Closing of lesson 3 • Two ratios A:B and C:D are equivalent 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. • Now please complete your exit ticket for Lesson 3: Equivalent Ratios sheet #29 Exit Ticket Lesson 3 For every two dollars that Pam saves in her account, her brother saves five dollars. • A. Determine a ratio to describe the money in Pam’s account to the money in her brother’s account. • B. If Pam has 40 dollars in her account, how much money does her brother have in his account? Use a tape diagram to support your answer. • C. Record the equivalent ratio. • D. Create another possible ratio that describes the relationship between Pam’s account and her brother’s account. Solutions to Exit ticket lesson 3 For every two dollars that Pam saves in her account, her brother saves five dollars. • A. Determine a ratio to describe the money in Pam’s account to the money in her brother’s account. 2:5 • B. If Pam has 40 dollars in her account, how much money does her brother have in his account? Use a tape diagram to support your answer. • Pam • Bro 20 20 20 20 2 x 20 = 40 20 20 20 5 x 20 = 100 Solutions to exit ticket lesson 3 • C. Record the equivalent ratio. • 40:100 • D. Create another possible ratio that describes the relationship between Pam’s account and her brother’s account. • Answers will vary: 4:10, 8:20, etc….