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What are we going to do? What does solve mean? Solve means __________.

Learning Objective. We will solve 1 problems involving proportional relationships. What are we going to do? What does solve mean? Solve means __________. CFU. Activate Prior Knowledge. A ratio is a relationship between two quantities. • A ratio can be written with words or numbers.

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What are we going to do? What does solve mean? Solve means __________.

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  1. Learning Objective We will solve1 problems involving proportional relationships. What are we going to do? What does solve mean? Solve means __________. CFU Activate Prior Knowledge A ratio is a relationship between two quantities. • A ratio can be written with words or numbers. Write each situation as a ratio. 1. At the park, there are five ducks for every six geese. 5 6 5:6 or Students, you already know how to write a situation as a ratio. Now, we will use ratios to solve problems involving proportional relationships. Make Connection 2. On a piano, there are five black keys for every seven white keys. 5 7 or 5:7 1 find the answer Vocabulary

  2. Concept Development • A proportional relationship is a set of equivalent ratios. • Equivalent ratios have equal values using different numbers. • To generate2 an equivalent ratio, multiplyor divideeach quantity in • a ratio by the same number. • Multiplying or dividing by the same number does NOT change the ratio. CFU Explain why the ratios are equivalent ratios. In your own words, what is a proportional relationship? A proportional relationship ___________. On a piano, the ratio of black keys to white keys is5to7. Proportional Relationship 5 7 25 35 and Animated ×2 ×3 ×4 Equivalent Ratios ×3 ×2 ×4 2 create Vocabulary If there are 20 black keys then there are 28 white keys. If there are 10 black keys then there are 14 white keys. If there are 15 black keys then there are 21 white keys. If there are 5 black keys then there are 7 white keys.

  3. Skill Development/Guided Practice A proportional relationship is a set of equivalent ratios. Equivalent ratios have equal values using different numbers. How did I/you identify information about the given ratio? How did I/you identify information about the unknown ratio? How did I/you represent the proportional relationship? How did I/you solve for the unknown? CFU Solve problems involving proportional relationships. 1a Read the problem carefully. Identify3 the given ratio. (underline) Identify information about the unknown ratio. (circle) Represent4 the proportional relationship. Hint: Use a table. Generate an equivalent ratio to solve for the unknown. Hint: Multiply or divide by the same value. Interpret5 the solution. 1 a 1b b 2 2 3 3 4 flour walnuts 2 cups 1 cup ×4 ×4 ×3 ×3 6 cups ? cups 3 cups If Neil uses six cups of flour, he should use 3 cups of walnuts. 3 find (synonym) 4 show (synonym) 5 explain (synonym) Vocabulary dollars gallons $4 1 $16 ? 4 If Selena spent 16 dollars, she bought 4 gallons of gas.

  4. Skill Development/Guided Practice (continued) A proportional relationship is a set of equivalent ratios. Equivalent ratios have equal values using different numbers. How did I/you identify information about the given ratio? How did I/you identify information about the unknown ratio? How did I/you represent the proportional relationship? How did I/you solve for the unknown? CFU Solve problems involving proportional relationships. 1a Read the problem carefully. Identify the given ratio. (underline) Identify information about the unknown ratio. (circle) Represent the proportional relationship. Hint: Use a table. Generate an equivalent ratio to solve for the unknown. Hint: Multiply or divide by the same value. Interpret the solution. 1 a 1b b 2 2 3 3 4 melons dollars 3 7 ×7 ×4 ×4 ×7 ? 12 28 If Harold spent $28, he bought 12 melons. red blue 3 4 If Maya has 28 blue marbles, she has 21 red marbles. ? 21 28

  5. Skill Development/Guided Practice (continued) A proportional relationship is a set of equivalent ratios. Equivalent ratios have equal values using different numbers. How did I/you identify information about the given ratio? How did I/you identify information about the unknown ratio? How did I/you represent the proportional relationship? How did I/you solve for the unknown? CFU Solve problems involving proportional relationships. 1a Read the problem carefully. Identify the given ratio. (underline) Identify information about the unknown ratio. (circle) Represent the proportional relationship. Hint: Use a table. Generate an equivalent ratio to solve for the unknown. Hint: Multiply or divide by the same value. Interpret the solution. 1 a 1b b 2 2 3 3 4 orange white 27 45 There are three orange fish for every five white fish. 4 4 6 4 4 6 9 9 3 ? 5 If there are 20 white fish, there are twelve orange fish. ? 20 12 dollars yams 24 18 Monique paid four dollars for every three yams. 3 ? 4 If Martin spent 16 dollars, he bought twelve yams. ? 16 12

  6. Skill Development/Guided Practice (continued) How did I/you determine what the question is asking? How did I/you determine the math concept required? How did I/you determine the relevant information? How did I/you solve and interpret the problem? How did I/you check the reasonableness of the answer? CFU 1 2 3 7. Vitor is planting flowers and bushes in his garden. He has 4 flowers for every 3 bushes to plant. He wants to have between 20 and 50 plants. Draw in the flowers ( ) and bushes ( ) on the garden to show a possible number of each. 4 5 Answers may vary.

  7. Skill Development/Guided Practice (continued) How did I/you determine what the question is asking? How did I/you determine the math concept required? How did I/you determine the relevant information? How did I/you solve and interpret the problem? How did I/you check the reasonableness of the answer? CFU 1 2 3 8. The Albus Franklin City Park is going to plant some trees. They want to plant between 16 and 30 trees. There will be 2 pine trees for each oak tree. Draw in the pine trees ( ) and oak trees ( ) in the park to show a possible number of each. 4 5 Answers may vary.

  8. Relevance A proportional relationship is a set of equivalent ratios. Equivalent ratios have equal values using different numbers. Solving problems involving proportional relationships will help you solve real-world problems. 1 Ericka’s Flower Shop designs floral bouquets. The florist uses four tulips for every three roses in each bouquet. If a bouquet has twelve tulips, how many roses are in the bouquet? If a bouquet has 12 tulips, there are 9 roses in the bouquet. Solving problems involving proportional relationships will help you do well on tests. 2 Sample Test Question: 93. Choose Yes or No to indicate whether each ratio is equivalent to . A B C D Does anyone else have another reason why it is relevant to solve problems involving proportional relationships? (Pair-Share) Why is it relevant to solve problems involving proportional relationships? You may give one of my reasons or one of your own. Which reason is more relevant to you? Why? CFU 6 10 5 7 O Yes O No O Yes O No O Yes O No O Yes O No tulips roses 3 5 4 3 2 5 12 9 15 25

  9. A proportional relationship is a set of equivalent ratios. Equivalent ratios have equal values using different numbers. Skill Closure Solve problems involving proportional relationships. Read the problem carefully. Identify the given ratio. (underline) Identify information about the unknown ratio. (circle) Represent the proportional relationship. Hint: Use a table. Generate an equivalent ratio to solve for the unknown. Hint: Multiply or divide by the same value. Interpret the solution. 1 a b 2 3 Word Bank 4 proportional relationship equivalent ratio generate adults children 4 1 ×8 ×8 ? 8 If there were 8 children in line, there were 32 adults. 32 Access Common Core Yuri created a table to solve the problem above. Explain the error Yuri made. Yuri placed the total number of children in line in the wrong column. It should be in the children column. adults children 4 1 8 ? Summary Closure What did you learn today about solving problems involving proportional relationships? (Pair-Share) Use words from the word bank.

  10. Independent Practice A proportional relationship is a set of equivalent ratios. Equivalent ratios have equal values using different numbers. Solve problems involving proportional relationships. Read the problem carefully. Identify the given ratio. (underline) Identify information about the unknown ratio. (circle) Represent the proportional relationship. Hint: Use a table. Create an equivalent ratio to solve for the unknown. Hint: Multiply or divide by the same value. Interpret the solution. 1 a b 2 3 4 water rice 2 cups 1 cup ×2 ×4 ×4 ×2 4 cups ? cups 2 cups If Jason adds 4 cups of water, he should add 2 cups of rice. avocados dollars 4 3 Raymond will pay $15 for 20 avocados. 20 ? 15

  11. Independent Practice (continued) A proportional relationship is a set of equivalent ratios. Equivalent ratios have equal values using different numbers. Solve problems involving proportional relationships. Read the problem carefully. Identify the given ratio. (underline) Identify information about the unknown ratio. (circle) Represent the proportional relationship. Hint: Use a table. Create an equivalent ratio to solve for the unknown. Hint: Multiply or divide by the same value. Interpret the solution. 1 a b 2 3 4 pencils pens 35 10 10 5 5 10 There are two pens for every seven pencils. 7 ? 2 If there are 20 pens, there are 70 pencils. ? 20 70

  12. Periodic Review 1 adults students 1 5 15 ? If there are 15 adults, there are 75 students. 75 macaws cockatoos 3 2 ? 12 If there are 12 cockatoos, there are 18 macaws. 18 Access Common Core Fill in the missing values for each proportional relationship. Explain how you found the missing values. ×15 ×6 ×15 ×6 12 15 21 1. 8 20 24 10 12 1 large building or cage for birds Vocabulary 2. 10 15 30 35 7 28 42 49 3. 24 32

  13. Periodic Review 2 inches miles 6 20 Twelve inches on the map represents 40 miles. 12 ? 40 Access Common Core 5 10 6 10 3 9 3. Choose Yes or No to indicate whether each ratio is equivalent to . 2. Choose Yes or No to indicate whether each ratio is equivalent to . 1. Choose Yes or No to indicate whether each ratio is equivalent to . 21 63 1 2 3 5 A B C A B C A B C O Yes O No O Yes O No O Yes O No O Yes O No O Yes O No O Yes O No O Yes O No O Yes O No O Yes O No 1 5 1 3 6 8 21 35 15 30 1 6 ×2 ×2

  14. Periodic Review 3 gold alloy 18 grams 6 grams The bracelet contains 2 grams of the alloy. It weighs 8 grams. ? grams 6 grams 2 grams Access Common Core 1. Eddie is building an arrangement of fruit to give as a gift. He plans to use four oranges for every three apples. If he uses twelve apples, how many oranges should he use? How many pieces of fruit are in the arrangement? 16 oranges : 12 apples : 28 total 3 3 8 oranges : 6 apples : 14 total 2. Eddie has baskets which usually hold between 12 to 26 fruits. How many different arrangements can Eddie make with a 4:3 ratio of oranges to apples? 12 oranges : 9 apples : 21 total 3. Using the same baskets, how many different arrangements can Eddie make if he changes his ratio of oranges to apples to 3:2? 1 measure of purity of gold 2 metal made by combining two or more metals Vocabulary 9 oranges : 6 apples : 15 total 12 oranges : 8 apples : 20 total 15 oranges : 10 apples : 25 total

  15. EDI – Cognitive, Teaching, and English Learner Strategies Cognitive Strategies Teaching Strategies Language Strategies Content Access Strategies

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