1. DO NOW 12.6.13 DIRECTIONS The following ratios are proportional. Find the value of the missing variable term. Can you determine your solution in a different way?

2. QUIZ # 1 Thursday, December 5, 2013 Name: ____________________ Period: __ DIRECTIONS: Write a proportion, then solve for x. DIRECTIONS: Solve for the variable in each proportion below: DIRECTIONS: State whether the two ratios form a proportion (Yes or No) DIRECTIONS: Calculate the UNIT RATE for each problem below: Mr. Sedar runs 5 miles in 45 minutes. What is his average speed per mile? $15 U.S. will exchange for 195 Pesos when entering Mexico. What is the unit rate per U.S. Dollar ($)? 6 8 10 Yes No 9 minutes per 1 mile 13 Pesos per 1 U.S. Dollar 6 54

3. What are we going to do? What does solve mean? Solve means __________. CFU 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 1 find the answer Vocabulary We will solve 1 problems involving proportional relationships. Learning Objective 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. 2. On a piano, there are five black keys for every seven white keys. 5757 5656 5:6 5:7 or NAME: __________________ 12.6.13

4. Concept Development A proportional relationship is a set of equivalent ratios. Equivalent ratios have different values, but are in the same ratio. To generate 2 an equivalent ratio, multiply or divide each quantity in a ratio by the same value. Proportional Relationship Equivalent Ratios Explain why the ratios are equivalent ratios. In your own words, what is a proportional relationship? A proportional relationship ___________. CFU 5757 25 35 and Animated 2 create Vocabulary

5. Read the problem carefully. Identify 3 the given ratio. (underline) Identify information about the unknown ratio. (circle) Represent 4 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 5 the solution. Solve problems involving proportional relationships. 1 2 3 4 a b 3 find (synonym) 4 show (synonym) 5 explain (synonym) Vocabulary 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 2 1a 1b 3 Skill Development/Guided Practice A proportional relationship is a collection of equivalent ratios. Equivalent ratios have different values, but are in the same ratio. 1.Neil’s recipe for walnut spice cake calls for two cups of flour for every cup of walnuts. If Neil uses six cups of flour, how many cups of walnuts should he use? _____________________________________________ 2. Selena is buying gas at four dollars for every gallon of gas. If Selena spent 16 dollars, how many gallons of gas did she buy? _____________________________________________ flourwalnuts 2 cups1 cup 6 cups? cups If Neil uses six cups of flour, he should use 3 cups of walnuts. 3 cups dollarsgallons $41 $16? If Selena spent 16 dollars, she bought 4 gallons of gas. 4

6. Skill Development/Guided Practice (continued) 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. Solve problems involving proportional relationships. 1 2 3 4 a b 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 2 1a 1b 3 A proportional relationship is a collection of equivalent ratios. Equivalent ratios have different values, but are in the same ratio. 3.A grocery store is selling three melons for seven dollars. If Harold spent $28 on melons, how many did he buy? _____________________________________________ 4. In Maya’s marble collection, she has three red marbles for every four blue marbles. If Maya has 28 blue marbles, how many red marbles are in her collection? _____________________________________________ melonsdollars 37 ? If Harold spent $28, he bought 12 melons. 28 If Maya has 28 blue marbles, she has 21 red marbles. redblue 34 ? 28 12 21

7. Skill Development/Guided Practice (continued) 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. Solve problems involving proportional relationships. 1 2 3 4 a b 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 2 1a 1b 3 A proportional relationship is a collection of equivalent ratios. Equivalent ratios have different values, but are in the same ratio. 5.A koi pond has 27 orange fish and 45 white fish. How many orange fish are there for every five white fish? A second koi pond has 20 white fish. If the fish are in the same ratio, how many orange fish are in the second koi pond? _____________________________________________ 6. Monique bought yams at the store. She spent 24 dollars on 18 yams. At this price, how much did Monique pay for every 3 yams? Martin bought yams at the same store and spent 16 dollars. How many yams did Martin buy? _____________________________________________ orangewhite 2745 3? There are three orange fish for every five white fish. 5 20? 12 If there are 20 white fish, there are twelve orange fish. dollarsyams 2418 3 ? Monique paid four dollars for every three yams. 4 16 ? 12 If Martin spent 16 dollars, he bought twelve yams.

8. 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 2 1 3 4 5 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. 2015 Answers will vary.

9. 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 2 1 3 4 5 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. 812 Answers will vary.

10. Solving problems involving proportional relationships will help you solve real-world problems. Solving problems involving proportional relationships will help you do well on tests. 1 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 2 Relevance A proportional relationship is a collection of equivalent ratios. Equivalent ratios have different values, but are in the same ratio. Sample Test Question: 93. Choose Yes or No to indicate whether each ratio is equivalent to. A B C D O Yes O No 6 10 5757 3535 2525 15 25 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? tulipsroses 43 12 If a bouquet has 12 tulips, there are 9 roses in the bouquet. ? 9

11. 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. Solve problems involving proportional relationships. 1 2 3 4 a b What did you learn today about solving problems involving proportional relationships? (Pair-Share) Use words from the word bank. Skill Closure Access Common Core Summary Closure A proportional relationship is a collection of equivalent ratios. Equivalent ratios have different values, but are in the same ratio. 1.There were four adults for every child in line at the movie theatre. If there were 8 children in line, how many adults were in line at the movie theatre? _____________________________________________ adultschildren 41 8? If there were 8 children in line, there were 32 adults. 32 Yuri created a table to solve the problem above. Explain the error Yuri made. adultschildren 41 ?8 Word Bank proportional relationship equivalent ratio generate Yuri placed the total number of children in line in the wrong column. It should be in the children column.

12. Independent Practice 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. Solve problems involving proportional relationships. 1 2 3 4 a b A proportional relationship is a collection of equivalent ratios. Equivalent ratios have different values, but are in the same ratio. 1.Jason is cooking rice for his family for dinner. The recipe calls for 2 cups of water for every 1 cup of rice. If he uses 4 cups of water, how much rice should he add? _____________________________________________ 2. Raymond is shopping for produce at the local farmer’s market. A fruit stand sells 4 avocados for $3. How much will he pay for 20 avocados? _____________________________________________ waterrice 2 cups1 cup 4 cups? cups If Jason adds 4 cups of water, he should add 2 cups of rice. 2 cups avocadosdollars 43 20? Raymond will pay $15 for 20 avocados. 15

13. Independent Practice (continued) 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. Solve problems involving proportional relationships. 1 2 3 4 a b A proportional relationship is a collection of equivalent ratios. Equivalent ratios have different values, but are in the same ratio. 3.In a box, there are 35 pencils and 10 pens. How many pens are there for every seven pencils? Another box has pencils and pens in the same ratio. If there are 20 pens, how many pencils are in the second box? _____________________________________________ pencilspens 3510 7? There are two pens for every seven pencils. 2 20? 70 If there are 20 pens, there are 70 pencils.

14. Periodic Review 1 Access Common Core 1.The 6 th grade classes are taking a field trip to the aviary 1. There is one adult for every five students. If there are fifteen adults on the field trip, how many students are taking the field trip? _____________________________________________ 2. The aviary has three macaws for every two cockatoos. If there are twelve cockatoos at the aviary, how many macaws are there? _____________________________________________ adults students 15 15? If there are 15 adults, there are 75 students. 75 macawscockatoos 32 12? If there are 12 cockatoos, there are 18 macaws. 18 Fill in the missing values for each proportional relationship. Explain how you found the missing values. 36918 4121628 1. 246814 52025 2. 142135 816404856 3. 1 large building or cage for birds Vocabulary 121521 82024 1012 10153035 7284249 2432

15. Periodic Review 2 Access Common Core 1. Choose Yes or No to indicate whether each ratio is equivalent to. 6 10 O Yes O No ABCABC 3535 6868 21 35 2. Choose Yes or No to indicate whether each ratio is equivalent to. 5 10 O Yes O No ABCABC 1212 1515 15 30 3. Choose Yes or No to indicate whether each ratio is equivalent to. 3939 O Yes O No ABCABC 21 63 1313 1616 1.A map of Seattle uses a scale of six inches for every twenty miles. How many miles are represented by twelve inches on the map? _________________________________________ inchesmiles 620 12? Twelve inches on the map represents 40 miles. 40

16. Periodic Review 3 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? 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? 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.An 18-karat 1 gold necklace weighs 24 grams: 18 grams of pure gold and 6 grams of an alloy 2. There is a matching bracelet that contains 6 grams of gold. How much of the alloy is in the bracelet? What is the weight of the bracelet? _______________________________________________ goldalloy 18 grams6 grams ? grams The bracelet contains 2 grams of the alloy. It weighs 8 grams. 2 grams 16 oranges : 12 apples : 28 total 12 oranges : 9 apples : 21 total 8 oranges : 6 apples : 14 total 9 oranges : 6 apples : 15 total 12 oranges : 8 apples : 20 total 15 oranges : 10 apples : 25 total 1 measure of purity of gold 2 metal made by combining two or more metals Vocabulary