1. 6 th Grade Number Sense 1.3 (6Q) Use proportions to solve problems (e.g., determine the value of N if 4/7 = N/21, find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. Lesson to be used by EDI-trained teachers only. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com Today, we will use proportions to solve problems. * Pre-requisite: AF 1.1 Solving one-step equations Activate (or provide) Prior Knowledge CFU Students, you already know how to solve for an unknown value using inverse operations. Today, we will apply this skill in using proportions to solve problems. Solve for the unknown value using an inverse operation. “Divide by 8” y = y = 3 8 8 “divide by 3” n = n = 5 3 3 Inverse operations are operations that undo each other. 1.2. Learning Objective Name __________________________ CFU What are we going to do today? Inverse Operations + and – ● and ÷

2. 6 th Grade Number Sense 1.3 (6Q) Use proportions to solve problems (e.g., determine the value of N if 4/7 = N/21, find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. Lesson to be used by EDI-trained teachers only. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com CFU Write the following ratio as a fraction. … with a colon. Explain your answer. (pair-share) “There are five trucks for every two mini-vans in the parking lot.” Which is a proportion? Which is not a proportion? How do you know? Choice ____ is/is not a proportion because ________. In your own words, what does a proportion declare? A proportion declares ________________. A B ? ? 5:2 3 4 5 8 3 4 6 8 = ProportionNOT a Proportion Concept Development A ratio is a relationship 1 between two quantities. A ratio can be written with words or numbers. A proportion declares that two ratios are equivalent 2. The cross multiplication of the two equivalent ratios is equal. 1 the way two things are connected 2 equal value For every three boys, there are four girls in the classroom. Ratio “three to four” 3:4 or 3 4

3. 6 th Grade Number Sense 1.3 (6Q) Use proportions to solve problems (e.g., determine the value of N if 4/7 = N/21, find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. Lesson to be used by EDI-trained teachers only. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com Step #1: Read the problem and identify 3 the given ratio. (underline) Step #2: Set up a proportion using the given ratios, if necessary. Hint: Match units across. Step #3: Cross-multiply and solve for the unknown value by applying an inverse operation. Step #4: Interpret 4 the solution of the proportion. 3 find 4 explain Skill Development/Guided Practice 1. In a classroom, the boy to girl ratio was 3:2. If there were 8 girls in the classroom, how many boys were there? 2. In a classroom, the girl to boy ratio was 3:4. If there were 12 boys in the classroom, how many girls were there? If there were 8 girls, then there were 12 boys in the classroom. Use proportions to solve problems. A ratio is a relationship between two quantities. A proportion declares that two ratios are equivalent. Proportion Cross Multiplication If there were 12 boys, then there were 9 girls in the classroom. CFU (#1) How did I/you identify the given ratio? (#2) How did I/you set up the proportion? (#4) How did I/you interpret the solution of the proportion?

4. 6 th Grade Number Sense 1.3 (6Q) Use proportions to solve problems (e.g., determine the value of N if 4/7 = N/21, find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. Lesson to be used by EDI-trained teachers only. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com Step #1: Read the problem and identify the given ratio. (underline) Step #2: Set up a proportion using the given ratios, if necessary. Hint: Match units across. Step #3: Cross-multiply and solve for the unknown value by applying an inverse operation. Step #4: Interpret the solution of the proportion. 3. At the roller skating party, the boy to girl ratio was 5:3. If 30 girls attended the party, how many boys were there? 4. At the local park, the duck to goose ratio was 5:4. If there were 20 geese in the park, how many ducks were there? If 30 girls attended, then there were 50 boys at the party. If 20 geese were in the park, then there were also 25 ducks. Use proportions to solve problems. A ratio is a relationship between two quantities. A proportion declares that two ratios are equivalent. Proportion Cross Multiplication Skill Development/Guided Practice (continued) CFU (#1) How did I/you identify the given ratio? (#2) How did I/you set up the proportion? (#4) How did I/you interpret the solution of the proportion?

5. 6 th Grade Number Sense 1.3 (6Q) Use proportions to solve problems (e.g., determine the value of N if 4/7 = N/21, find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. Lesson to be used by EDI-trained teachers only. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 5. In Maya’s marble collection, she has three red marbles for every four blue marbles. If Maya has 21 red marbles, how many blue marbles are in her collection? 6. In a grocery store, there are two apples for every three mangoes. If there are 16 apples in the store, how many mangoes are there? If Maya has 21 red marbles, then she has 28 blue marbles. If there are 16 apples in the store, then there are 24 mangoes. Skill Development/Guided Practice (continued) Step #1: Read the problem and identify the given ratio. (underline) Step #2: Set up a proportion using the given ratios, if necessary. Hint: Match units across. Step #3: Cross-multiply and solve for the unknown value by applying an inverse operation. Step #4: Interpret the solution of the proportion. Use proportions to solve problems. A ratio is a relationship between two quantities. A proportion declares that two ratios are equivalent. Proportion Cross Multiplication CFU (#1) How did I/you identify the given ratio? (#2) How did I/you set up the proportion? (#4) How did I/you interpret the solution of the proportion?

6. 6 th Grade Number Sense 1.3 (6Q) Use proportions to solve problems (e.g., determine the value of N if 4/7 = N/21, find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. Lesson to be used by EDI-trained teachers only. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 7. A map of San Francisco uses a scale 5 of 8 centimeters equals 12 miles. How many miles are represented by 10 centimeters on the map? 5 ratio of measurement 8. A map of Boston uses a scale of 6 centimeters equals 8 miles. How many miles are represented by 9 centimeters on the map? A distance of 12 miles is represented by 9 centimeters on the map. A distance of 15 miles is represented by 10 centimeters on the map. Skill Development/Guided Practice (continued) Step #1: Read the problem and identify the given ratio. (underline) Step #2: Set up a proportion using the given ratios, if necessary. Hint: Match units across. Step #3: Cross-multiply and solve for the unknown value by applying an inverse operation. Step #4: Interpret the solution of the proportion. Use proportions to solve problems. A ratio is a relationship between two quantities. A proportion declares that two ratios are equivalent. Proportion Cross Multiplication CFU (#1) How did I/you identify the given ratio? (#2) How did I/you set up the proportion? (#4) How did I/you interpret the solution of the proportion?

7. 6 th Grade Number Sense 1.3 (6Q) Use proportions to solve problems (e.g., determine the value of N if 4/7 = N/21, find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. Lesson to be used by EDI-trained teachers only. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 1. Using proportions to solve problems will help you calculate measurements. CFU Does anyone else have another reason why it is relevant to use proportions to solve problems? (pair-share) Why is it relevant to use proportions to solve problems? You may give me one of my reasons or one of your own. Which reason is more relevant to you? Why? Let f represent the amount of flour. 2 2 Sam must use 12 cups of flour. 2. Using proportions to solve problems will help you do well on tests. Sam is baking cookies for his classroom winter party. The recipe says for every 2 cups of sugar he must use 3 cups of flour. He wants to bake more cookies than the recipe will make. If he uses 8 cups of sugar, how many cups of flour must he use? Relevance A ratio is a relationship between two quantities. A proportion declares that two ratios are equivalent.

8. 6 th Grade Number Sense 1.3 (6Q) Use proportions to solve problems (e.g., determine the value of N if 4/7 = N/21, find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. Lesson to be used by EDI-trained teachers only. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com Skill Closure A ratio is a relationship between two quantities. A proportion declares that two ratios are equivalent. Step #1: Read the problem and identify the given ratio. (underline) Step #2: Set up a proportion using the given ratios, if necessary. Hint: Match units across. Step #3: Cross-multiply and solve for the unknown value by applying an inverse operation. Step #4: Interpret the solution of the proportion. 1. In a classroom, the boy to girl ratio was 5:3. If there were 9 girls in the classroom, how many boys were there? 2. In a dog park, the ratio of beagles to greyhounds is 3:4. If there are 16 greyhounds in the park, how many beagles are there? If there were 9 girls, then there were 15 boys in the classroom. If there are 16 greyhounds in the dog park, then there are 12 beagles. Summary Closure What did you learn today about using proportions to solve problems? Day 1 ______________________________________________________________________ Day 2 ______________________________________________________________________ Use proportions to solve problems. _______________________________________________________________ Yuri is trying to set up a proportion to solve a word problem about pigs and cats. His first attempt was incorrect. Explain why his setup is incorrect and what possible error he may have made. Yuri’s proportion Constructed Response Closure Word Bank Proportion Ratio Solution Proportion Cross Multiplication

9. 6 th Grade Number Sense 1.3 (6Q) Use proportions to solve problems (e.g., determine the value of N if 4/7 = N/21, find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. Lesson to be used by EDI-trained teachers only. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 1. In a classroom, the boy to girl ratio was 6:5. If there were10 girls in the classroom, how many boys were there? 2. Aram went fishing this weekend. The ratio of catfish to guppies he caught was 2:5. He caught 20 guppies. How many catfish did he catch? If there were 10 girls, then there were 12 boys in the classroom. If Aram caught 20 guppies, then he caught 8 catfish. Use proportions to solve problems. Step #1: Read the problem and identify the given ratio. (underline) Step #2: Set up a proportion using the given ratios, if necessary. Hint: Match units across. Step #3: Cross-multiply and solve for the unknown value by applying an inverse operation. Step #4: Interpret the solution of the proportion. Independent Practice Name_______________________ A ratio is a relationship between two quantities. A proportion declares that two ratios are equivalent. Proportion Cross Multiplication

10. 6 th Grade Number Sense 1.3 (6Q) Use proportions to solve problems (e.g., determine the value of N if 4/7 = N/21, find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. Lesson to be used by EDI-trained teachers only. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 3. Ericka’s Flower Shop designs floral bouquets. The florist uses four tulips for every three roses in each bouquet. If there are 20 tulips in a bouquet, how many roses are there? 4. A map of Seattle uses a scale of 6 inches equals 10 miles. How many miles are represented by 9 inches on the map? A distance of 15 miles is represented by 9 inches on the map. If there are 20 tulips in a bouquet, then there are 15 roses. Use proportions to solve problems. Step #1: Read the problem and identify the given ratio. (underline) Step #2: Set up a proportion using the given ratios, if necessary. Hint: Match units across. Step #3: Cross-multiply and solve for the unknown value by applying an inverse operation. Step #4: Interpret the solution of the proportion. Independent Practice (continued) A ratio is a relationship between two quantities. A proportion declares that two ratios are equivalent. Proportion Cross Multiplication

11. 6 th Grade Number Sense 1.3 (6Q) Use proportions to solve problems (e.g., determine the value of N if 4/7 = N/21, find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. Lesson to be used by EDI-trained teachers only. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 1. At a birthday party, the girl to boy ratio was 4:6. If 18 boys attended the party, how many girls were there? 2.At an animal shelter, the ratio of dogs to cats is 8:10. If there are 25 cats at the animal shelter, how many dogs are there? If 18 boys attended, then there were 12 girls at the party. If there are 25 cats at the animal shelter, then there are 20 dogs. Use proportions to solve problems. Step #1: Read the problem and identify the given ratio. (underline) Step #2: Set up a proportion using the given ratios, if necessary. Hint: Match units across. Step #3: Cross-multiply and solve for the unknown value by applying an inverse operation. Step #4: Interpret the solution of the proportion. Periodic Review 1 A ratio is a relationship between two quantities. A proportion declares that two ratios are equivalent. Proportion Cross Multiplication Name_______________________

12. 6 th Grade Number Sense 1.3 (6Q) Use proportions to solve problems (e.g., determine the value of N if 4/7 = N/21, find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. Lesson to be used by EDI-trained teachers only. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 4. A map of Miami uses a scale of 3 inches equals 10 miles. How many miles are represented by 12 inches on the map? 3. The ratio of penguins to hippos at the zoo is 7:2. If there are 42 penguins at the zoo, how many hippos are there? If 42 penguins are at the zoo, then there are 12 hippos. A distance of 40 miles is represented by 12 inches on the map. Use proportions to solve problems. Step #1: Read the problem and identify the given ratio. (underline) Step #2: Set up a proportion using the given ratios, if necessary. Hint: Match units across. Step #3: Cross-multiply and solve for the unknown value by applying an inverse operation. Step #4: Interpret the solution of the proportion. Periodic Review 1 (continued) A ratio is a relationship between two quantities. A proportion declares that two ratios are equivalent. Proportion Cross Multiplication

13. 6 th Grade Number Sense 1.3 (6Q) Use proportions to solve problems (e.g., determine the value of N if 4/7 = N/21, find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. Lesson to be used by EDI-trained teachers only. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 1. The ratio of kids to adults in a movie theater is 9:6. If there are 10 adults in the theater, how many kids are there? 2. A map of Minneapolis uses a scale of 2 inches equals 6 miles. How many miles are represented by 3 inches on the map? If there are 10 adults, then there are 15 kids in the theater. A distance of 9 miles is represented by 3 inches on the map. Use proportions to solve problems. Step #1: Read the problem and identify the given ratio. (underline) Step #2: Set up a proportion using the given ratios, if necessary. Hint: Match units across. Step #3: Cross-multiply and solve for the unknown value by applying an inverse operation. Step #4: Interpret the solution of the proportion. Periodic Review 2 A ratio is a relationship between two quantities. A proportion declares that two ratios are equivalent. Proportion Cross Multiplication Name_______________________

14. 6 th Grade Number Sense 1.3 (6Q) Use proportions to solve problems (e.g., determine the value of N if 4/7 = N/21, find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. Lesson to be used by EDI-trained teachers only. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 3. A map of Cleveland uses a scale of 9 cm equals 12 miles. How many miles are represented by 15 cm on the map? 4. The ratio of books to dolls in Zoila’s room is 15:6. If there are 35 books in her room, how many dolls does Zoila have? A distance of 20 miles is represented by 15 cm on the map. If Zoila has 35 books, then she has 14 dolls in her room. Use proportions to solve problems. Step #1: Read the problem and identify the given ratio. (underline) Step #2: Set up a proportion using the given ratios, if necessary. Hint: Match units across. Step #3: Cross-multiply and solve for the unknown value by applying an inverse operation. Step #4: Interpret the solution of the proportion. Periodic Review 2 (continued) A ratio is a relationship between two quantities. A proportion declares that two ratios are equivalent. Proportion Cross Multiplication

15. 6 th Grade Number Sense 1.3 (6Q) Use proportions to solve problems (e.g., determine the value of N if 4/7 = N/21, find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. Lesson to be used by EDI-trained teachers only. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 1. The ratio of blue to red pens on Ms. Garson’s desk is 8:10. If there are 20 blue pens on her desk, how many red pens are there? 2. A map of Jacksonville uses a scale of 6 cm equals 10 miles. How many miles are represented by 15 cm on the map? If there are 20 blue pens, then there are 25 red pens on Ms. Garson’s desk. A distance of 25 miles is represented by 15 cm on the map. Use proportions to solve problems. Step #1: Read the problem and identify the given ratio. (underline) Step #2: Set up a proportion using the given ratios, if necessary. Hint: Match units across. Step #3: Cross-multiply and solve for the unknown value by applying an inverse operation. Step #4: Interpret the solution of the proportion. Periodic Review 3 A ratio is a relationship between two quantities. A proportion declares that two ratios are equivalent. Proportion Cross Multiplication Name_______________________

16. 6 th Grade Number Sense 1.3 (6Q) Use proportions to solve problems (e.g., determine the value of N if 4/7 = N/21, find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. Lesson to be used by EDI-trained teachers only. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 3. A map of Denver uses a scale of 5 cm equals 20 miles. How many miles are represented by 2 cm on the map? 4. The ratio of plates to bowls in Mr. Therrell’s cupboard is 12:8. If there are 21 plates in his cupboard, how many bowls are there? A distance of 8 miles is represented by 2 cm on the map. If there are 21 plates in Mr. Therrell’s cupboard, then he has 14 bowls. Use proportions to solve problems. Step #1: Read the problem and identify the given ratio. (underline) Step #2: Set up a proportion using the given ratios, if necessary. Hint: Match units across. Step #3: Cross-multiply and solve for the unknown value by applying an inverse operation. Step #4: Interpret the solution of the proportion. Periodic Review 3 (continued) A ratio is a relationship between two quantities. A proportion declares that two ratios are equivalent. Proportion Cross Multiplication

17. 6 th Grade Number Sense 1.3 (6Q) Use proportions to solve problems (e.g., determine the value of N if 4/7 = N/21, find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. Lesson to be used by EDI-trained teachers only. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com Learning Objective : Today, we will use proportions to solve problems. Cognitive StrategiesTeaching Strategies ElaborationDemonstration Targeted vocabulary: ratio, relationship, proportion, equivalent, identify, interpret, scale Language Strategies Vocabulary Words Academic relationship, equivalent, identify, interpret Content ratio, proportion Support scale Vocabulary Strategy Multiple-Meaning Synonym identify, interpret Definition ratio, relationship, proportion, equivalent, scale Homophone Internal Context Clue Listen, SpeakSimilar Sounds Read Tracked Reading Decoding Rules Write Writing Content Access Strategies Comprehensible Input Cognates Contextual Clues Graphic Organizer Contextualized Definitions Pictures EDI – Cognitive, Teaching and English Learners Strategies

18. 6 th Grade Number Sense 1.3 (6Q) Use proportions to solve problems (e.g., determine the value of N if 4/7 = N/21, find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. Lesson to be used by EDI-trained teachers only. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com Blank Page