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Today, we will use proportions to solve problems.

Learning Objective. Name __________________________. Today, we will use proportions to solve problems. * Pre-requisite: AF 1.1 Solving one-step equations. Inverse Operations. + and –. ● and ÷. CFU What are we going to do today?. Activate (or provide) Prior Knowledge.

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Today, we will use proportions to solve problems.

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  1. Learning Objective Name __________________________ Today, we will use proportions to solve problems. * Pre-requisite: AF 1.1 Solving one-step equations Inverse Operations + and – ● and ÷ CFU What are we going to do today? Activate (or provide) Prior Knowledge Inverse operationsare operations that undo each other. Solve for the unknown value using an inverse operation. 1. 2. 8 8 3 3 “divide by 3” “Divide by 8” n = y = y = 3 n = 5 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.

  2. Concept Development A ratio is a relationship1 between twoquantities. • A ratio can be written with words or numbers. 3 3:4 or 4 “three to four” Proportion ? 3 6 5 3 = 4 4 8 8 ? Ratio For every three boys, there are four girls in the classroom. A proportion declares that two ratios are equivalent2. • The cross multiplication of the two equivalent ratios is equal. 1 the way two things are connected 2 equal value NOT a Proportion 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 ________________. 5:2 B A

  3. Skill Development/Guided Practice A ratio is a relationship between two quantities. A proportion declares that two ratios are equivalent. Proportion Use proportions to solve problems. Cross Multiplication If there were 8 girls, then there were 12 boys in the classroom. 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. Skill Development/Guided Practice (continued) A ratio is a relationship between two quantities. A proportion declares that two ratios are equivalent. Proportion Use proportions to solve problems. Cross Multiplication If 20 geese were in the park, then there were also 25 ducks. If 30 girls attended, then there were 50 boys at the party. 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. Skill Development/Guided Practice (continued) A ratio is a relationship between two quantities. A proportion declares that two ratios are equivalent. Proportion Use proportions to solve problems. Cross Multiplication 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. 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. Skill Development/Guided Practice (continued) A ratio is a relationship between two quantities. A proportion declares that two ratios are equivalent. Proportion Use proportions to solve problems. Cross Multiplication A distance of 15 miles is represented by 10 centimeters on the map. A distance of 12 miles is represented by 9 centimeters on the map. 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. Relevance Let f represent the amount of flour. 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? 2 2 Sam must use 12 cups of flour. A ratio is a relationship between two quantities. A proportion declares that two ratios are equivalent. 1. Using proportions to solve problems will help youcalculate measurements. 2. Using proportions to solve problems will help you do well on tests. 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?

  8. A ratio is a relationship between two quantities. A proportion declares that two ratios are equivalent. Proportion Skill Closure Use proportions to solve problems. Yuri’s proportion Cross Multiplication If there are 16 greyhounds in the dog park, then there are 12 beagles. If there were 9 girls, then there were 15 boys in the classroom. Constructed Response Closure Word Bank Proportion Ratio Solution 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. _______________________________________________________________ _______________________________________________________________ Summary Closure What did you learn today about using proportions to solve problems? Day 1______________________________________________________________________ Day 2______________________________________________________________________

  9. Name_______________________ Independent Practice A ratio is a relationship between two quantities. A proportion declares that two ratios are equivalent. Proportion Use proportions to solve problems. Cross Multiplication If Aram caught 20 guppies, then he caught 8 catfish. If there were 10 girls, then there were 12 boys in the classroom.

  10. Independent Practice (continued) A ratio is a relationship between two quantities. A proportion declares that two ratios are equivalent. Proportion Use proportions to solve problems. Cross Multiplication If there are 20 tulips in a bouquet, then there are 15 roses. A distance of 15 miles is represented by 9 inches on the map.

  11. Name_______________________ Periodic Review 1 A ratio is a relationship between two quantities. A proportion declares that two ratios are equivalent. Proportion Use proportions to solve problems. Cross Multiplication If there are 25 cats at the animal shelter, then there are 20 dogs. If 18 boys attended, then there were 12 girls at the party.

  12. Periodic Review 1 (continued) A ratio is a relationship between two quantities. A proportion declares that two ratios are equivalent. Proportion Use proportions to solve problems. Cross Multiplication 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.

  13. Name_______________________ Periodic Review 2 A ratio is a relationship between two quantities. A proportion declares that two ratios are equivalent. Proportion Use proportions to solve problems. Cross Multiplication 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.

  14. Periodic Review 2 (continued) A ratio is a relationship between two quantities. A proportion declares that two ratios are equivalent. Proportion Use proportions to solve problems. Cross Multiplication If Zoila has 35 books, then she has 14 dolls in her room. A distance of 20 miles is represented by 15 cm on the map.

  15. Name_______________________ Periodic Review 3 A ratio is a relationship between two quantities. A proportion declares that two ratios are equivalent. Proportion Use proportions to solve problems. Cross Multiplication A distance of 25 miles is represented by 15 cm on the map. If there are 20 blue pens, then there are 25 red pens on Ms. Garson’s desk.

  16. Periodic Review 3 (continued) A ratio is a relationship between two quantities. A proportion declares that two ratios are equivalent. Proportion Use proportions to solve problems. Cross Multiplication If there are 21 plates in Mr. Therrell’s cupboard, then he has 14 bowls. A distance of 8 miles is represented by 2 cm on the map.

  17. EDI – Cognitive, Teaching and English Learners Strategies

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