Lesson 7.2.2 Setting Up and Solving Proportions

1 Course: 7th Grade Math DETAIL Lesson PLAN Student Objective Use proportional relationships to solve multistep ratio and percent problems. Lesson Lesson Replacement Lesson Setting Up and Solving Proportions Homework Proportion word problems (7 questions). Bellwork Teacher selected Prior Knowledge Review bellwork and homework. Yesterday, we learned about ratios. A ratio is the comparison of two quantities by division. We also, learned about Proportions . A proportion states that 2 ratios are equal. We learned that you can use cross multiplication to determine if 2 ratios are equal to each other. We also solved Proportions that had a variable. Anticipatory Set we are going to continue our study of Proportions , but we will focus on Setting up a proportion from scratch given particular situation.

2 Show PowerPoint: Body Types Why learn? Proportions can be used to find missing numbers in a real world math problem. Later on in the third nine weeks we will see how Proportions can be used to solve problems involving scale models and similar figures. Engineers use scale models to build high tech aircraft. If two figures are similar (same shape, but different size), a proportion can be used to find a missing side length on one of the shapes. Teacher Input Review bellwork and homework. Pass out notes Show PowerPoint on Body Types to introduce today s Lesson on Proportions . Why learn? Show circle map. Define a Proportion. Review how to determine if two ratios form a proportion (cross multiply). Work 1 guided practice problem with students.

3 Review how to solve a proportion if a variable is involved. Work 1 guided practice problem with students. Discuss how to set up a proportion for a given situation using a flow map. Students must remember that when Setting up a proportion you must put like units across from each other. Work guided practice problems involving goggles and football. Students will work 2 you try problems (independently). Classwork: Proportion Word Problem WS (6 problems) Think, Pair, Share Extra Practice: Ratio and Proportion extra practice problems Homework: Proportion Word Problem WS (7 problems) Assessment Observation and questioning. Closure 1. When Setting up a proportion, it is important that the same units are _____? across from each other. Inches across from _____?

4 Inches Dollars across form ____? dollars Pounds across from ____? pounds 2. Once you set up the proportion, what do you do? cross multiply Once you cross multiply your are left with a 1 step _____to solve. equation Student Notes Setting Up Proportions Proportions What are they? How do you set them up? When will we use them? Definition: States that 2 ratios are equal. = To determine if 2 ratios To solve Proportions with form a proportion: a variable: = cross multiply = cross multiply Setting up a proportion: Proportions Put the like units across from each Similar Figures: Important to Remember There is not just one correct way to set up a proportion.

5 The key ( ) is to make sure that you put the like units across from each other. Swimming goggles are 12 for $ At this rate, how much would it cost for 17 goggles? Ratio 1 . Ratio 2 1st way: 2nd way: Answer: $ Answer: $ Setting up and Solving Proportions . When Setting up a proportion, the key is to make sure that you put the like units across from each other. inches inches miles miles feet feet Write a proportion for the situation. Then solve. A football player runs 25 yards in seconds. How many seconds should it take the same football player to run 100 yards? = 25x = 250 x = 10 You Try!

6 1. Jim s heartbeat is 142 beats per 2 minutes. Which proportion would give Jim s heartbeat in 8 minutes? A) C) B) D) Both B and C 2. Write a proportion for the situation. Then solve. 3 ounces for $ ; 5 ounces for x dollars. Step 1 Take the information in the first sentence and make that your first ratio. Step 2 Take the information in the second sentence and set the second ratio up to where the like units are across from each other. Step 3 Cross multiply. Step 3 Solve the one-step equation. Name_____ Date_____ Period: _____ Proportion Word Problems Answer each question using Proportions . Round your answer to the nearest whole number.

7 1) If you can buy one can of pineapple chunks for $2, then how many can you buy with $10? 2) One jar of crushed ginger cost $2. How many jars can you buy for $4? 3) Ming was planning a trip to West Samoa. Before going, she did some research and learned that the exchange rate is 6 Tala for $2. How many Tala would she get if she exchanged $6? 4) Jasmine bought 32 kiwi fruit for $16. If Jasmine has $4, how many kiwi can she buy? 5) Shawna s original rectangle was 24 inches wide and 12 inches tall. If she reduced the size of the rectangle to 2 inches tall, then what is the new width? 6) If you can buy four bulbs of elephant garlic for $8, then how many can you buy with $32? Name_____ Date_____ Period: ____ Simplify each RATIO.

8 Write your answer 3 different ways. 1) 2) 4 : 8 Cross multiply to determine if each set of ratios form a proportion. 3) 4) 5) Yes or No Yes or No Yes or No Solve each proportion. 6) = 7) = 8) = 9) = 10) = 11) = 12) Write a proportion for the following situation. Then solve. 20 ounces at $7; 17 ounces at x dollars Name:_____ Date:_____ Period:_____ Set up a proportion for each situation. Then solve. No credit if not solved using Proportions ! 1) 3 subscriptions to a particular magazine is $63.

9 How much would 28 subscriptions cost? 3) 3 miles in minutes; miles in x minutes. 2) 4 runs in 3 innings; x runs in 9 innings. 4) 20 pounds for $ ; 12 pounds for x dollars. 5) You estimate that you can do 12 math problems in 45 minutes. How long should it take to work 20 problems. 6) Ty scores 75 points in 6 games. At this rate, how many points did Ty score in 4 games? 7) A student types 120 words in 3 minutes. How many minutes does it take for the student to type 200 words?