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What are we going to do? What does quantity mean? Quantity means __________. CFU Students, you already know how to use equivalent ratios to find an unknown value. Now, we will solve problems involving percent of a quantity. Make Connection If ratios are equivalent, then you can find a missing value. 1 amount Vocabulary We will solve problems involving a percent of a quantity 1. Learning Objective Activate Prior Knowledge If 6 pounds of beans cost $15, how much will 2 pounds of beans cost? How much will 8 pounds of beans cost? If 12 cups of flour are needed to bake 9 pies, then how many cups are needed to bake 3 pies? How many cups of flour are needed to bake 12 pies? pounds dollars cups pies RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. EE.3 Apply the properties of operations to generate equivalent expressions.

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50% of 120 is 60, or half of the students. What is 25% of the students? How do you know? (write on the double number line) What is 75% of the students? How do you know? (write on the double number line) A percent (%) is part of 100. A percent of a quantity is part of a total. Equivalent ratios on a double number line can be used to show the percent relationship 2. Percent of a Quantity Concept Development 2 the way two things are connected Vocabulary CFU The survey showed that 50% of the students play an instrument. 60 of the 120 students surveyed play an instrument. Students 0%10%20%30%40%50%60%70%80%90%100% 5%10%20%25%50% 1% students took a survey. Students Percent ÷ 2÷ 2 × 3× 3 ÷ 2÷ 2 × 3× 3 75% 25% ÷ 2÷ 2 ÷ 2÷

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A percent (%) is part of 100. A percent of a quantity is part of a total. Equivalent ratios on a double number line can be used to show the percent relationship 2. Strategy Development (Optional) People 0%10%20%30%40%50%60%70%80%90%100% 10%20%25%50% 1% people answered a food survey % of the people surveyed reported they had food allergies. How many people had food allergies? _________________________________________________________________ 2. 75% of the people reported that they eat a full, healthy breakfast. How many people eat a full, healthy breakfast? _________________________________________________________________ The Strategy Select a lower percentage that is simple to calculate, then use this simple percent to find the percent in the problem. What percent am I asked to find and what percent am I given? Which simple percent divides both given and needed percent? After I calculate the simple percent, what do I multiply by to find the percent in the problem? Thinking Process 5% ÷ 5 × 2 ÷ 4 × 3 Find 40%, given 100% 20% ( 10% and 5% also work) 20% × 2 = 40% (220 ÷ 5) × 2 (220 ÷ 4) × 3 Explain how you would apply the strategy to #2. CFU FIND THE GCF before multiplying or dividing

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A percent (%) is part of 100. A percent of a quantity is part of a total. Equivalent ratios on a double number line can be used to show the percent relationship. Skill Development/Guided Practice 3 make a note 4 explain Vocabulary On the double number line, record 3 the given information and the percent to find. Determine which simple percent to calculate; 5, 10, 20, 25, or 50%. (circle) Calculate this percent of the quantity. Solve for the unknown by using the simple percent and quantity. Interpret 4 the solution. Solve problems involving a percent of a quantity using a double number line. 1 a people answered a food survey % of the people surveyed reported they had food allergies. How many people had food allergies? _________________________________________________________________ 2. 75% of the people reported that they eat a full, healthy breakfast. How many people eat a full, healthy breakfast? _________________________________________________________________ 0%10%20%30%40%50%60%70%80%90%100% 5%10%20%25%50% 1% People 220 ÷ ÷ 5 = × 2 44 × 2 = of the 220 people surveyed had food allergies. ÷ ÷ 4 = × 3 = 165 × % 165 of the 220 people surveyed eat a full, healthy breakfast. 55 “Divide down... …Multiply up” How did I/you determine which simple percent to use? How did I/you use the double number line to solve the percent problem? CFU 2 3 FIND THE GCF before multiplying or dividing.

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A percent (%) is part of 100. A percent of a quantity is part of a total. Equivalent ratios on a double number line can be used to show the percent relationship. Skill Development/Guided Practice (continued) On the double number line, record the given information and the percent to find. Determine which simple percent to calculate; 5, 10, 20, 25, or 50%. (circle) Calculate this percent of the quantity. Solve for the unknown by using the simple percent and quantity. Interpret the solution. Solve problems involving a percent of a quantity using a double number line. 1 a How did I/you determine which simple percent to use? How did I/you use the double number line to solve the percent problem? CFU On his MP3 player, Sal had 123 songs that were rock. That was 75% of all his songs. How many total songs did he have on his MP3 player? 4. Andrea has 102 pigs at her Mom’s farm. That is 60% of all her pigs. Find the total number of pigs Andrea owns. Songs 75% 123 ÷ ÷ 3 = × 4 41 × 4 = Pigs “Divide down... …Multiply up” Sal has 164 songs on his MP3 player. 102 ÷ ÷ 3 = × 5 = 170 × Andrea owns 170 pigs total.

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What did you learn today about solving problems involving a percent of a quantity? (Pair-Share) Use words from the word bank. A percent (%) is part of 100. A percent of a quantity is part of a total. Equivalent ratios on a double number line can be used to show the percent relationship. Skill Closure Access Common Core Summary Closure Explain how you determined which simple percent to use and how you used it to solve the problem. On the double number line, record the given information and the percent to find. Determine which simple percent to calculate; 5, 10, 20, 25, or 50%. (circle) Calculate this percent of the quantity. Solve for the unknown by using the simple percent and quantity. Interpret the solution. Solve problems involving a percent of a quantity using a double number line. 1 a % of 80 patients in one hospital were in intensive care. How many patients were in intensive care? 0%10%20%30%40%50%60%70%80%90%100% 5%10%20%25%50% 1% Word Bank percent quantity given simple percent Patients 75% 80 ÷ 4 80 ÷ 4 = × 3× 3 × 3 20 × 3 = of the 80 patients are in intensive care.

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Independent Practice A percent (%) is part of 100. A percent of a quantity is part of a total. Equivalent ratios on a double number line can be used to show the percent relationship. On the double number line, record the given information and the percent to find. Determine which simple percent to calculate; 5, 10, 20, 25, or 50%. (circle) Calculate this percent of the quantity. Solve for the unknown by using the simple percent and quantity. Interpret the solution. Solve problems involving a percent of a quantity using a double number line. 1 a people came to the football game. 60% used student passes. How many people got in using a student pass? 2. Five schools were in the band competition. Forty-five band members were from our school, which was 25% of the total band members. How many total band members were in the competition? “Divide down... …Multiply up” People 2500 ÷ ÷ 5 = × × 3 = Band Members 1,500 people of the 2500 got in using a student pass × 4 = 180 × There were 180 total band members in the competition.

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Independent Practice (continued) A percent (%) is part of 100. A percent of a quantity is part of a total. Equivalent ratios on a double number line can be used to show the percent relationship. On the double number line, record the given information and the percent to find. Determine which simple percent to calculate; 5, 10, 20, 25, or 50%. (circle) Calculate this percent of the quantity. Solve for the unknown by using the simple percent and quantity. Interpret the solution. Solve problems involving a percent of a quantity using a double number line. 1 a students were asked to choose their favorite snow- cone flavor. Twenty percent voted for strawberry. How many students preferred strawberry? 4. Farmer John has 120 cows. Seventy-five percent of his cows are underweight. Find the quantity of cows that are underweight. “Divide down... …Multiply up” “Divide down... …Multiply up” Students 160 ÷ ÷ 5 = of the 160 students preferred the flavor of strawberry. Cows 120 ÷ ÷ 4 = × 3 = 90 × of Farmer John’s cows are underweight. 75%

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Periodic Review 1 Access Common Core 1. A clothing store offers a 25% discount on all items in the store. The original price of a sweater is $40; how much is the discount amount? 2. The basketball player set a record by scoring 55 points in one game. 40% of his points were one-point free throws. How many points were free throws? For every multiple of 5%, find the number of coffee mugs. Record the amounts on the double number line. 0%10%20%30%40%50%60%70%80%90%100% 5%10%20%25%50% 1% ÷ 4 = 10 The sweater will be discounted $ % ÷ 5 = × 2 = 22 The player got 22 points from the free throw line coffee mugs were sold last weekend ÷ 10 26

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