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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 an 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, how many cups are needed to bake 3 pies? How many cups of flour are needed to bake 12 pies? 5 4 1. pounds dollars 6 15 28 20 2. cups pies 12 9 3 16 Common Core 7.RP

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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. Percent of a Quantity Concept Development 2 the way things are connected Vocabulary Complete the statement below. Explain your answer. If Joanna has downloaded 60 MB of the file, the download is _____ complete. Complete the statement below. Explain your answer. If Joanna has downloaded _______, the download is 80% complete. CFU If she has downloaded 30 MB, the download is 25% complete. Megabytes 0%10%20%30%40%50%60%70%80%90%100% 5%10%20%25% 50% 1% 01224486072 90 96120 6 30 Johanna is downloading a 120 MB file. 75% 25% If she has downloaded 48 MB, the download is 40% complete.If she has downloaded 72 MB, the download is 60% complete.If she has downloaded 90 MB, the download is 75% complete. 50% 96 MB

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1% Strategy Development (Optional) People 0%10%20%30%40%50%60%70%80%90%100% 220 220 people answered a food survey. 1. 40% 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 A simple percent (5%, 10%, 20%, 25%, or 50%) can be used to calculate any percent in the problem. Examples: 40% = 2 20% 75% = 3 25% 70% = 7 10% 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 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 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. 10%20%25%50%5% 75% People Percent 220 100 220 ÷ 5 100 ÷ 5 (220 ÷ 5) 2 (100 ÷ 5) 2 ÷ 5 2 2 2 2 220 100 220 ÷ 4 100 ÷ 4 (220 ÷ 4) 3 (100 ÷ 4) 3 ÷ 4 3 3 3 3 1. 2. People Percent

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0%10%20%30%40%50%60%70%80%90%100% 5%10% 1% Skill Development/Guided Practice 3 make a note 4 explain Vocabulary 220 people answered a food survey. 1. 40% 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? ___________________________________________________________ People 2204488 88 of the 220 people surveyed had food allergies. 165 75% 165 of the 220 people surveyed eat a full, healthy breakfast. 55 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. 20%25%50% 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%. 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 2 3 4 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 People Percent 220 100 44 20 88 40 ÷ 5 2 2 2 2 People Percent 220 100 55 25 165 75 ÷ 4 3 3 3 3

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3. 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. 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%. 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 2 3 4 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 Songs 75% 12341164 Pigs Sal has 164 songs on his MP3 player. 10217034 Andrea’s mom owns 170 pigs total. 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. Songs Percent 123 75 41 25 164 100 ÷ 3 4 4 4 4 People Percent 102 60 34 20 170 100 ÷ 3 5 5 5 5

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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 2 3 4 What did you learn today about solving problems involving a percent of a quantity? (Pair-Share) Use words from the word bank. 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. 1. 75% 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% 1% Word Bank percent quantity given simple percent Patients 75% 80 20 60 60 of the 80 patients are in intensive care. Answers may vary. 50% 20%25% 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. Patients Percent 80 100 20 25 60 75 ÷ 4 3 3 3 3

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1. 2500 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? Independent Practice People 2500 500 1500 Band Members 1,500 people of the 2500 got in using a student pass. 45 180 There were 180 total band members in the competition. 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 2 3 4 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. People Percent 2500 100 500 20 1500 60 ÷ 5 3 3 3 3 Band Members Percent 45 25 180 100 4 4 4 4

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3. 160 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. Independent Practice (continued) Students 160 32 32 of the 160 students preferred the flavor of strawberry. Cows 120 90 30 90 of Farmer John’s cows are underweight. 75% 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 2 3 4 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. Students Percent 160 100 32 20 ÷ 5 Cows Percent 120 100 30 25 90 75 ÷ 4 3 3 3 3

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0%10%20%30%40%50%60%70%80%90%100% 5%10%20%25%50% 260 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? Periodic Review 1 Access Common Core For every multiple of 5%, find the number of coffee mugs. Record the amounts on the double number line. The sweater will be discounted $10. 40 25% 10 The player got 22 points from the free throw line. 55 22 260 coffee mugs were sold last weekend. 0 13 26 39 52 65 78 91 104 117 130 143 156 169 182 195 208 221 234 247 Price Percent 40 100 10 25 ÷ 4 Points Percent 55 100 11 20 22 40 ÷ 5 2 2 2 2

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