What are we going to do? What does quantity mean? Quantity means __________.

1. Learning Objective We will solve problems involving a percent of a quantity1. What are we going to do? What does quantity mean? Quantity means __________. CFU RP.3Use 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.1Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. EE.3Apply the properties of operations to generate equivalent expressions. Activate Prior Knowledge If ratios are equivalent, then you can find a missing value. 12 6 2 8 cups pounds 1. 2. 9 15 If 6 pounds of beans cost $15, how much will 2 pounds of beans cost? How much will 8 pounds of beans cost? dollars pies 3 12 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 5 20 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? 1 amount Vocabulary 4 16

2. Concept Development • A percent(%) is part of 100. • A percent of a quantity is partof a total. • Equivalent ratios on a double number line can be used to show the percent relationship2. Percent of a Quantity CFU 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) 120 students took a survey. The survey showed that 50% of the students play an instrument. 60 of the 120 students surveyed play an instrument. Students 0 12 24 48 60 72 96 120 90 6 30 5% 10% 20% 25% 50% 1% 25% 75% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% ÷2 ÷2 ×3 120 60 30 Students 90 2 the way two things are connected Vocabulary 100 50 25 Percent 75 ÷2 ÷2 ×3

3. Strategy Development (Optional) • 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 relationship2. The Strategy FIND THE GCF before multiplying or dividing Select a lower percentage that is simple to calculate, then use this simple percent to find the percent in the problem. Thinking Process 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? Find 40%, given 100% 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? _________________________________________________________________ 20% ( 10% and 5% also work) 20% × 2 = 40% CFU Explain how you would apply the strategy to #2. People (220 ÷ 5) × 2 (220 ÷ 4) × 3 220 5% 10% 20% 25% 50% 1% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% × 3 × 2 ÷ 4 ÷ 5

4. Skill Development/Guided 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. Solve problems involving a percent of a quantity using a double number line. 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 the double number line, record3 the given information and the percent to find. Determine which simple percent to calculate; 5, 10, 20, 25, or50%. (circle) Calculate this percent of the quantity. Solve for the unknown by using the simple percent and quantity. Interpret4 the solution. 1 2 2 a 3 3 4 220 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? _________________________________________________________________ FIND THE GCF before multiplying or dividing. “Divide down... 88 of the 220 people surveyed had food allergies. …Multiply up” 165 of the 220 people surveyed eat a full, healthy breakfast. People 220 ÷ 5 = 44 × 2 × 3 44 × 2 = 88 165 220 44 55 88 220 ÷ 4 = 55 3 make a note 4 explain Vocabulary 55 × 3 = 165 5% 10% 20% 25% 50% 1% 75% × 2 × 3 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% ÷ 4 ÷ 5

5. Skill Development/Guided 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. Solve problems involving a percent of a quantity using a double number line. 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 the double number line, record the given information and the percent to find. Determine which simple percent to calculate; 5, 10, 20, 25, or50%. (circle) Calculate this percent of the quantity. Solve for the unknown by using the simple percent and quantity. Interpret the solution. 1 2 2 a 3 3 4 “Divide down... 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. …Multiply up” Songs Pigs × 5 × 4 170 164 102 34 41 123 75% × 4 × 5 ÷ 3 ÷ 3 123 ÷ 3 = 41 102 ÷ 3 = 34 41 × 4 = 164 34 ×5 = 170 Sal has 164 songs on his MP3 player. Andrea owns 170 pigs total.

6. 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 Solve problems involving a percent of a quantity using a double number line. On the double number line, record the given information and the percent to find. Determine which simple percent to calculate; 5, 10, 20, 25, or50%. (circle) Calculate this percent of the quantity. Solve for the unknown by using the simple percent and quantity. Interpret the solution. 1 2 a 3 4 1. 75% of 80 patients in one hospital were in intensive care. How many patients were in intensive care? Word Bank 80 ÷ 4 = 20 percentquantitygivensimple percent Patients 20×3 = 60 80 60 × 3 20 60 of the 80 patients are in intensive care. ×3 75% ÷ 4 Access Common Core Explain how you determined which simple percent to use and how you used it to solve the problem. 60 of the 80 patients are in intensive care. 5% 10% 20% 25% 50% Summary Closure 1% What did you learn today about solving problems involving a percent of a quantity? (Pair-Share) Use words from the word bank. 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

7. 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. Solve problems involving a percent of a quantity using a double number line. On the double number line, record the given information and the percent to find. Determine which simple percent to calculate; 5, 10, 20, 25, or50%. (circle) Calculate this percent of the quantity. Solve for the unknown by using the simple percent and quantity. Interpret the solution. 1 2 a 3 4 “Divide down... 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? …Multiply up” People Band Members × 4 × 3 180 1500 500 2500 45 × 3 × 4 ÷ 5 45 × 4 = 180 2500 ÷ 5 = 500 500 × 3 = 1500 1,500 people of the 2500 got in using a student pass. There were 180 total band members in the competition.

8. 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. Solve problems involving a percent of a quantity using a double number line. On the double number line, record the given information and the percent to find. Determine which simple percent to calculate; 5, 10, 20, 25, or50%. (circle) Calculate this percent of the quantity. Solve for the unknown by using the simple percent and quantity. Interpret the solution. 1 2 a 3 4 “Divide down... “Divide down... 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. …Multiply up” …Multiply up” Students Cows × 3 32 120 30 90 160 75% × 3 ÷ 5 ÷ 4 160 ÷ 5 = 32 120 ÷ 4 = 30 30 × 3 = 90 90 of Farmer John’s cows are underweight. 32 of the 160 students preferred the flavor of strawberry.

9. Periodic Review 1 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? 55 40 10 10 25% 55 ÷ 5 = 11 40 ÷ 4 = 10 11 × 2 = 22 The player got 22 points from the free throw line. The sweater will be discounted $10. Access Common Core 260 coffee mugs were sold last weekend. For every multiple of 5%, find the number of coffee mugs. Record the amounts on the double number line. 0 130 26 260 5% 10% 20% 25% 50% 1% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% ÷ 10