# We will solve problems involving a percent of a quantity1.

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We will solve problems involving a percent of a quantity1.
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.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. Activate Prior Knowledge If ratios are equivalent, then you can find a missing value. If 6 pounds of beans cost \$15, how much will 2 pounds of beans cost? How much will 8 pounds of beans cost? 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 1. pounds dollars 6 15 2 8 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 2. cups pies 12 9 3 4 16

Percent of a Quantity A percent (%) is part of 100.
Concept Development 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. Percent of a Quantity 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? CFU 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 12 24 48 60 72 96 120 6 30 90 1% 5% 10% 20% 25% 50% 0% 10% 20% 25% 30% 40% 50% 60% 70% 75% 80% 90% 100% ÷ 2 ÷ 2 × 3 Students 120 60 30 90 Percent 100 50 25 75 2 the way two things are connected Vocabulary ÷ 2 ÷ 2 × 3

FIND THE GCF before multiplying or dividing
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. 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% 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% Explain how you would apply the strategy to #2. CFU People (220 ÷ 5) × 2 (220 ÷ 4) × 3 220 1% 5% 10% 20% 25% 50% 0% 10% 20% 30% 40% × 3 50% 60% 70% 80% 90% 100% × 2 ÷ 4 ÷ 5

FIND THE GCF before multiplying or dividing.
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. 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 On the double number line, record3 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. Interpret4 the solution. Solve problems involving a percent of a quantity using a double number line. 1 a 2 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. 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 5% 25% 1% People × 2 220 ÷ 5 = 44 × 3 44 × 2 = 88 44 55 88 165 220 220 ÷ 4 = 55 55 × 3 = 165 75% 3 make a note 4 explain Vocabulary × 2 × 3 ÷ 4 ÷ 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. 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 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 “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 × 4 × 5 164 170 41 123 34 102 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.

percent quantity given simple percent
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 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 1. 75% of 80 patients in one hospital were in intensive care. How many patients were in intensive care? 80 ÷ 4 = 20 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 5% 25% 1% Patients 20 × 3 = 60 20 × 3 60 80 60 of the 80 patients are in intensive care. × 3 75% ÷ 4 Access Common Core Word Bank percent quantity given simple percent 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. Summary Closure What did you learn today about solving problems involving a percent of a quantity? (Pair-Share) Use words from the word bank.

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 2 3 4 “Divide down... 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 × 3 180 500 1500 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.

× 3 × 3 ÷ 5 ÷ 4 Students Cows 32 30 90 120 160 ÷ 5 = 32 120 ÷ 4 = 30
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 2 3 4 “Divide down... “Divide down... 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 32 160 30 90 120 75% × 3 ÷ 5 ÷ 4 160 ÷ 5 = 32 120 ÷ 4 = 30 30 × 3 = 90 32 of the 160 students preferred the flavor of strawberry. 90 of Farmer John’s cows are underweight.

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? 10 40 10 55 25% 40 ÷ 4 = 10 55 ÷ 5 = 11 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% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 5% 25% 1% 260 26 130 ÷ 10

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