Lesson 26: Percent of a Quantity
Lesson 26 NYS COMMON CORE MATHEMATICS CURRICULUM 6β’1 Lesson 26: Percent of a Quantity Student Outcomes ο§ Students find the percent of a quantity. Given a part and the percent, students solve problems involving finding the whole. Classwork Example 1 (5 minutes) Example 1 Five of the ππ girls on Alden Middle Schoolβs soccer team are πth grade students. Find the percentage of πth graders on the team. Show two different ways of solving for the answer. One of the methods must include a diagram or picture model. Method 1 π% π ππ% π ππ% ππ% ππ% πππ% ππ ππ ππ ππ Method 2 π π ππ = = = ππ% ππ π πππ Students take time to make their own diagram or model and discuss with a partner. Students will be reviewing the work they completed in Lesson 25. If they make a tape diagram, they begin by deciding to divide the tape diagram into 5 equal rectangles. Each rectangle will represent 5 girls. From there they will need to divide the 100% into 5 equal sections. If time permits, students share the model they chose and explain why it did or did not help them solve the problem. Students need to come to the conclusion that 5 25 = 20 , which is the same as 20%. 100 Note: Students who are struggling may need help figuring out which model to use and how to divide up the diagram. Help them think through the different options. Would it make sense to count by 5s, 10s, 20s, 25s, etc.? Lesson 26: Date: Percent of a Quantity 10/21/1412:58 PM5/15/14 © 2014 Common Core, Inc. Some rights reserved. commoncore.org 201 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 26 NYS COMMON CORE MATHEMATICS CURRICULUM 6β’1 Example 2 (5 minutes) Example 2 Of the ππ girls on the Alden Middle School soccer team, ππ% also play on a travel team. How many of the girls on the middle school team also play on a travel team? One method: ππ% = ππ ππ = . Therefore, ππ of the ππ girls are also on the travel team. πππ ππ Another method: Use of tape diagram shown below. π% ππ% π π ππ% ππ% ππ% ππ ππ ππ πππ% ππ ππ of the girls also play on a travel team. Example 3 (5 minutes) Example 3 The Alden Middle School girlsβ soccer team won ππ% of its games this season. If the team won ππ games, how many games did it play? Solve the problem using at least two different methods. Method 1: ππ% = ππ π π = = πππ ππ π π×π β ππ = π × π β ππ(πππππ πππππ) ππ total games Method 2: π% ππ% ππ% π π π ππ% ππ% π ππ πππ% ππ The girls played a total of ππ games. Lesson 26: Date: Percent of a Quantity 10/21/1412:58 PM5/15/14 © 2014 Common Core, Inc. Some rights reserved. commoncore.org 202 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 26 NYS COMMON CORE MATHEMATICS CURRICULUM 6β’1 Exercises (20 minutes) At this time, the students break out into pairs or small thinking groups to solve the problems. Exercises 1. 2. There are ππ animal exhibits at the local zoo. What percent of the zooβs exhibits does each animal class represent? Exhibits by Animal Class Number of Exhibits Percent of the Total Number of Exhibits Mammals 30 ππ π ππ = = = ππ% ππ ππ πππ Reptiles & Amphibians 15 ππ π π ππ = = = = ππ% ππ ππ π πππ Fish & Insects 12 ππ π ππ = = = ππ% ππ ππ πππ Birds 3 π π π = = = π% ππ ππ πππ A sweater is regularly $ππ. It is ππ% off the original price this week. a. Would the amount the shopper saved be considered the part, whole, or percent? Part because the $ππ is the whole amount of the sweater, and we want to know the part that was saved. b. How much would a shopper save by buying the sweater this week? Show two methods for finding your answer. Method 1: ππ% = ππ × ππ π = πππ π π = $π saved π Method 2: π π π ππ% ππ ππ% ππ ππ ππ% πππ% The shopper would save $π. 3. A pair of jeans was ππ% off the original price. The sale resulted in a $ππ discount. a. Is the original price of the jeans considered the whole, part, or percent? The original price is the whole. Lesson 26: Date: Percent of a Quantity 10/21/1412:58 PM5/15/14 © 2014 Common Core, Inc. Some rights reserved. commoncore.org 203 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 26 NYS COMMON CORE MATHEMATICS CURRICULUM b. 6β’1 What was the original cost of the jeans before the sale? Show two methods for finding your answer. Method 1: ππ π = πππ ππ ππ% = π×πβ ππ = ππ × π β ππ The original cost was $ππ. Method 2: π π ππ ππ ππ ππ ππ ππ ππ ππ 100 ππ ππ ππ ππ ππ ππ ππ ππ ππ 80 π 4. ππ πππ Purchasing a TV that is ππ% off will save $πππ. a. Name the different parts with the words: PART, WHOLE, PERCENT. PERCENT PART ππ% off b. WHOLE $πππ Original Price What was the original price of the TV? Show two methods for finding your answer. Method 1: π% ππ% ππ% ππ% π ππ πππ πππ ππ% πππ ππ% πππ ππ% ππ% πππ πππ ππ% πππ ππ% πππ πππ% πππ Method 2: ππ% = ππ πππ ππ × π β πππ = πππ × π β πππ The original price was $πππ. Lesson 26: Date: Percent of a Quantity 10/21/1412:58 PM5/15/14 © 2014 Common Core, Inc. Some rights reserved. commoncore.org 204 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 26 NYS COMMON CORE MATHEMATICS CURRICULUM 6β’1 Closing (5 minutes) ο§ Describe additional questions. ο§ Discuss the main differences in solving strategies. ο§ Were there times when you preferred to use one method over another method? ο§ How did the steps change when you were given the part instead of the total? Lesson Summary Models and diagrams can be used to solve percent problems. Tape diagrams, ππ × ππ grids, double number line diagrams, and others can be used in a similar way to using them with ratios to find the percent, the part, or the whole. Exit Ticket (5 minutes) Lesson 26: Date: Percent of a Quantity 10/21/1412:58 PM5/15/14 © 2014 Common Core, Inc. Some rights reserved. commoncore.org 205 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 26 NYS COMMON CORE MATHEMATICS CURRICULUM Name ___________________________________________________ 6β’1 Date____________________ Lesson 26: Percent of a Quantity Exit Ticket 1. Find 40% of 60 using two different strategies, one of which must include a pictorial model or diagram. 2. 15% of an amount is 30. Calculate the whole amount using two different strategies, one of which must include a pictorial model. Lesson 26: Date: Percent of a Quantity 10/21/1412:58 PM5/15/14 © 2014 Common Core, Inc. Some rights reserved. commoncore.org 206 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 26 NYS COMMON CORE MATHEMATICS CURRICULUM 6β’1 Exit Ticket Sample Solutions 1. Find ππ% of ππ using two different strategies, one of which must include a pictorial model or diagram. ππ% of ππ ππ% = 2. ππ π ππ = = πππ ππ ππ ππ% of ππ is ππ. ππ% of an amount is ππ. Calculate the whole amount using two different strategies, one of which must include a pictorial model. ππ% = ππ ππ = πππ πππ The whole quantity is πππ. Problem Set Sample Solutions 1. What is ππ% of ππ? Create a model to prove your answer. π 2. If ππ% of a number is ππ, what was the original number? πππ 3. In a ππ × ππ grid that represents πππ, one square represents π . Use the grids below to represent ππ% and ππ% of πππ. ππ% ππ% of πππ is Lesson 26: Date: ππ% πππ . ππ% of πππ is πππ . Percent of a Quantity 10/21/1412:58 PM5/15/14 © 2014 Common Core, Inc. Some rights reserved. commoncore.org 207 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
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