Lesson Plan -- Percent of a Number/Increase and Decrease

Transcription

1 Lesson Plan -- Percent of a Number/Increase and Decrease Chapter Resources - Lesson 4-11 Find a Percent of a Number - Lesson 4-11 Find a Percent of a Number Answers - Lesson 4-12 Percent of Increase and Decrease - Lesson 4-12 Percent of Increase and Decrease Answers 1

2 LESSON 4-11 California Standards Gr. 5 NS 1.2: Interpret percents as part of a hundred; find decimal and percent equivalents for common fractions and explain why they represent the same value; compute a given percent of a whole number. Gr. 6 NS 1.4: Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned, and tips. Words to Remember Percent: A ratio whose denominator is 100 Represented by the symbol % 35% 5 35 } Getting Started In Lesson 4-9 you learned how to write a percent as a fraction and as a decimal. In Lesson 4-7 you learned how to solve proportions. In this lesson, you will learn several methods you can use to find the percent of a number. E Finding the Percent of a Number Find the percent of the number. a. 20% of 35 b. 25% of 12 Solution a. Write the percent as a fraction. 20% of } Write 20% as a fraction and multiply. 1 5 /20 35 } 100 // 5 Multiply } 5 Simplify. 5 7 Simplify. ANSWER 20% of 35 is 7. b. Write the percent as a decimal. 25% of (12) Write 25% as a decimal and multiply. 5 3 Multiply. ANSWER 25% of 12 is 3. 42

3 T Find the percent of the number % of % of % of % of % of % of 30 Proportions You can also find the percent of a number using proportions. Write the percent as a fraction and set it equal to a fraction with the unknown value in the numerator and the given value in the denominator. E Finding Percents of Quantities Jerome has 230 baseball cards in his collection. If he plans to sell 20% of his collection, how many cards will Jerome sell? Solution To find how many cards Jerome will sell, find 20% of } x } 230 Write a proportion x 100 Write the cross products x Multiply. x5 46 Solve. ANSWER Jerome will sell 46 of his baseball cards. T Use a proportion to find the answers. 7. Darnell bought 20% of the raffle tickets for the school raffle. If 300 tickets were sold, how many did Darnell buy? 8. Elise needs to read a 180 page book. She plans to read 10% of the book each day. How many pages of the book does Elise read on the first day? 43

4 Summarize Finding the Percent of a Number Write the percent as a fraction or decimal and multiply it by the given value. An alternative method is to write a proportion using the percent as a fraction equal to a fraction with the unknown value over the given value. Solve the proportion. Finding Percents of Quantities Determine of what value you must take the percent. Write a proportion to solve for this value. Solve. Match the question with a correct method for finding the percent of the number. 1. What is 43% of 19? A. 17 } x } What is 17% of 34? B. 8 } What is 67% of 123? C. 43 } What is 8% of 20? D. Find the percent of a number. 67 x } 5 } What is 10% of 35? 6. What is 50% of 18? 7. What is 25% of 8? 8. What is 60% of 10? 9. What is 5% of 20? 10. What is 12% of 100? 11. What is 40% of 15? 12. What is 95% of 30? Write a proportion for the given situation. 13. Haley owns 132 figurines. She plans to sell 25% of her collection. 14. Jorge mows 10 lawns every week. This week the weather is bad, so he only mows 20% of the lawns. 15. Peter usually walks 8 dogs a day. Today he only walks 25% of the dogs. 44

5 Write and solve a proportion for the given situation. Explain your answer. 16. Veronica has a collection of 30 famous people s signatures. She wants to sell 10% of the signatures. How many signatures does Veronica sell? 17. Hyun usually washes 40 cars in a weekend. With bad weather, he only washes 75% of his normal amount. How many cars does Hyun wash? 18. Cora makes 65% of the shots she attempts in a basketball game. At today s game, she took 20 shots. How many shots did Cora make in the game? 19. Isaac buys lunch 25% of the time that he is at work. This month he worked 16 days. How many days did Isaac buy lunch? 20. Fill in the missing words. To determine the of a number, you set up a with one fraction being the and the other fraction with the unknown in the. 21. Write a proportion. What proportion could you use to find 40% of 30? 22. Solve. Hazel has a 200 page book to read. She plans to read 10% of the book each day. How many pages does Hazel plan to read each day? LUNCH BOX 45

6 Answer Key Lesson 4-11, pp Try this: tickets pages Practice: 1. C 2. A 3. D 4. B Sample answer: 25 } x } Sample answer: 20 } x } 10

7 Answer Key 15. Sample answer: 25 } x } Sample answer: } } x ; x 5 3; When Veronica sells 10% of 30 signatures, 30 she sells 3 signatures. 17. Sample answer: } } x 40 ; x 5 30; When Hyun washes 75% of 40 cars, he washes 30 cars. 18. Sample answer: } } x 20 ; x 5 13; When Cora makes 65% of 20 shots, she makes 13 shots. 19. Sample answer: } } x 16 ; x 5 4; When Isaac buys lunch 25% of 16 days, he buys lunch 4 days. 20. percent; proportion; percent; numerator 21. Sample answer: 40 } x } pages

8 LESSON 4-12 California Standards Gr. 7 NS 1.6: Calculate the percentage of increases and decreases of a quantity. Gr. 3/4/5/6/7 MR 1.1: Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, identifying missing information (Gr. 6/7 only), sequencing and prioritizing information, and observing patterns. Words to Remember Percent of change: Shows how much a new amount has increased or decreased from the original amount amount of change Percent of change 5}} original amount Amount of change: The difference between two quantities Percent of increase: Results when the new amount is greater than the original amount Percent of decrease: Results when the new amount is less than the original amount Getting Started In Lesson 4-9 you learned how to write a percent as a fraction. In this lesson, you will use a fraction to find a percent of change. E Finding the Amount of Change Find the amount of change and determine whether it is an increase or a decrease. a. Original amount: 52 b. Original amount: 120 New amount: 70 New amount: 95 Solution Look at the two amounts. The amount of change is the larger number minus the smaller number. a. Amount of change 5 larger number 2 smaller number ANSWER Because the new amount is larger, this is an increase. b. Amount of change 5 larger number 2 smaller number ANSWER Because the new amount is smaller, this is a decrease. 46

9 E Finding the Percent of Increase At the beginning of the year, Wayne could type 30 words per minute. By the end of the year, Wayne was typing 48 words per minute. What is the percent of increase in the number of words Wayne could type? Solution amount of change Percent of change 5 }} original amount Use the percent of change equation } Substitute values } 30 Subtract Write the fraction as a decimal. 5 60% Write the decimal as a percent. Because the new amount is larger, this is a percent of increase. ANSWER The percent of increase is 60%. E Finding the Percent of Decrease Whether you are looking for a percent of increase or a percent of decrease, the numerator is always the larger number subtracted by the smaller number. The denominator is always the original amount. A movie store rented 145 movies in May. The same movie store rented 120 movies in June. What is the percent of decrease in the number of movies rented from May to June? Solution amount of change Percent of change 5 }} original amount Use the percent of change equation } Substitute values } 145 Subtract % Write the fraction as a decimal. Write the decimal as a percent. Because the new amount is smaller, this is a percent of decrease. ANSWER The percent of decrease is about 17%. T Find the percent of increase or decrease. 1. Original amount: Original amount: 51 New amount: 102 New amount: % 5 5 % 47

10 Summarize amount of change Percent change 5}} original amount Finding the Percent of Increase Use the percent change equation. The numerator is the new value the original amount. The denominator is the original amount. Subtract. Write the fraction as a decimal. Finding the Percent of Decrease Use the percent change equation. The numerator is the original amount the new value. The denominator is the original amount. Subtract. Write the fraction as a decimal. Determine whether the percent of change is an increase or a decrease. 1. Original amount: Original amount: 29 New amount: 36 New amount: Original amount: Original amount: 37 New amount: 30 New amount: 51 Find the percent of increase. 5. Original amount: Original amount: 23 New amount: 100 New amount: Original amount: 8 8. Original amount: 15 New amount: 16 New amount: 27 Find the percent of decrease. 9. Original amount: Original amount: 97 New amount: 4 New amount: Original amount: Original amount: 28 New amount: 38 New amount: 12 48

11 Decide if the percent of change will be an increase or a decrease. Then determine the percent of change. Explain your answer. 13. Olivia read 25 books last summer. This summer she read a total of 40 books. 14. This year there are 234 sixth grade students. Last year there were 250 sixth grade students. 15. A garden center sold 132 plants this weekend. Last weekend it sold 115 plants. 16. Ralph hit 32 balls in the batting cage last week. This week he hit 28 balls. 17. Fill in the missing words. To determine the of change, the of the fraction is the amount of or and the denominator is the amount. 18. Find the percent of change. Ursula knew how to play 15 pieces of music. After band camp, she now knows how to play 18 pieces of music. Find the percent of increase or decrease. 49

12 Answer Key Lesson 4-12, pp Try this: } 5 } % increase } 5 } 6 ø 12% decrease Practice: 1. increase 2. decrease 3. decrease 4. increase 5. ø18% 6. ø30% % 8. 80% 9. 60% 10. ø23% % 12. ø57% 13. increase; ø60%; Sample answer: The number of books Olivia read increased by about 60% from last summer to this summer. 14. decrease; ø6%; Sample answer: The number of sixth grade students decreased by about 6% from last year to this year. 15. increase; ø15%; Sample answer: The number of plants the garden center sold increased by about 15% from last weekend to this weekend. 16. decrease; ø13%; Sample answer: The number of balls Ralph hit decreased by about 13% from last week to this week. 17. percent; numerator; increase; decrease; original % increase