Lesson 5 CCLS Solve Problems with Percent - Weebly

1 Lesson 5 Part 1: Introduction CCLS. Solve Problems with Percent You have learned how to make tables of equivalent ratios to Solve Problems . Take a look at this problem . On the first math test, Keiko answered 19 out of 25 questions correctly. On the second test she got 17 out of 20 correct. On which test did she get a better grade? Explore It Use the math you already know to help Solve the problem . Write a ratio in fraction form to compare the number correct to the total questions for each test. Can you compare these two ratios as they are written? Explain why or why not.. Look at the table. How are 50, 75, and 100 related to 25? . What do you need to do to complete the table? . Now complete the table. Number Correct 19. Test 1. Total 25 50 75 100. How are 40, 60, 80 and 100 related to 20?

2 Use this information to complete a table of equivalent ratios for the second test. Look at the two tables. Which ratios Number Correct 17. can you use to compare the test Test 2. Total 20 40 60 80 100. results? Why? . On which test did Keiko get a better grade? Explain. 38 L5: Solve Problems with Percent Curriculum Associates, LLC Copying is not permitted. Part 1: Introduction Lesson 5. Find Out More The ratios on the previous page, 76 and 85 , can be expressed as fractions, decimals and 100. 100.. percents. A Percent is a rate for every 100 or per 100. The symbol % signifies Percent . Base-ten models can be used to represent fractions, decimals, and percents. Fraction: 76 Fraction: 85 . 100. 100.. Decimal: Decimal: Percent : 76% Percent : 85%. Here are some fractions, decimals, and percents that you will see and use often.

3 Fraction 1 1 1 or 25 1 or 50 3 or 75 1 or 100 . 100. 10. 4. 100. 2. 100. 4. 100. 1. 100.. Decimal or or Percent 1% 10% 25% 50% 75% 100%. Sometimes it is easier to use an equivalent fraction when given a decimal or Percent . Example: What is 80? Think: What is 1 of 80? 80 4 4 5 20. 4.. Reflect 1 Why do you think percents are used to compare ratios when the wholes are different? . L5: Solve Problems with Percent 39. Curriculum Associates, LLC Copying is not permitted. Part 2: Modeled Instruction Lesson 5. Read the problem below. Then explore different ways to Solve Problems involving Percent of a number. At Madison Middle School, 60% of the 800 students participate in music. How many students participate in music? Picture It You can use a bar model to Solve the problem .

4 80 80 80 80 80 80 80 80 80 80. 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%. The bar model shows 800 students divided into 10 groups of 80. Each group of 80 represents 10%. Model It You can write an expression to find the number of students. Use words: 60% of 800.. Use numbers: 60. ? 800. 100.. Remember: of means to multiply 40 L5: Solve Problems with Percent Curriculum Associates, LLC Copying is not permitted. Part 2: Guided Instruction Lesson 5. Connect It Now you will Solve the problem from the previous page using a bar model and related expression. 2 In the bar model, how many groups of 80 make up 60%? What is the total number of students in these groups? 3 Using your answer to number 2, what is 60% of 800 students? 4 The expression from the previous page is shown below.

5 Fill in the blanks to show how to multiply. 60 800 5 or 100 . 1. 5 Explain how to find a Percent of a number.. 6 Imagine that 55% of the 800 students participate in music instead of 60%. How could you use the idea of halves with the bar model to find 55% of 800? . Try It Use what you've just learned about the Percent of a number to Solve these Problems . Show your work on a separate sheet of paper. 7 Charlie wants a new pair of shoes that cost $40. His mom pays 75% of the cost and Charlie pays 25%. How much do they each pay? 8 A school will have a fall festival if at least 40% of the 500 students plan to attend. How many students must agree to attend in order for the school to have the festival? L5: Solve Problems with Percent 41. Curriculum Associates, LLC Copying is not permitted.

6 Part 3: Modeled Instruction Lesson 5. Read the problem below. Then explore different ways to find the whole when a part and the Percent are given. Eric wants to buy a video game that costs $24, but he only wants to spend 40% of his savings. How much must Eric save in order to buy the game? Picture It You can use a double number line to find the whole when a part and the Percent are given. $24 is 40% 100% represents the of Eric's total amount of Eric's savings. savings. $ dollars 0 6 24 ? % Percent 0 10 20 30 40 50 60 70 80 90 100. 40 4 4 510 and 24 4 4 5 6. Model It You can make a table of equivalent ratios to find the whole when a part and the Percent are given. $ 6 12 24 ? % 10 20 40 100. Start with the ratio 24 to 40. Find half of both quantities in 24 to 40: 12 to 20.

7 Find half of both quantities in 12 to 20: 6 to 10. 42 L5: Solve Problems with Percent Curriculum Associates, LLC Copying is not permitted. Part 3: Guided Instruction Lesson 5. Connect It Now you will Solve the problem from the previous page using the double number line and the table. 9 Look at the table and the double number line. How many dollars is 10% of the total? How many times greater than 10% is 100%? So, how many times greater than $6 is the dollar amount that equals 100%? 10 Look at the double number line. Using the ratio 6 to 10, explain how you can find an equivalent ratio that has 100 as the second quantity. 11 How much does Eric have to save in order to buy the game? 12 What does the answer to the problem mean? Fill in the blanks to help you understand.

8 10 5 100% and 10 $6 5 $ If $24 is 40%, then $ is 100%. So, 40% of $ is $24. 13 You can use what you know about finding Percent of a number to check your answer. Fill in the blanks. 40% of $60. 40 60 5 or $ 100 . 1. 14 How can you find the whole when you know part and the Percent ? .. Try It Use what you've just learned about finding the whole to Solve this problem . Show your work on a separate sheet of paper. 15 150 students at York Middle School took part in the school clean up. This is 30% of the school's total students. How many students go to York Middle School? L5: Solve Problems with Percent 43. Curriculum Associates, LLC Copying is not permitted. Part 4: Guided Practice Lesson 5. Study the model below. Then Solve Problems 16 18. Student Model If you find equivalent At Sydney's school, 300 of the 500 girls and 450 of the 600 boys ratios with the attend the Spring Carnival.

9 Which group has greater attendance? denominator of 100, you can use percents. Look at how you can use equivalent ratios and percents to Solve the problem . Girls Boys 300 5 60 450 5 75 . 500. 100. 600. 100.. 60% 75%. Pair/Share Why can't you say, 450.. 300, so the boys have Solution: The boys have better attendance because 75% > 60%. better attendance? . 16 Cesar turned in his third research report. His teacher said that Cesar How can you use an equivalent ratios table to had completed 20% of the reports for the school year. How many help you Solve the research reports will he do during the school year? problem ? Show your work. Pair/Share Suppose you think of 20% as 20 or 1 . 100 . 5. How can you Solve the problem using 1 instead 5.. of 20%? Solution: 44 L5: Solve Problems with Percent Curriculum Associates, LLC Copying is not permitted.

10 Part 4: Guided Practice Lesson 5. 17 Nia answered 80% of the 40 questions on a test correctly. How many When you write a correct answers did she have? number equation from a Show your work. word equation, what symbol do you use for the word of? . Pair/Share Did you use a fraction or a decimal to Solve this problem ? Why? Solution: 18 Andrei's grandfather offered to give him a gift of 50% of the amount I think that it would be of money he saved in one year. Andrei saved $120 dollars. How easy to Solve this problem much did his grandfather give him as a gift? using a fraction. A $50. B $60. C $120. D $180. Mitch chose D as the correct answer. How did he get this answer? Pair/Share How can you show that your answer is 20%. of 120? L5: Solve Problems with Percent 45.