Develop Skills and Strategies Lesso 5 art 1 Introductin

©Curriculum Associates, LLC Copying is not permitted.L5: Solve Problems with Percent40

Lesson 5 Part 1: Introduction

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

How are 40, 60, 80 and 100 related to 20?

Use this information to complete a table of equivalent ratios for the second test

Look at the two tables Which ratios can you use to compare the test results? Why?

On which test did Keiko get a better grade? Explain

Test 1Number Correct 19

Total 25 50 75 100

Test 2Number Correct 17

Total 20 40 60 80 100

Develop Skills and Strategies

MAFS6.RP.1.3c

©Curriculum Associates, LLC Copying is not permitted.41L5: Solve Problems with Percent

Lesson 5Part 1: Introduction

Find Out More

The ratios on the previous page, 76 ··· 100 and 85 ··· 100 , can be expressed as fractions, decimals and

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 ··· 100 Fraction: 85 ··· 100

Decimal: 0 76 Decimal: 0 85

Percent: 76% Percent: 85%

Here are some fractions, decimals, and percents that you will see and use often

Fraction 1 ··· 100 1 ·· 10 1 ·· 4 or 25 ··· 100 1 ·· 2 or 50 ··· 100 3 ·· 4 or 75 ··· 100 1 ·· 1 or 100 ··· 100

Decimal 0 01 0 1 or 0 10 0 25 0 5 or 0 50 0 75 1 00

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 0 25 · 80?

Think: What is 1 ·· 4 of 80? 80 4 4 5 20

Reflect

1 Why do you think percents are used to compare ratios when the wholes are different?

Part 2: Modeled Instruction Lesson 5

©Curriculum Associates, LLC Copying is not permitted.

L5: Solve Problems with Percent42

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.

80

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

80 80 80 80 80 80 80 80 80

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 ··· 100 . 800

Remember: of means to multiply

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 Fill in the blanks to show how to multiply

60 ··· 100 • 800 ··· 1 5 or

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?

Lesson 5



Part 3: Modeled Instruction

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.

$ dollars 0 6 ?

0 10 100% percent

24

20 30 40 50 60 70 80 90

$24 is 40%of Eric’ssavings.

100% represents thetotal amount of Eric’ssavings.

40 4 4 510 and24 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.

$ dollars 6 12 ?

% percent 10 20 100

Start with the ratio 24 to 40

Find half of both quantities in 24 to 40: 12 to 20

Find half of both quantities in 12 to 20: 6 to 10

2440

Lesson 5


Part 3: Guided Instruction

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

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 ··· 100 • 60 ·· 1 5 or $

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?

Student Model

Lesson 5



Why can’t you say, “450 . 300, so the boys have better attendance?”

Pair/Share

Suppose you think of 20% as 20 ··· 100 or 1 ·· 5 How can you solve the problem using 1 ·· 5 instead of 20%?

Pair/Share

Part 4: Guided Practice

Study the model below. Then solve problems 16–18.

At Sydney’s school, 300 of the 500 girls and 450 of the 600 boys

attend the Spring Carnival. Which group has greater attendance?

Look at how you can use equivalent ratios and percents to solve

the problem.

Solution:

16 Cesar turned in his third research report His teacher said that Cesar had completed 20% of the reports for the school year How many research reports will he do during the school year?

Show your work.

Solution:

The boys have better attendance because 75% > 60%.

Girls Boys

300 ···· 500 5 60 ···· 100 450 ···· 600 5 75 ···· 100

60% 75%

If you find equivalent ratios with the denominator of 100, you can use percents.

How can you use an equivalent ratios table to help you solve the problem?

Part 4: Guided Practice Lesson 5


How can you show that your answer is 50% of 120?

Pair/Share

Did you use a fraction or a decimal to solve this problem? Why?

Pair/Share

17 Nia answered 80% of the 40 questions on a test correctly How many correct answers did she have?

Show your work.

Solution:

18 Andrei’s grandfather offered to give him a gift of 50% of the amount of money he saved in one year Andrei saved $120 dollars How much did his grandfather give him as a gift?

A $50

B $60

C $120

D $180

Mitch chose D as the correct answer How did he get that answer?

When you write a number equation from a word equation, what symbol do you use for the word “of?”

I think that it would be easy to solve this problem using a fraction.

Lesson 5



Solve the problems.

1 Jason’s father bought a computer for $800. He made equal payments of 25% of the total cost. How much was each payment?

A $25

B $32

C $200

D $400

2 Antonio has read 147 pages of a book. He has completed 70% of the book. How many more pages does he need to read to finish the book?

pages

3 During the basketball season, Cory made 21 of the 60 baskets she attempted. Krista made 18 of the 45 baskets she attempted. Paula made 17 of the 50 baskets she attempted. Write the names of the players in order from the least percentage of baskets made to the greatest percentage of baskets made.

Least Greatest

NAME NAME NAME

Part 5: MAFS Practice

Lesson 5


4 Jackson’s mom limits the amount of time he is allowed to play video games. After Jackson plays for 9 minutes, his mom tells him that he has used up 30% of his time. How many more minutes can Jackson play before he uses all of his time?

Show your work.

Answer Jackson can play more minutes.

5 Ashley has sold 70% of the 20 candy bars she is supposed to sell for her softball team. How many candy bars does she have left to sell?

Show your work.

Answer Ashley has more candy bars to sell.

Go back and see what you can check off on the Self Check on page 1.Self Check

Part 5: MAFS Practice

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Develop Skills and Strategies Lesso 5 art 1 Introductin