Grade 6 Mathematics · Unit 4: Understand and Use PercentagesStandard 6.AT.4

Lesson 4.5Determine the Whole Given the Part and Percent

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can determine the whole when I know a part and the percent that part represents.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

Word	What it means	Example
PartSpanish: Parte	The amount you already know — the piece of the whole that the percent describes.	$42 is the sale price
WholeSpanish: Total	The full amount the percent is measured against. The whole is always 100%.	the original price
Double number lineSpanish: Recta numérica doble	Two lines lined up — dollars on one, percents on the other — so matching marks show the same amount two ways.	$0, $7, $70 · 0%, 10%, 100%
EquationSpanish: Ecuación	A math sentence with an equal sign. Here it says percent × whole = part, with the whole unknown.	0.7v = 26,600 — the percent times the unknown whole equals the part
PercentSpanish: Porcentaje	A ratio comparing a number to 100. To compute with it, write it in decimal form: 60% = 0.6.	60% = 0.6 · 70% = 0.7
Inverse operationSpanish: Operación inversa	The operation that undoes another operation.	Division undoes multiplication.

How it worksWorked examplefinding the whole from a part and its percent

These numbers are not on your problems. The steps are. Follow them with your own numbers.

A team has won 24 games, and that is 40% of the games it played. How many games did the team play?

Pair up what you know: 24 games matches 40%.
Step down to ten percent: divide both terms by four, giving 6 games.
Step up to one hundred percent: multiply both terms by ten.
Check forward: forty percent of your total should return the 24 wins.

Answer: The team played 60 games in all.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

A club collected 35 cans, and that is 25% of its collection goal. How many cans is the goal?

Pair up what you know: cans matches %.
Divide both terms by five: cans matches five percent.
Multiply both terms by twenty: cans matches one hundred percent.
Check forward: one quarter of your total should return cans.

Answer:the club's full collection goal

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

The part is and it matches %.
Ten percent of the whole is .
The whole is because .
I checked my answer by finding % of it.

Word bank partwholepercentdouble number lineequivalent ratioscaledividemultiplyten percentone hundred percenttablecheck

Watch outA common mistake

A common mistake when finding the whole is multiplying by the percent instead of dividing. For "$42 is 60% of the original price," computing 0.6 × 42 = $25.20 makes the original price SMALLER than the sale price — impossible for a discount. Since percent × whole = part, the whole is found by dividing: 42 ÷ 0.6 = $70. Whenever the percent is less than 100%, the whole must come out larger than the part, so a smaller answer is the tell.

Grade 6 Mathematics · Unit 4: Understand and Use PercentagesStandard 6.AT.4

Lesson 4.5Determine the Whole Given the Part and Percent

Version ASupported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

Learning target I can determine the whole when I know a part and the percent that part represents.

Part 1Understand the ideamodels and meaning

1Write the name of the correct group on each line.
Sort each number by the role it plays in "$42 is 60% of the original price."

Groups: The part The percent The unknown whole
- $42
- 60%
- the original price
- the amount Akela paid
- 0.6
- 100%
Hint Which number was actually paid?

Part 2Apply itreal-world problems

2Circle the letter of the best answer. Show how you know.
$20 is 50% of what number?
1. A$10
2. B$25
3. C$40
4. D$70
Hint 50% means half of the whole.
0%50%100%

Work
1. 1Whole100% is what number?
2. 2Find 10%Divide by 10.
3. 3BuildAdd or multiply to the percent.
4. 4CheckIs it under or over the whole?
3Circle the letter of the best answer. Show how you know.
Which equation says "30 is 25% of some number n"?
1. A0.25n = 30
2. Bn = 0.25 × 30
3. C25n = 30
4. Dn = 30 + 25
Hint Which number is the part, and which is the percent?
Show your work
4Circle the letter of the best answer. Show how you know.
$42 is 60% of the original price. Should the original price be more or less than $42?
1. AMore, because 60% is less than the whole
2. BLess, because 60 is a big number
3. CExactly $42
4. DYou cannot tell
Hint What percent stands for the whole?
Show your work
5Circle the letter of the best answer. Show how you know.
75 minutes is 15% of the school day. How long is the school day?
1. A11.25 minutes
2. B90 minutes
3. C500 minutes
4. D1,125 minutes
Hint Write the equation: 0.15d = 75.
0%50%100%

Work
1. 1Whole100% is what number?
2. 2Find 10%Divide by 10.
3. 3BuildAdd or multiply to the percent.
4. 4CheckIs it under or over the whole?

Part 3Explain and correctreasoning

6Find the mistake. Explain it, then show the correct work.
Find the error
1. 1Setup$42 is 60% of the original price. Find the original price.
2. 2Step 160% = 0.6
3. 3Step 20.6 × 42 = 25.20
4. 4Step 3The original price was $25.20.
Which step has the mistake? Explain what went wrong, then show the correct work.

Hint Should the original price be more or less than $42?
Correct work
Correct answer:

Explain your thinkingHow can you tell, before doing any arithmetic, whether the answer should be bigger or smaller than the number you were given?

Sentence starter If the percent is less than 100%, the given number is a ___, so the whole must be ___ than it.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help

Grade 6 Mathematics · Unit 4: Understand and Use PercentagesStandard 6.AT.4

Lesson 4.5Determine the Whole Given the Part and Percent

Version BCore practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

Learning target I can determine the whole when I know a part and the percent that part represents.

Part 1Understand the ideamodels and meaning

1Complete the table. Show how you found each value.

$42 is 60% of the original price. Complete the ratio table to reach 100%.

Percent Dollars
60% 42
10%
100%

Show your work
2Use the model to solve. Show your work.

A sweater's sale price of $42 is 60% of the original price. Each section is 10%. Use the bar model to find the original price.
Show your work
Answer:
3Circle the letter of the best answer. Show how you know.
Which statement correctly names the pieces of "18 students is 30% of the class"?
1. A18 is the whole, 30% is the part
2. B30 is the part, 18 is the percent
3. CThe class size is the part
4. D18 is the part, 30% is the percent, the class size is the whole
Show your work

Percent	Dollars
60%	42
10%
100%

Part 2Apply itreal-world problems

4Circle the letter of the best answer. Show how you know.
A car is now worth $26,600, which is 70% of its purchase price. What was the purchase price?
1. A$18,620
2. B$26,670
3. C$38,000
4. D$45,200
0%50%100%

Work

Part 3Explain and correctreasoning

5Find the mistake. Explain it, then show the correct work.
Find the error
1. 1Setup18 students is 30% of the class. How many students are in the class?
2. 2Step 130% = 0.3
3. 3Step 218 ÷ 0.3 = 60
4. 4Step 3There are 60% of students in the class.
Which step has the mistake? Explain what went wrong, then show the correct work.

Correct work
Correct answer:

Explain your thinkingHow can you tell, before doing any arithmetic, whether the answer should be bigger or smaller than the number you were given?

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help

Grade 6 Mathematics · Unit 4: Understand and Use PercentagesStandard 6.AT.4

Lesson 4.5Determine the Whole Given the Part and Percent

ChallengeExtension

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

Learning target I can determine the whole when I know a part and the percent that part represents.

Part 1Understand the ideamodels and meaning

1Complete the table. Show how you found each value.

Each row gives a part and a percent. Find the whole.

Part Percent Whole
$42 60% 70
$26,600 70%
75 min 15%
18 students 30%

Show your work

Part	Percent	Whole
$42	60%	70
$26,600	70%
75 min	15%
18 students	30%

Part 2Explain and correctreasoning

2Find the mistake. Explain it, then show the correct work.
Find the error
1. 1SetupA jacket is on sale for $60, which is 80% of the original price. Find the original price.
2. 2Step 1The discount is 20%.
3. 3Step 220% of 60 = 12.
4. 4Step 3The original price was 60 + 12 = $72.
Which step has the mistake? Explain what went wrong, then show the correct work.

Correct work
Correct answer:
3Answer in complete sentences.

A toy store's puzzle stock was 25% 300-piece, 15% 500-piece, and the rest 1,000-piece. During a sale the store sold ALL of its 300-piece and 500-piece puzzles — 120 puzzles in total. How many of each type did the store have before the sale? Explain your reasoning.
Write your answer

Explain your thinkingHow can you tell, before doing any arithmetic, whether the answer should be bigger or smaller than the number you were given?

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help