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

Lesson 4.5Solve for the Whole

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.	the sale price
WholeSpanish: Total	The full amount the percent is measured against. The whole is always 100%.	the first 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, $42, $70 above 0%, 10%, 60%, 100%
EquationSpanish: Ecuación	A math sentence with an equal sign. Here it says percent × whole = part, with the whole unknown.	0.7 × w = 26,600
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 multiplying

How it worksWorked examplesolving for the whole with an equation

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

A bike sold for $138, which is 60% of its first price. What was the first price of the bike?

Let w stand for the first price — that is the unknown whole.
Write the equation: 0.6 × w = 138
Undo the multiplication by dividing both sides by 0.6
Check forward: sixty percent of your answer should return the sale price.

Answer: The first price of the bike was $230.

Now you trySame steps, your turn

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

A tablet sold for $153, which is 45% of its first price. What was the first price of the tablet?

Let w stand for .
Write the equation: × w =
Undo the multiplication: w = ÷
Solve and then check forward: w =

Answer:the first price of the tablet

Say it and write itSentence starters

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

The part is and the percent is %.
My equation is × w = .
To solve I divided by because .
My answer makes sense because the whole is than the part.

Word bank partwholepercentequationvariableunknowndividemultiplyinversehundredthssolvecheck

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 4.5Solve for the Whole

Apply Day · 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.

1Complete each step, then write the final answer.

$5 is 50% of what amount?
Show your work
Hint Put 50% and 5 in the first column. What scale factor takes 50% to 100%?
Final answer:
2Complete each step, then write the final answer.

6 is 25% of what number?
Show your work
Hint Put 25% and 6 in the first column. What scale factor takes 25% to 100%?
Final answer:
3Complete each step, then write the final answer.

$16 is 80% of the price. What is the price?
Show your work
Hint Put 80% and 16 in the first column. Find 20% first. Then multiply to reach 100%.
Final answer:

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 4.5Solve for the Whole

Apply Day · 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.

1Complete each step, then write the final answer.

9 is 30% of a number. Ella writes 0.3 × 9 = 2.7 and says the number is 2.7. Find the correct number.
Show your work
Final answer:
2Complete each step, then write the final answer.

27 is 45% of what number?
Show your work
Final answer:
3Complete each step, then write the final answer.

$14 is 20% of what amount?
Show your work
Final answer:

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 4.5Solve for the Whole

Apply Day · 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.

1Circle the letter of the best answer. Show how you know.
Marcus completed 18 math problems, which represents exactly 60% of his homework assignment. How many total problems are on the assignment?
1. A24 problems
2. B28 problems
3. C30 problems
4. D36 problems
0%50%100%

Work
2Complete each step, then write the final answer.

A puppy weighs 26 pounds. That is 200% of its weight 3 months ago. Leo says it weighed 52 pounds then. Find the correct weight.
Show your work
Final answer:
3Complete each step, then write the final answer.

42 is 35% of what number?
Show your work
Final answer:

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