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 use equivalent ratio tables to determine the whole when I know a part and the percent it represents.

Why This Matters Every percent problem has three pieces: the part, the whole, and the percent. So far the whole has always been handed to you. Today it is the missing piece — a sale price without the original price, a car's current value without its sticker price. Your job is to work backwards to the whole. For example, Akela paid $42 for a sweater on sale, and that was 60% of the original price. What was the original price?

Start hereWords for this lesson

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

WordWhat it meansExample
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 example

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

24 stickers are 40% of a pack. How many stickers are in the pack?

  1. 40% ÷ 4 = 10%, so 24 ÷ 4 = 6.
  2. 10% × 10 = 100%, so 6 × 10 = 60.
  3. Check: 0.40 × 60 = 24.

Answer: 60 stickers

Now you trySame steps, your turn

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

Sheng's car is now worth $26,600, which is 70% of what his parents paid for it. Find the original price.

Answer:

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 out!A 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

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 use equivalent ratio tables to determine the whole when I know a part and the percent it represents.

Why This Matters Every percent problem has three pieces: the part, the whole, and the percent. So far the whole has always been handed to you. Today it is the missing piece — a sale price without the original price, a car's current value without its sticker price. Your job is to work backwards to the whole. For example, Akela paid $42 for a sweater on sale, and that was 60% of the original price. What was the original price?

Part 1Understand the ideamodels and meaning
  1. 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
  1. 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 In a ratio table, 50% pairs with $20.

    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?
  2. 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
  3. 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
  4. 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 15% is three groups of 5%. Split 75 minutes into 3 equal groups to find 5%.

    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
  1. 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.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
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 use equivalent ratio tables to determine the whole when I know a part and the percent it represents.

Why This Matters Every percent problem has three pieces: the part, the whole, and the percent. So far the whole has always been handed to you. Today it is the missing piece — a sale price without the original price, a car's current value without its sticker price. Your job is to work backwards to the whole. For example, Akela paid $42 for a sweater on sale, and that was 60% of the original price. What was the original price?

Part 1Understand the ideamodels and meaning
  1. 1Circle 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
  2. 2Use the model to solve. Show your work.
    Total10%10%10%10%10%10%10%10%10%10%

    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:
  3. 3Complete the table. Show how you found each value.

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

    PercentDollars
    60%42
    10%
    100%
    Show your work
Part 2Apply itreal-world problems
  1. 4Circle the letter of the best answer. Show how you know.

    18 students are 30% of an after-school group. How many students are in the whole group?

    1. A6
    2. B30
    3. C60
    4. D180
    0%50%100%
    Work
  2. 5Circle 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
  1. 6Find 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?

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
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 use equivalent ratio tables to determine the whole when I know a part and the percent it represents.

Why This Matters Every percent problem has three pieces: the part, the whole, and the percent. So far the whole has always been handed to you. Today it is the missing piece — a sale price without the original price, a car's current value without its sticker price. Your job is to work backwards to the whole. For example, Akela paid $42 for a sweater on sale, and that was 60% of the original price. What was the original price?

Part 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

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

    PartPercentWhole
    $4260%70
    $26,60070%
    75 min15%
    18 students30%
    Show your work
Part 2Explain and correctreasoning
  1. 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:
  2. 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?

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help