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

Lesson 4.5Determine the Whole Given the Part and Percent

Set B · Version ASecond form · supported 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?

RememberDetermine the Whole Given the Part and Percent

Finding the whole with an equivalent ratio table When you know a part and the percent it represents, the whole is missing. An equivalent ratio table keeps the percent and amount paired as you scale to 100%. A number line and an equation can show the same relationship.

  1. Write the known percent and part in matching columns.
  2. Apply the same scale factor to both columns until the percent reaches 100%; the matching amount is the whole.
  3. Check by finding the given percent of that whole.

Words: Part (Parte)Whole (Total)Double number line (Recta numérica doble)Equation (Ecuación)Percent (Porcentaje)

  1. 1Circle the letter of the best answer. Show how you know.

    What is 10% of 320?

    1. A3.2
    2. B32
    3. C64
    4. D320
    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. 2Circle the letter of the best answer. Show how you know.

    What is 50% of 84?

    1. A34
    2. B42
    3. C50
    4. D168
    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?
  3. 3Circle the letter of the best answer. Show how you know.

    What is 20% of 150?

    1. A20
    2. B30
    3. C35
    4. D75
    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?
  4. 4Circle the letter of the best answer. Show how you know.

    Sheng's parents bought a new car last year. Its value today is $26,600, which is 70% of what they paid for it. $42 is 60% of the original price. What was the original price?

    1. A$25.20
    2. B$60
    3. C$70
    4. D$102
    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?
  5. 5Circle the letter of the best answer. Show how you know.

    Sheng's parents bought a new car last year. Its value today is $26,600, which is 70% of what they paid for it. Which equation finds the whole when 75 minutes is 15% of the school day?

    1. A0.15d = 75
    2. Bd = 0.15 × 75
    3. C75d = 0.15
    4. Dd = 75 + 15
    Show your work
  6. 6Circle the letter of the best answer. Show how you know.

    Sheng's parents bought a new car last year. Its value today is $26,600, which is 70% of what they paid for it. If the percent given is less than 100%, the whole must be…

    1. ASmaller than the part
    2. BLarger than the part
    3. CEqual to the part
    4. DImpossible to find
    Show your work

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

Set B · Version BSecond form · core 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 question by what it asks you to find.

    Groups: Find the whole Find the part
    • 12 is 40% of what number?
    • What is 40% of 12?
    • $30 is 25% of the total. What is the total?
    • What is 25% of $30?
  2. 2Write the letter of the matching item on each line.

    Match each part-and-percent pair to its whole.

    1. $42 is 60%
    2. 75 min is 15%
    3. 18 is 30%
    4. $9 is 25%
    • A$70
    • B500 min
    • C60
    • D$36
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    $10 is 50% of what number?

    1. A$5
    2. B$20
    3. C$60
    4. D$100
    0%50%100%
    Work
  2. 4Circle the letter of the best answer. Show how you know.

    $9 is 25% of what number?

    1. A$2.25
    2. B$34
    3. C$36
    4. D$225
    0%50%100%
    Work
  3. 5Circle the letter of the best answer. Show how you know.

    To find the whole from a part and a percent, you…

    1. AMultiply the part by the percent
    2. BAdd the part and the percent
    3. CSubtract the percent from 100
    4. DDivide the part by the percent in decimal form
    Show your work
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Find the error

    1. 1Setup20 is 40% of what number?
    2. 2Step 140% = 0.4
    3. 3Step 220 × 0.4 = 8
    4. 4Step 3The number is 8.

    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