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

Lesson 4.4Find and Compare with Percentages

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can find the percent of a number using an equation or a model.

Start hereWords for this lesson

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

WordWhat it meansExample
PercentSpanish: Porcentaje A way to compare a number to 100, shown with the % sign. 45% = 0.45
BaseSpanish: Base The whole amount you start with — the number right after the word “of.” 45% of 300 → base is 300
PartSpanish: Parte How much of the base (the whole) you get. It is your answer. 45% of 300 is 135
EquationSpanish: Ecuación A number sentence with an equal sign. The percent one is: part = percent × base. part = 0.45 × 300
DiscountSpanish: Descuento Money taken off the first price to make it cheaper. $40 shirt at 25% off: discount = $10
Double number lineSpanish: Recta numérica doble Two number lines that line up percents with amounts. 0%–100% over 0–300

How it worksWorked examplefinding the percent of a number

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

A store display holds 250 hats, and 36% of them are blue. How many of the hats are blue?

  1. Name the pieces: the base is 250 hats, the percent is 36%, the part is unknown.
  2. Write the percent in hundredths: 36% becomes 0.36
  3. Write the equation: part = 0.36 × 250
  4. Multiply, then check that the part is smaller than the base.

Answer: 90 of the hats in the display are blue.

Now you trySame steps, your turn

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

A farm keeps 140 goats, and 45% of them are brown. How many of the goats are brown?

  1. Base: goats Percent: % Part: unknown
  2. Percent written in hundredths:
  3. Equation: part = ×
  4. Multiply: part = goats
Answer:number of brown goats

Say it and write itSentence starters

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

  • The base is and the percent is %.
  • Written in hundredths, % is .
  • My equation is part = × .
  • The part is , which is smaller than the base because .

Word bank percentbasewholepartequationdecimalhundredthsmultiplydouble number lineofcheckestimate

Watch outA common mistake

A common mistake in Find the Percent of a Number is multiplying by the percent number itself instead of its decimal form — for example, finding 30% of 80 by computing 30 × 80 = 2,400 instead of 0.30 × 80 = 24. Always divide the percent by 100 to get the decimal, then multiply that decimal by the base.

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

Lesson 4.4Find and Compare with Percentages

Version ASupported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can find the percent of a number using an equation or a model.

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

    Find each percent of a number using the formula: Part = Percent × Base.

    PercentBasePart
    25%6015
    40%80
    15%200

    Hint The finished row shows the recipe: 25% of 60 became 0.25 × 60 = 15. Your rows use the same formula.

    Show your work
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    What is 20% of 150?

    1. A20
    2. B30
    3. C35
    4. D75

    Hint '20% of 150' means you want a PART of 150 — the answer should be smaller than 150.

    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.

    What is 50% of 84?

    1. A34
    2. B42
    3. C50
    4. D168

    Hint 50% is a friendly percent — it means exactly one-half of the number.

    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. 4Circle the letter of the best answer. Show how you know.

    What is 10% of 320?

    1. A3.2
    2. B32
    3. C64
    4. D320

    Hint 10% means one-tenth — there's a shortcut that needs no multiplication at all.

    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. 5Circle the letter of the best answer. Show how you know.

    What percent of 50 is 15?

    1. A15%
    2. B30%
    3. C35%
    4. D50%

    Hint This question is backwards from the others: you have the part (15) and the whole (50), and you need the PERCENT.

    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.

    Spot the Common Mistake

    1. 1Find 30% of 8030% of 80
    2. 2Multiply by the percent number30 × 80 = 2,400
    3. 3Final answer30% of 80 = 2,400

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Hint A percent is not a whole number — change 30% to a decimal before you multiply.

    Correct work
    Correct answer:

Explain your thinkingWhat steps do you follow every time you find the percent of a number?

Sentence starter To find ___% of ___, I first convert the percent to ___, then I multiply ___ × ___ = ___.

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 4.4Find and Compare with Percentages

Version BCore practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can find the percent of a number using an equation or a model.

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

    Complete each row to find the percent of a number.

    PercentBasePart
    10%250
    75%120
    35%200
    8%50
    Show your work
  2. 2Use the model to solve. Show your work.
    Total25%25%25%25%

    200 ÷ 4 = 50. Each 25% section = 50 points. So 25% of 200 = 50.

    Show your work
    Answer:
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    An arcade prize costs 240 tickets. If you have a coupon for 15% off, how many tickets do you save?

    1. A15 tickets
    2. B24 tickets
    3. C36 tickets
    4. D204 tickets
    0%50%100%
    Work
  2. 4Circle the letter of the best answer. Show how you know.

    A student scored 72 out of 90 on a test. What percent did they score?

    1. A72%
    2. B75%
    3. C80%
    4. D90%
    Show your work
Part 3Explain and correctreasoning
  1. 5Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1Find 15% of 6015% of 60
    2. 2Change the percent to a decimal15% = 0.15
    3. 3Multiply by the wrong number0.15 × 15 = 2.25
    4. 4Final answer15% of 60 = 2.25

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:

Explain your thinkingWhat steps do you follow every time you find the percent of a number?

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 4.4Find and Compare with Percentages

ChallengeExtension

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can find the percent of a number using an equation or a model.

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

    A video game character starts with 500 health points. Complete the table to find how many health points are lost or gained.

    EventPercent ChangeCalculationHealth Points After
    Hit by enemyLose 20%500 × 0.20 = 100 lost400
    Health potionGain 50% of current
    Poison trapLose 10% of current
    Show your work
Part 2Explain and correctreasoning
  1. 2Find the mistake. Explain it, then show the correct work.

    Find the Percent Error

    1. 1Find 30% of 9030% of 90
    2. 2Convert percent to decimal30% = 3.0
    3. 3Multiply3.0 × 90 = 270
    4. 4Final answer30% of 90 = 270

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:
  2. 3Answer in complete sentences.

    A class has 32 students. 25% are in the math club, 50% are in the reading club, and 12.5% are in both. How many students are in each group? Can the total of all three groups be more than 32? Explain why or why not.

    Write your answer

Explain your thinkingWhat steps do you follow every time you find the percent of a number?

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