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.

Why This Matters It's Discount Day at the arcade. Different games are offering percent-off deals on ticket prices. The claw machine is 25% off its usual 60-ticket price, and the racing game is 40% off 80 tickets. You need to calculate the discounts to figure out how many tickets each game actually costs!

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 example

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

140 tickets; 45% are student tickets. How many?

  1. 45% = 0.45
  2. 0.45 × 140 = 63

Answer: 63 student tickets

Now you trySame steps, your turn

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

Find 40% of 80. Step 1 — what is the base? (80, the number after “of”)

Answer:

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 out!A common mistake

A common mistake in Find the Percent of a Number is multiplying by the percent number itself instead of its decimal form

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.

Why This Matters It's Discount Day at the arcade. Different games are offering percent-off deals on ticket prices. The claw machine is 25% off its usual 60-ticket price, and the racing game is 40% off 80 tickets. You need to calculate the discounts to figure out how many tickets each game actually costs!

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 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?
  2. 3Circle 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?
  3. 4Circle 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?
  4. 5Circle the letter of the best answer. Show how you know.

    What is 40% of 50?

    1. A5
    2. B20
    3. C40
    4. D90

    Hint 10% is one of 10 equal groups. First find 10% of 50.

    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 ___ × ___ = ___.

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 4.4Find 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.

Why This Matters It's Discount Day at the arcade. Different games are offering percent-off deals on ticket prices. The claw machine is 25% off its usual 60-ticket price, and the racing game is 40% off 80 tickets. You need to calculate the discounts to figure out how many tickets each game actually costs!

Part 1Understand the ideamodels and meaning
  1. 1Use 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:
  2. 2Complete 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
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 game has 120 points. A player earns 35% of the points. How many points is that?

    1. A35
    2. B42
    3. C85
    4. D155
    0%50%100%
    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?

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 4.4Find 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.

Why This Matters It's Discount Day at the arcade. Different games are offering percent-off deals on ticket prices. The claw machine is 25% off its usual 60-ticket price, and the racing game is 40% off 80 tickets. You need to calculate the discounts to figure out how many tickets each game actually costs!

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

    A game costs $80. It is 25% off. What is the sale price?

    1. A$20
    2. B$60
    3. C$55
    4. D$100
    0%50%100%
    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% join the math club and 50% join the reading club. How many students are in each club? How many more are in reading?

    Write your answer

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

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