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

Lesson 4.2Relate Fractions, Decimals, and Percentages

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can write equivalent fractions, decimals, and percents for the same value.

Why This Matters You're designing the scoring system for a new arcade game. Players earn points as fractions of the total possible score. The leaderboard shows scores as percentages, but the game engine uses decimals. You need to convert between all three forms to build the display! A player scored 3/4 of the total possible points. Write that score as a decimal and as a percent.

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% = 45 out of 100
DecimalSpanish: Decimal A number with a dot, like 0.5, that shows a part less than one. 0.45 = 45 hundredths
EquivalentSpanish: Equivalente Having the same value, just written a different way. 3/4 = 0.75 = 75%
BenchmarkSpanish: Referencia A familiar number you use to guess, like 50% or 1/2. 50% = one half
DiscountSpanish: Descuento Money taken off the first price to make it cheaper. $40 shirt at 25% off: discount = $10
HundredthsSpanish: Centésimos The second place after the decimal point; parts out of 100. 0.09 = 9 hundredths

How it worksWorked example

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

20 students voted. 7 chose green. Write the green votes as a fraction, a decimal, and a percent.

  1. Fraction: 7/20.
  2. 20 × 5 = 100, so 7/20 = 35/100.
  3. 35/100 = 0.35 = 35%.

Answer: 7/20 = 0.35 = 35%

Now you trySame steps, your turn

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

Let's change 1/5 into a fraction out of 100, then a decimal and a percent.

Answer:

Say it and write itSentence starters

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

  • / is the same value as written as a decimal.
  • To change a decimal into a percent I .
  • % means out of every hundred.
  • I know these three forms are equivalent because .

Word bank percentdecimalfractionequivalenthundredthsdenominatornumeratorsimplest formbenchmarkscalewholepart

Watch out!A common mistake

A common mistake in Relate Fractions, Decimals, and Percents is treating the numerator and denominator as the percent's digits

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

Lesson 4.2Relate Fractions, Decimals, and Percentages

Version ASupported practice

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

Learning target I can write equivalent fractions, decimals, and percents for the same value.

Why This Matters You're designing the scoring system for a new arcade game. Players earn points as fractions of the total possible score. The leaderboard shows scores as percentages, but the game engine uses decimals. You need to convert between all three forms to build the display! A player scored 3/4 of the total possible points. Write that score as a decimal and as a percent.

Part 1Understand the ideamodels and meaning
  1. 1Write the name of the correct group on each line.

    Sort these values — which are greater than 50% and which are less than 50%?

    Groups: Greater than 50% Less than 50%
    • 3/4
    • 0.8
    • 65%
    • 7/10
    • 1/3
    • 0.25
    • 40%
    • 2/5

    Hint 50% is the same as 1/2 or 0.5 — that is your comparison line for every card.

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

    Convert 3/5 to a percent.

    1. A35%
    2. B53%
    3. C60%
    4. D65%

    Hint Percent means out of 100. What do you multiply the denominator 5 by to get 100?

    Rewrite each fraction
    Work it out
    Simplify
    1. 1Same size piecesCommon denominator first.
    2. 2OperateOnly then add or subtract.
    3. 3SimplifyDivide out common factors.
  2. 3Circle the letter of the best answer. Show how you know.

    Convert 7/20 to a percent.

    1. A14%
    2. B20%
    3. C35%
    4. D70%

    Hint The denominator 20 is friendly: 20 × 5 = 100, and percents are always 'out of 100'.

    Rewrite each fraction
    Work it out
    Simplify
    1. 1Same size piecesCommon denominator first.
    2. 2OperateOnly then add or subtract.
    3. 3SimplifyDivide out common factors.
  3. 4Circle the letter of the best answer. Show how you know.

    Which decimal is equivalent to 45%?

    1. A0.045
    2. B0.45
    3. C4.5
    4. D45.0

    Hint Percent means 'out of 100', so 45% is the fraction 45/100.

    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 fraction is equal to 0.75?

    1. A3/4
    2. B3/5
    3. C7/5
    4. D7/10

    Hint 0.75 is read 'seventy-five hundredths' — the place value tells you the denominator.

    Show your work
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1Convert 3/5 to a percent3/5
    2. 2Read the digits as the percentThe numerator is 3 and the denominator is 5, so the student writes 35%.
    3. 3Final answer3/5 = 35%

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

    Hint Do the digits 3 and 5 tell you how many parts out of 100?

    Correct work
    Correct answer:

Explain your thinkingWhat number did you multiply by to turn each denominator into 100, and how did that fraction out of 100 give you the percent?

Sentence starter I multiplied the top and bottom of ___ by ___ to get ___/100, so the percent is ___%.

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 4.2Relate Fractions, Decimals, and Percentages

Version BCore practice

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

Learning target I can write equivalent fractions, decimals, and percents for the same value.

Why This Matters You're designing the scoring system for a new arcade game. Players earn points as fractions of the total possible score. The leaderboard shows scores as percentages, but the game engine uses decimals. You need to convert between all three forms to build the display! A player scored 3/4 of the total possible points. Write that score as a decimal and as a percent.

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

    Complete each row. Build the fraction out of 100 first — that column hands you the percent.

    FractionEquivalent fraction out of 100DecimalPercent
    2/5
    0.125
    90%
    5/8
    Show your work
  2. 2Mark and label each value on the number line.

    Place each value on the number line: A = 3/8, B = 0.6, C = 85%

    00.10.20.30.40.50.60.70.80.91
    Show your thinking
  3. 3Write the name of the correct group on each line.

    Order these values from least to greatest by sorting them into the correct position.

    Groups: 1st (Smallest) 2nd 3rd 4th 5th (Largest)
    • 1/5
    • 0.35
    • 2/5
    • 55%
    • 3/4
Part 2Apply itreal-world problems
  1. 4Circle the letter of the best answer. Show how you know.

    A game shows your score as 7/8 complete. What percent is that?

    1. A75%
    2. B78%
    3. C87.5%
    4. D88%
    Rewrite each fraction
    Work it out
    Simplify
Part 3Explain and correctreasoning
  1. 5Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1Convert 5/8 to a percent5/8
    2. 2Divide the bottom by the top8 ÷ 5 = 1.6
    3. 3Multiply by 1001.6 × 100 = 160%
    4. 4Final answer5/8 = 160%

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

    Correct work
    Correct answer:

Explain your thinkingWhat number did you multiply by to turn each denominator into 100, and how did that fraction out of 100 give you the percent?

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 4.2Relate Fractions, Decimals, and Percentages

ChallengeExtension

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

Learning target I can write equivalent fractions, decimals, and percents for the same value.

Why This Matters You're designing the scoring system for a new arcade game. Players earn points as fractions of the total possible score. The leaderboard shows scores as percentages, but the game engine uses decimals. You need to convert between all three forms to build the display! A player scored 3/4 of the total possible points. Write that score as a decimal and as a percent.

Part 1Understand the ideamodels and meaning
  1. 1Mark and label each value on the number line.

    Place 1/3, 0.4, and 38% on the number line. Which is greatest?

    00.10.20.30.40.50.60.70.80.91
    Show your thinking
Part 2Explain and correctreasoning
  1. 2Find the mistake. Explain it, then show the correct work.

    Find the Conversion Error

    1. 1Convert 2/3 to a percent2/3
    2. 2Divide numerator by denominator2 ÷ 3 = 0.67
    3. 3Move decimal two places0.67 → 67%
    4. 4Final answer2/3 = 67%

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

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

    A student says 3/8 is greater than 40% because 3 and 8 are bigger numbers than 4 and 0. Is the student correct? Convert both values to the same form and explain.

    Write your answer

Explain your thinkingWhat number did you multiply by to turn each denominator into 100, and how did that fraction out of 100 give you the percent?

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