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

Lesson 4.3Estimate the Percent of a Number

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can estimate the percent of a number using benchmark percents, rounding, and compatible numbers.

Start hereWords for this lesson

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

WordWhat it meansExample
estimateSpanish: estimación A reasoned answer that is close enough to be useful, found without exact computation. about 70% used
benchmark percentSpanish: porcentaje de referencia A friendly percent — 1%, 10%, 25%, 50%, 75%, 100% — used as a landmark for estimating. 10%, 25%, 50%, 75%
compatible numbersSpanish: números compatibles Numbers close to the originals that are easy to compute with mentally. 8.6% of 216 → 10% of 220: both nudged to numbers that divide nicely.
double number lineSpanish: recta numérica doble Two parallel number lines that pair amounts with their percents at the same positions. 0, 30, 60 GB over 0%, 50%
the wholeSpanish: el todo The quantity that counts as 100% in a problem — and it can change between questions. all of the storage
DecomposeSpanish: Descomponer Break a percent into friendly pieces that are easy to find. 15% = 10% + 5%

How it worksWorked exampleestimating a percent with benchmarks

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

A tablet holds 64 GB of storage and 47 GB are already used. About what percent of the tablet is full?

  1. Name the whole: all 64 GB stands for one hundred percent.
  2. Mark benchmarks: halfway is 32 GB, and three quarters of the way is 48 GB.
  3. Locate the used amount, 47 GB — it sits right at the three-quarter mark.
  4. Estimate with that benchmark, not with exact division.

Answer: About three quarters — roughly seventy-five percent — of the tablet is full.

Now you trySame steps, your turn

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

A water tank holds 80 L and has 22 L in it right now. About what percent of the tank is full?

  1. The whole is L, and it stands for one hundred percent.
  2. Half of the tank is L. One quarter of the tank is L.
  3. The amount 22 L sits closest to which benchmark?
  4. Estimate: about %
Answer:about what percent of the tank is full

Say it and write itSentence starters

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

  • The whole in this problem is , so it stands for one hundred percent.
  • The benchmark closest to is .
  • My estimate is about % because .
  • I know my estimate is reasonable because .

Word bank estimateaboutbenchmarkwholepartdouble number linehalfone quarterthree quartersclose toreasonablecompare

Watch outA common mistake

Keeping the same whole for every question — when the problem says 'of the used storage,' the whole changes from 6 GB to 4 GB, and estimates anchored to the old whole are wrong before any arithmetic happens.

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

Lesson 4.3Estimate the Percent of a Number

Version ASupported practice

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

Learning target I can estimate the percent of a number using benchmark percents, rounding, and compatible numbers.

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

    Margaret's phone has 6 GB of storage and 4 GB is used. About what percent is used?

    1. AAbout 25%
    2. BAbout 40%
    3. CAbout 70%
    4. DAbout 150%

    Hint What is the whole?

    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    On the double number line for 6 GB, what amount lines up with 25%?

    1. A1.25 GB
    2. B1.5 GB
    3. C2.5 GB
    4. D4 GB

    Hint 25% means one quarter.

    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.

    Which benchmark percents make good landmarks on a number line?

    1. A0%, 25%, 50%, 75%, 100%
    2. B3%, 17%, 62%, 94%
    3. COnly 50%
    4. DOnly 100%

    Hint Which percents can you find mentally?

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

    To estimate 8.6% of 216 by rounding, which numbers should you use?

    1. A1% of 216
    2. B8% of 300
    3. C10% of 220
    4. D86% of 216

    Hint Round each number to something friendly.

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

    What is 10% of 220?

    1. A2.2
    2. B22
    3. C44
    4. D220

    Hint Write 10% as a decimal.

    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 2Explain and correctreasoning
  1. 6Answer in complete sentences.

    The word 'approximately' appears in the storage problem. What does it tell you about the answer you need?

    Sentence starter 'Approximately' tells me ___ .
    So instead of computing exactly, I can ___ .
    Write your answer

Explain your thinkingYou sorted a move into 'Benchmark percent' and your partner into 'Compatible numbers.' Which number did each strategy change — the percent or the whole — and why does changing that one keep the estimate close?

Sentence starter This is ___ because it changes the ___, and the estimate stays close since ___.

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 4.3Estimate the Percent of a Number

Version BCore practice

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

Learning target I can estimate the percent of a number using benchmark percents, rounding, and compatible numbers.

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

    The Green-Team recycled 216 pounds; 8.6% was metal. Using compatible numbers 10% and 200, the estimate is:

    1. A2 pounds
    2. B20 pounds
    3. C86 pounds
    4. D208 pounds
    0%50%100%
    Work
  2. 2Circle the letter of the best answer. Show how you know.

    Photos use 3.5 GB of the 4 GB of used storage. About what percent of the USED storage is photos?

    1. AAbout 35%
    2. BAbout 58%
    3. CAbout 87%
    4. DAbout 99%
    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    Margaret has a 6 GB phone with 4 GB used. Question A asks what percent of the total 6 GB is used. Question B asks what percent of the used 4 GB is photos. Why is the whole different in the two questions?

    1. AThe phone gained storage between the questions
    2. BThe whole never changes in a percent problem
    3. CThe second question asks about the used storage, so 4 GB becomes 100%
    4. DBecause photos are more important than mail
    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    Estimate 24% of 81 with benchmarks.

    1. AAbout 2
    2. BAbout 8
    3. CAbout 20
    4. DAbout 40
    Show your work
  5. 5Circle the letter of the best answer. Show how you know.

    Your estimate for 8.6% of 216 was 22 pounds (using 10% of 220). Is the exact answer higher or lower than 22?

    1. AHigher, because rounding always shrinks the answer
    2. BLower, because both 10% and 220 rounded UP
    3. CExactly 22
    4. DImpossible to tell
    Show your work
Part 2Explain and correctreasoning
  1. 6Answer in complete sentences.

    Estimate 47% of 312. Show which strategy you used — benchmark, rounding, or compatible numbers — and give your estimate.

    Write your answer

Explain your thinkingYou sorted a move into 'Benchmark percent' and your partner into 'Compatible numbers.' Which number did each strategy change — the percent or the whole — and why does changing that one keep the estimate close?

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 4.3Estimate the Percent of a Number

ChallengeExtension

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

Learning target I can estimate the percent of a number using benchmark percents, rounding, and compatible numbers.

Part 1Understand the ideamodels and meaning
  1. 1Write the letter of the matching item on each line.

    Match each percent problem to the benchmark combination that estimates it.

    1. 15% of 200
    2. 75% of 80
    3. 20% of 350
    4. 11% of 400
    • A10% + 5%: 20 + 10 = 30
    • B50% + 25%: 40 + 20 = 60
    • C10% doubled: 35 × 2 = 70
    • D10% + 1%: 40 + 4 = 44
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    Two students estimate 8.6% of 216. Ana uses 10% of 220 = 22. Ben uses 10% of 200 = 20. Whose estimate is closer to the exact answer, 18.576?

    1. AAna's — 22 is closer to 18.576
    2. BThey are equally close
    3. CBen's — 20 is 1.4 away; Ana's 22 is 3.4 away
    4. DNeither is a valid estimate
    Show your work
  2. 3Circle the letter of the best answer. Show how you know.

    For which problem is ESTIMATING clearly the right tool, rather than exact computation?

    1. ADeciding if a $58 jacket at 25% off fits your $45 budget
    2. BProgramming a bank to compute interest on every account
    3. CReporting a medicine dose
    4. DScoring a state test
    Show your work
  3. 4Circle the letter of the best answer. Show how you know.

    A store marks a $79.95 item 32% off. Which mental estimate best checks the discount?

    1. AAbout 3.2 dollars off
    2. BAbout 32 dollars off, because 32% means $32
    3. CAbout one third of 80, so about $26 off
    4. DAbout half of 80, so $40 off
    Show your work
Part 3Explain and correctreasoning
  1. 5Answer in complete sentences.

    Write your own estimation problem about percent, using a real situation from your life. Then solve it with a benchmark and say whether your estimate runs high or low.

    Write your answer
  2. 6Answer in complete sentences.

    Margaret has 6 GB of total phone storage, of which 4 GB is used and 3.5 GB is photos. Estimate what percent of the TOTAL storage is photos. Compare it with 87.5%, the percent of the USED storage that is photos. Why do these percentages differ?

    Write your answer

Explain your thinkingYou sorted a move into 'Benchmark percent' and your partner into 'Compatible numbers.' Which number did each strategy change — the percent or the whole — and why does changing that one keep the estimate close?

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