Neft Teacher · Learn It

Unit 4 · Standard 6.AT.4

Estimate the Percent of a Number

Lesson 4-3 · Learn It — how the math works

Why we're learning this

Margaret checked the cloud storage on her phone: 6 GB total, 4 GB used. Approximately what percent of her storage is used — and of the used storage, approximately what percent are photos?

✱ Math Workbench

Learn It

Approximately — the problem is asking for an estimate

The word approximately tells you an exact answer is not required. Benchmarks, rounding and compatible numbers get you close, fast.

Picture itSee what the math looks like before you read about it

A phone's storage screen shows a bar nearly full: 6 GB total, with photos taking the biggest colored stripe and small slivers for mail, messages, and documents.
Where you see this in real lifeA phone's storage screen shows a bar nearly full: 6 GB total, with photos taking the biggest colored stripe and small slivers for mail, messages, and documents.

Watch me solve itI do — read one step at a time

The problem looks like this
A double number line showing 6 GB corresponding to 100% with benchmark jumps of 25%. Double Number Line Model GB % 0 GB 0% 1.5 GB 25% 3 GB 50% 4.5 GB 75% 6 GB 100%
  1. is 6 GB — that is 100%.
  2. I mark the bottom line in benchmark jumps of 25%: 0%, 25%, 50%, 75%, 100%.
  3. Equivalent ratios give the top line: 25% of 6 GB is 1.5 GB, so the top reads 0, 1.5, 3, 4.5, 6.
  4. 4 GB used lands between 4.5 (75%) and 3 (50%), close to 4.5 — so about 70% of the storage is used.

Watch out — mistakes students make here

  • 3.5 out of 4 is clearly below 100%, but not that close to it.
  • The phone's capacity never changed — the QUESTION changed.
  • The whole is set by the question, and this pair of questions sets it differently.

Try it with meWe do — you answer first, then check

Same steps, new numbers.

  1. The Green-Team recycled 216 pounds of material; 8.6% was metal.
  2. Round both: 8.6% is about 10%, and 216 is about 220.
  3. 10% of 220 = 0.1 × 220 = 22. About 22 pounds of metal.
  4. work too: 10% of 200 = 20. Both agree — around 20 pounds.

On your ownYou do — solve this one by yourself

Before you start, remember:

  • 24% of 81 using a benchmark. Say which benchmark you chose and why.
  • Then check: is your a little high or a little low?

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

My answer

Stuck? Open one hint at a time.

Hint 1

Write 10% as a decimal.

Hint 2

0.1 × 200.

Hint 3

One tenth of 200.

Check my answer
✅ Answer: 20 pounds
10% of 200 = 0.1 × 200 = 20 pounds of metal.

Turn & TalkSay it out loud with a partner

Margaret's phone has 6 GB total and 4 GB used. On the , 4 GB lands between the 50% mark (3 GB) and the 75% mark (4.5 GB), closer to 4.5. Why does that make 'about 70%' a reasonable instead of an exact one?

Try starting with:

  • 4 GB is between the ___% mark and the ___% mark, closer to ___%.4 GB está entre la marca de ___% y la marca de ___%, más cerca de ___%.
  • I know 70% is reasonable because ___.Sé que 70% es razonable porque ___.
Use these wordsbenchmark percentdouble number lineestimate