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Assess Reasonableness of Answers to Word Problems

Students practice checking whether their answers to two-step word problems make sense using mental math, estimation, and re-reading the problem. They learn to use rounding and benchmark numbers to estimate an expected answer range before calculating.

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Assess Reasonableness of Answers to Word Problems

Grade 3 · Two-Step Word Problems · question 1 of 3

0 of 12

12 rungs. A star at the top.

A school collects 36 cans, then 40 more, and recycles 21. Which of these is the best estimate of the cans it still has?

How it is taught

0:00 of 4:53

A reasonable answer is close to a quick estimate.

An estimate uses numbers that are easy to think.

Read it: Estimate first, then check

A shop has 284 cups, gets 412 more, then sells 197. Round each amount: 300 + 400 − 200 is about 500.

  1. Round each amount to the nearest hundred: 300, 400 and 200.
  2. Work the two steps on the rounded numbers: 300 + 400 = 700, then 700 − 200 = 500.
  3. Check the exact answer, 499, against the estimate: it is close to 500.

Rounded numbers are quick to add and take away in your head.

The same two steps on rounded numbers land near the exact answer.

An exact answer far from the estimate tells you a step went wrong.

Round each amount, work the same two steps, then check the exact answer is close.

Working the exact numbers and never checking: a slip like 284 + 412 = 596 goes unseen.

The estimate says about 500. 596 − 197 is 399, far from 500, so look again: 284 + 412 = 696.

A bus has 38 riders. 22 more get on, then 19 get off. About how many riders are on the bus now? — 40. Round to the nearest ten: 40 + 20 = 60, then 60 − 20 = 40.

Estimate first: 28 books + 3 boxes of 9

Maya has 28 books. She buys 3 more boxes with 9 books in each box. How many books does she have now?

Before we solve, let's estimate. A good answer should feel close to our guess.

Round 28 up to 30, because 28 is close to 30.

Round 9 up to 10, because 9 is close to 10.

Three boxes of about 10 books is around 30 books.

Add: 30 plus 30 is about 60. Our answer should be close to 60.

Maya's booksMaya has 28 books.She buys 3 boxes with 9 books each.How many books now?ESTIMATESOLVE28≈ 309≈ 103 × 10 ≈ 3030 + 30 ≈ 60ESTIMATE≈60books3 × 9 = 2728 + 27 = 55ACTUAL55books55 ≈ 60 ✓ reasonable!ANSWER55books — close to 60 ✓Estimate first to check your answer!
Grade 3 · Two-step word problems

Now solve for real. Three times nine is twenty-seven.

Add the 28 books she already had: 28 plus 27 is 55.

Is 55 close to our estimate of 60? Yes! Just five away — that's reasonable.

Maya has 55 books. Estimating first helps us catch mistakes. Great work!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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