Estimation to check answers to calculations
Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy
What a learner can do afterwards
- Estimate 487 × 23 by rounding to 500 × 20 and use this to check a calculated answer
- Determine whether an exact answer or an estimate is more appropriate in a given context
- Spot an unreasonable answer by comparing with a quick mental estimate
1 · Read
You already know how to round numbers to make a quick estimate. Now you'll use that same idea to check your calculations, especially when you multiply or divide bigger numbers.
To estimate 487 x 23, round each number first: 487 rounds to 500, and 23 rounds to 20. So 500 x 20 = 10,000 is your estimate. The exact answer is 11,201. Since 11,201 is close to 10,000, the exact answer looks about right.
Sometimes you need the exact answer, and sometimes an estimate is enough. If you're working out exact change or exact money, you need the precise number. If you just want a rough idea, like roughly how much paint to buy, an estimate does the job.
If your worked-out answer is way off from your estimate, like ten times too big or too small, check your work. A missing digit or a slipped decimal point is often the cause.
Round first to make an estimate, then check your exact answer against it, and decide whether the situation needs exact or roughly right.
More to read
Round two- and three- digit numbers to the nearest ten on the vertical number line
Rounding swaps fiddly numbers for friendly ones. To estimate 487 times 23, round to 500 times 20, which is 10,000. The true answer of 11,201 sits close by. A pupil answer of 1,201 is nowhere near, so the estimate exposes it instantly.
1.4 Multiply Whole Numbers
Exact answers suit counting and money; estimates suit crowds and guesses. You need exactly 52 times 48 for stock, but about 2,500 for a quick sense check. Rounding both numbers to one friendly digit each keeps mental maths light. 50 times 50 = 2,500 previews the true 2,496 nicely.
3.1 Use a Problem-Solving Strategy
Checking is a full problem solving step, not an afterthought. After computing 298 + 405 = 703, estimate 300 + 400 = 700 to confirm the neighbourhood. If estimate and answer disagree wildly, rework before moving on. Nurses measuring medicine need exactness, while paint buyers do fine with rough tins.
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2 · Watch
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Where it sits
Learn first
Optional connections
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18 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.