Round each number to its first digit, then calculate: 38 × 52 ≈ 40 × 50 = 2000. If the calculator says 197.6 or 19 760, something slipped.
You type 3.2 × 48 and the calculator shows 15.36. Looks plausible. But before you trust it, how big should the answer be?
An estimate is a quick answer that is close, found by rounding the numbers to something easy. A good habit: round each number to its first digit (keep its size), do the easy calculation, and compare with the real answer.
38×52≈40×50=2000
If the exact answer is near the estimate, it is reasonable. If it is ten times too big or too small, check the decimal point.
Predict: Read the problem and decide what you think before you try anything. A wrong guess is fine: it shows you what to look for.
Try: Try it on the board and compare the result with your prediction.
Investigate: Work out why it happens, one step at a time.
Modify: Change the problem on purpose and see what happens.
Practise: A few on your own, to check you have it.
Make: Make your own problem using what you have learned. Expect a few tries; that is normal.
Make your prediction first. Help opens once you've locked it in.
PredictRead the problem and decide what you think before you try anything. A wrong guess is fine: it shows you what to look for.
Estimate 38 × 52
Is the exact answer going to be a bit more or a bit less than 2000? Why?
TryTry it on the board and compare the result with your prediction.
Estimate and exact
The orange bar is the estimate, the blue bar the exact answer. They are nearly the same length.
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Set a = 49 and b = 21. What is the estimate? Is it more or less than the exact answer?
Use the board. This ticks when you get there.
InvestigateWork out why it happens, one step at a time.
Estimates catch slips
Round each number to its first digit.
Estimate 6.8×31 by rounding each number to its first digit.
Lina estimates 19.6 × 4.1. Click the line where her working goes wrong.
ModifyChange the problem on purpose and see what happens.
Other operations, other sizes
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Estimate 387 + 512 by rounding to the first digit. Set a near 387 and b near 512: what is the estimate?
Use the board. This ticks when you get there.
Estimate 4.9×81.
Estimate 612÷29.
PractiseA few on your own, to check you have it.
Estimating
Estimate 58×19.
Estimate 7.9×4.2.
Review: round 6.45 to 1 decimal place.
MakeMake your own problem using what you have learned. Expect a few tries; that is normal.
Close but under
Then find a pair where the exact answer is more than 2000, and write which rounding you used and why.
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Need a hint?
The estimate must be 40 × 50, so a is near 40 and b near 50.
Another hint
Try a = 38 and b = 52.
Set a and b so that the estimate is exactly 2000 but the exact answer is less than 2000.
Use the board. This ticks when you get there.
For teachers
Students estimate by rounding each number to its first digit, compare the estimate with the exact answer, and use it to catch slips such as a misplaced decimal point (AC9M7N05, node 3). About 40 minutes.
I can estimate a calculation by rounding each number to its first digit.
I can compare an estimate with the exact answer and say whether it is reasonable.
I can use an estimate to find a slip, such as a decimal point in the wrong place.
Before class
Do the Run board yourself first. Students need rounding (previous lesson) and multiplying by multiples of 10 (Year 6).
The one idea: round to the leading digit and keep the size, calculate the easy numbers, and compare with the exact answer. The commonest mistakes are losing the size (Lina rounds 19.6 to 2), losing a zero in the calculation, and trusting a calculator answer because it looks plausible.
Estimation is only worth teaching if it is used. In class, make students estimate before pressing = for the whole lesson.
Running the lesson
Predict: students who chose 200 lost a zero; 90 added the numbers.
Run: ask whether the exact answer is more or less than the estimate, and why.
Investigate: have students write their estimate before the calculator answer is shown.
Modify: ask when rounding both numbers up gives an estimate that is too big.
Make: collect pairs of numbers; check which have an exact answer above and below 2000.
The hard part (on purpose)
Keeping the size when rounding: 19.6 is about 20, not 2. Ask 'how many zeros should the estimate have?' before computing.
When students get stuck
A student rounds 19.6 to 2 (Lina's slip). Ask: Is 19.6 nearer 2 or 20? Fix: Round to the first digit and keep its size: 20.
A student computes 5 × 80 = 40. Ask: How many zeros in 5 × 8, and how many in 80? Fix: Count the zeros: 40 for 5 × 8, then one more for 80, so 400.
A student says any calculator answer must be reasonable. Ask: What if a decimal point was typed in the wrong place? Fix: Estimate first, then compare.
Stretch and support
Stretch: Round one number up and the other down so that the estimate is closer to the exact answer. When is that a good idea?
Support: Round to the nearest ten or hundred, and write the rounded numbers before multiplying.
Where it leads
Next: Ratios, where estimating also helps check sharing and scaling.
Where it leads: estimating in modelling problems (money, measurement), and significant figures in Year 8 and 9.
What each step is for
estimate 38 × 52: Committing to an estimate shows whether they round to the first digit and keep the size (2000), lose a zero (200) or gain one (20 000).
estimate and exact: Moving a and b shows the estimate (rounded numbers) staying close to the exact answer, and both bars the same size.
estimates catch slips: Keeping the size of each rounded number (19.6 is 20, not 2) is the whole skill; an estimate of the wrong size cannot catch a decimal slip.
other operations, other sizes: Estimating works for adding, dividing and with decimals; an estimate can be above or below the exact answer.
estimating: Estimates for multiplying and for a decimal product, a calculator check with a division, and a rounding review.
close but under: Finding numbers whose estimate is exactly 2000 but whose exact product is less shows an estimate is a close value, not a bound.
Now you can
Estimate a calculation by rounding each number to its first digit.
Compare an estimate with the exact answer and say whether it is reasonable.
Use an estimate to find a slip, such as a decimal point in the wrong place.