ACARA v9 CONTENT DESCRIPTION “check and explain the reasonableness of solutions to problems including financial contexts using estimation strategies appropriate to the context”
Builds on rounding, place value and the four operations, including the reasonableness check met with multiplication. Year 5 makes estimation a deliberate tool: rounding numbers to easy ones, estimating the result of a calculation, and using that estimate to judge whether an exact answer is reasonable. Estimation matters most in everyday and financial situations, where a quick, sensible check on a total, a price or some change guards against careless mistakes.
Estimating by rounding
Estimating starts with rounding: replacing numbers with nearby easy ones, usually to the nearest ten, hundred or whole dollar. To estimate three hundred and twelve plus four hundred and eighty-nine, round to three hundred plus five hundred, which is eight hundred, close to the exact answer of eight hundred and one. Rounding both numbers the same way keeps the estimate close, and the easier the rounded numbers, the quicker the estimate. An estimate is not the exact answer but a sensible guide to about how big it should be.
Estimating by rounding
Replace numbers with nearby easy ones.
Estimate 312 + 489 by rounding.
Estimating products and quotients
The same rounding works for multiplication and division. To estimate thirty-nine times twenty-one, round to forty times twenty, which is eight hundred, near the exact answer. To estimate two hundred and three divided by four, round to two hundred divided by four, which is fifty. Choosing numbers that are easy to multiply or divide, sometimes called compatible numbers, makes mental estimation possible even for large calculations. The estimate gives a ballpark figure to expect before, or instead of, working out the exact result.
Estimating products and quotients
Compatible numbers make mental estimates easy.
Estimate 39 x 21 with easy numbers.
Is the answer reasonable?
An estimate is most useful for checking whether an answer is reasonable. After working out, or being told, a result, a quick estimate shows whether it is in the right range. If four hundred and twelve plus three hundred and eighty-nine is given as one thousand eight hundred and one, an estimate of eight hundred shows the answer is far too large, so a mistake has been made. If forty-eight times twenty-one is given as about one thousand, that matches an estimate of fifty times twenty, so it is reasonable. Checking against an estimate catches slips like a misplaced digit or a wrong operation.
Is the answer reasonable?
An estimate catches answers that are way off.
Round the numbers, estimate, and see if the answer fits.
Estimating with money
Estimation is especially handy with money. Rounding each price to the nearest dollar gives a quick total: four dollars ninety-five, three dollars ten and six dollars twenty round to five, three and six dollars, about fourteen dollars altogether. This is enough to know whether there is enough to pay, without adding the cents exactly. Because prices are often just under a whole dollar, rounding up slightly tends to give an estimate a little above the true total, which is a safe way to check there is enough money.
Estimating with money
Round each price to a whole dollar.
Estimate the total of $4.95 + $3.10 + $6.20.
Checking a money answer
The same idea checks money answers and change. For three items at nineteen dollars ninety-five each, rounding to twenty dollars gives about sixty dollars, so a total near sixty is reasonable and a total of two hundred is not. To estimate change from fifty dollars for a bill of thirty-eight dollars forty, round the bill to forty dollars and subtract: about ten to twelve dollars change. Estimating first means an exact answer, or a till receipt, can be trusted or questioned at a glance.
Checking a money answer
Whole-dollar rounding gives a quick, safe check.
Round prices to whole dollars, then estimate.
Checking with confidence
Checking reasonableness with confidence means estimating on purpose: round to easy or compatible numbers, work out a quick estimate, and compare it with the exact answer or the situation. In money problems, rounding to whole dollars gives a fast, safe check on totals and change. An estimate will not match exactly, and it is not meant to, but an exact answer far from a sensible estimate is a signal to look again. This habit of checking turns careful estimation into a reliable guard against mistakes in every kind of problem.
Quick self-check
1. To estimate 312 + 489 by rounding, you work out...
2. A good estimate for 39 x 21 is...
3. Someone says 412 + 389 = 1,801. An estimate shows this is...
4. To estimate the total of $4.95 + $3.10 + $6.20, round to...