Estimate quantities
Theory
Estimating quantities is a Year 3 skill: making a sensible guess of how many or how much without counting every one. This Year 3 maths page shows how to estimate by grouping in tens, by using benchmarks, and by rounding numbers to the nearest ten or hundred, then how to use an estimate to check an answer is reasonable. Curriculum: VC2M3N06 / AC9M3N05.
An estimate is a sensible guess that is close to the real amount. It is not the exact number, but it is near enough to be useful, like saying a footy crowd is about 40 000 people.
There are three easy ways to estimate. You can group in tens and count \(10, 20, 30, \dots\), using ten-frames or rows of ten. You can use a benchmark, which is a size you already know, such as a school bus holding about 50 people or a bucket holding about 10 litres. Or you can round each number to the nearest ten or hundred and work with the easy numbers.
Rounding changes a number to the nearest ten or hundred. To round to the nearest ten you look at the ones digit; to round to the nearest hundred you look at the tens digit. The sign \(\approx\) means about equal to, so \(74 \approx 70\).
Estimating does not need formulas, but these rounding facts make it quick and reliable.
| Round to the nearest… | Look at this digit | 0–4 | 5–9 |
|---|---|---|---|
| Ten | ones digit | round down | round up |
| Hundred | tens digit | round down | round up |
How to estimate a quantity
- Choose a way to estimate. Group the things in tens, picture a benchmark you know, or round the numbers.
- Round each number. To the nearest ten, look at the ones digit; to the nearest hundred, look at the tens digit.
- Work with the easy numbers. Count in tens, or add, subtract or multiply the rounded numbers.
- Check it is sensible. Compare a worked-out answer with your estimate. If they are far apart, check the working again.
| \(74\) | \(\text{is between}\) | \(70 \text{ and } 80\) |
| \(\text{ones digit } 4\) | \(<\) | \(5\) |
| \(74\) | \(\approx\) | \(70\) |
Rounded to the nearest ten, \(74 \approx 70\).
| \(286\) | \(\approx\) | \(300\) |
| \(511\) | \(\approx\) | \(500\) |
| \(300 + 500\) | \(=\) | \(800\) |
The total is about \(800\).
| \(712\) | \(\approx\) | \(700\) |
| \(289\) | \(\approx\) | \(300\) |
| \(700 - 300\) | \(=\) | \(400\) |
The difference is about \(400\).
| \(\text{full tens}\) | \(\to\) | \(10, 20, 30\) |
| \(30 + 4\) | \(=\) | \(34\) |
| \(34\) | \(\approx\) | \(30\) |
There are \(34\) stickers, which is about \(30\).
(i) Estimate the total to the nearest ten.
(ii) How many counters are there exactly?
| \(4 \times 10\) | \(=\) | \(40\) |
| \(40 + 3\) | \(=\) | \(43\) |
| \(43\) | \(\approx\) | \(40\) |
(i) About \(40\).
(ii) \(43\) counters.
| \(3 \times 20\) | \(=\) | \(60\) |
There are about \(60\) apples.
| \(\$412\) | \(\approx\) | \(\$400\) |
| \(\$189\) | \(\approx\) | \(\$200\) |
| \(\$400 + \$200\) | \(=\) | \(\$600\) |
The total is about \(\$600\).
| \(305\) | \(\approx\) | \(300\) |
| \(198\) | \(\approx\) | \(200\) |
| \(300 - 200\) | \(=\) | \(100\) |
A sensible answer is about \(100\), so \(507\) is not reasonable.
Common pitfalls
Frequently asked questions
What is an estimate in maths?
An estimate is a sensible guess that is close to the real amount. It is not the exact number, but it is near enough to be useful, like saying a bag holds about \(50\) marbles.
How do you round a number to the nearest ten?
Look at the ones digit. If it is \(0\) to \(4\), round down and keep the tens the same. If it is \(5\) to \(9\), round up to the next ten. For example, \(74 \approx 70\) and \(56 \approx 60\).
How do you round to the nearest hundred?
Look at the tens digit. If it is \(0\) to \(4\), round down to the hundred below. If it is \(5\) to \(9\), round up to the hundred above. For example, \(286 \approx 300\) and \(511 \approx 500\).
How do you estimate the answer to an addition?
Round each number first, then add the easy numbers. To estimate \(286 + 511\), round to \(300 + 500\), which gives about \(800\).
What is a benchmark?
A benchmark is an amount you already know, used to compare. If a school bus holds about 50 people, two buses hold about 100.
How does estimating help you check an answer?
Round the numbers and work out a rough answer. If the real answer is far from the estimate, something is wrong. For \(305 - 198\) the estimate is about \(100\), so an answer of \(507\) must be wrong.