What rounding is for
Rounding replaces an awkward number with a nearby friendly one so we can estimate, compare and talk about numbers sensibly. A stadium holding 47,812 people holds about 50,000. A child who understands that purpose can judge their own answers: rounding 47,812 to 40,000 is obviously not the nearest ten thousand, because 50,000 is closer.
Step one: the number line
Draw a number line from 30 to 40 and mark 37. Ask which end it is closer to. Children can see that 37 is three away from 40 and seven away from 30, so 37 rounds to 40. Do this for many numbers before mentioning any rule. Then draw 60 to 70 and mark 62; it is closer to 60.
Make the two candidate answers explicit every time: when rounding to the nearest ten, the answer must be one of the two multiples of ten the number sits between. Children who write down both neighbours first almost never produce an answer that is not a multiple of ten.
Step two: the halfway problem
Thirty-five is exactly halfway between 30 and 40. The number line cannot decide, so mathematicians agreed: halfway rounds up. That is the only place the 5-or-more rule is really a rule rather than an observation. Everything above halfway (36, 37, 38, 39) is visibly closer to 40; everything below (31, 32, 33, 34) is visibly closer to 30; 35 rounds up by agreement.
Step three: the digit rule as a shortcut
Once children can round on a number line, show them the shortcut. To round to the nearest ten, look at the ones digit. Zero to four: keep the tens digit. Five to nine: increase the tens digit by one. Either way, the ones digit becomes zero.
To round to the nearest hundred, look at the tens digit and make everything after the hundreds digit zero. To the nearest thousand, look at the hundreds digit. The digit you look at is always the one immediately to the right of the place you are rounding to.
Worked examples
Round 348 to the nearest ten. Neighbours: 340 and 350. Ones digit is 8, so round up. Answer: 350.
Round 348 to the nearest hundred. Neighbours: 300 and 400. Tens digit is 4, so keep. Answer: 300.
Round 2,650 to the nearest hundred. Neighbours: 2,600 and 2,700. Tens digit is 5, so round up. Answer: 2,700.
Round 2,650 to the nearest thousand. Neighbours: 2,000 and 3,000. Hundreds digit is 6, so round up. Answer: 3,000.
Round 995 to the nearest ten. Neighbours: 990 and 1,000. Ones digit is 5, so round up. Answer: 1,000. This one catches children who try to write 9100.
Using rounding to estimate
The point of rounding is estimating. Before a child works out 298 plus 403, ask them to round: 300 plus 400 is 700, so the answer should be close to 700. After the exact calculation (701), the estimate confirms it. Make estimating a habit for every multi-digit calculation, and a lot of place-value errors disappear because children notice their answer is nowhere near the estimate.
Common mistakes
- Rounding to the wrong place: rounding 348 to 350 when asked for the nearest hundred. Writing both neighbours first fixes this.
- Rounding the digit but forgetting to zero the rest: 348 to the nearest ten written as 358.
- Carrying across a place: 995 to the nearest ten is 1,000, not 9100 or 990.
- Rounding in stages: rounding 2,449 to the nearest ten first (2,450) and then to the nearest hundred (2,500). The correct answer to the nearest hundred is 2,400. Always round from the original number.