Long division — for parents
Year 4 is when long division appears for the first time. It's usually the first "long" algorithm children meet that runs left to right, the opposite of the column-addition and subtraction they already know. That reversal is the main source of mistakes.
What your child should master by year-end
- Divide any multi-digit number (up to 4 digits) by a one-digit divisor (2–9).
- Handle a remainder (always smaller than the divisor).
- Lay out the division using the "divide, multiply, subtract, bring down" cycle.
- Check the result with the inverse: quotient × divisor + remainder = dividend.
- Estimate the answer by rounding the dividend to a nearby multiple of the divisor.
Common mistakes
Missing zero in the quotient
When the current piece of the dividend is smaller than the divisor, you write 0 in the quotient and carry on to the next digit. Children often skip the zero and end up with an answer that's one place value too small.
Example: 408 ÷ 4 = 102 (correct), 12 (wrong).
Help: count the quotient digits. 408 ÷ 4 should produce a three-digit quotient; getting 12 (two digits) is a red flag.Remainder larger than the divisor
If a quotient digit is "too small", the difference after subtraction is at least as big as the divisor. That means the divisor fits one more time and the digit should be raised by 1.
Help: after each subtraction, compare the remainder to the divisor. If remainder >= divisor, fix the quotient digit.Going right to left
Some children try to divide from the right (the ones), copying column addition and subtraction. It doesn't work that way — division always starts on the left.
Help: a concrete picture. When you share £84 among 4 people, you start with the tenners (£10 notes, the tens place) and only then move on to the coins (the ones). That's exactly left-to-right.Stopping at the wrong place
When the division has a remainder, children sometimes either drop the remainder entirely or round it the wrong way.
Help: remind them that the remainder is a positive integer smaller than the divisor. If a problem asks for an exact answer, it must be written as "quotient r remainder".Activities at home
Bowl of grapes
Pour out 24 grapes (or any small item). Ask: "Share these equally among 6 people. How many does each get? Anything left over?" Then up the numbers: 47 between 5, 53 between 6...
Shop game
Your child shares £100 (or another round amount) among siblings, guests or toys. They see how the money divides up, when a remainder appears, and when it's a clean share.
Inverse check by routine
After every long-division exercise, have your child do the inverse check (quotient × divisor + remainder). The habit builds confidence that the division was correct.
Why the algorithm works
The "divide-multiply-subtract-bring-down" cycle works because it repeatedly handles smaller pieces of the dividend. First you share out the hundreds, then the tens (along with anything left over from the hundreds), then the ones (along with anything left from the tens). That's why you can split the number digit by digit — each step solves a partial problem.
If your child understands this principle, they don't have to memorise the procedure mechanically. They picture sharing sweets out of bags of different sizes.