Short division
National Curriculum: this is in the Year 4 programme of study, part of key stage 2 (Years 3 to 6). Schools have to teach the key stage 2 programme by the end of Year 6, and can introduce content earlier or later within it.
Children in Year 4 are 8 or 9, and turn 9 during the school year.
What it is
Short division, the bus stop method, divides a number one digit at a time, carrying each leftover to the next digit. Year 4 works divisions like this one, which come out exactly.
- 6 into 1 does not go, so the 1 is carried to the next digit.
- 6 into 19 goes 3 times, with 1 left over. Write 3 above the 9 and carry the 1 to the next digit.
- 6 into 12 goes 2 times. Write 2 above the 2.
- 192 ÷ 6 = 32.
In Year 5 the numbers get longer and no longer share out evenly. The extra Year 5 skill is deciding what the amount left over means: sometimes it is the answer, sometimes it rounds the answer up, and sometimes the question ignores it.
- 6 into 1 does not go, so the 1 is carried to the next digit.
- 6 into 19 goes 3 times, with 1 left over. Write 3 above the 9 and carry the 1 to the next digit.
- 6 into 16 goes 2 times, with 4 left over. Write 2 above the 6 and carry the 4 to the next digit.
- 196 ÷ 6 = 32 remainder 4.
The method leans almost entirely on times-table recall: every step asks "how many sixes in this?" plus a small subtraction. A child still counting up their tables has to do that inside every digit, and the method turns slow and error-prone.
When children learn it
Short division is taught from Year 4, once tables to 12 × 12 are expected. Year 4 covers two- and three-digit numbers that divide exactly, with nothing left over. Remainders are a Year 5 requirement (ages 9 to 10): children divide numbers of up to four digits by a one-digit number and say what the amount left over means in the question. Long division, for dividing by two-digit numbers, comes in Year 6.
What it looks like when it goes wrong
These patterns come up again and again in children's answers on this skill. Each one points at a specific missing idea, not carelessness.
- The remainder disappears. 196 ÷ 6 answered as just 32, or a word problem answered without asking what the remainder means. If 196 people travel in minibuses that seat 6, the answer 32 leaves four people behind; the question needs 33. Interpreting a remainder is the next skill after this one rather than part of it, so a child who divides correctly and stops has not made a mistake in the division.
- The leftover is lost between digits. The remainder from one digit never joins the next: after "sixes in 19 is 3 remainder 1", the next step reads 6 instead of 16. One lost carry and every digit after it is wrong.
- A table fact one out. "Sixes in 19" answered as 4 — one multiple too high, overshooting 19 — or as 2, stopping a group early. One digit of the answer is out, and the carried remainder that follows is wrong too.
How to help at home
- Before practising division, check the matching table is quick. If 6 × 7 needs thinking time, 43 ÷ 6 will too — the table is the thing to practise first.
- After a word problem, ask what the remainder means here. Sometimes it rounds the answer up (minibuses needed), sometimes it is dropped (full boxes packed), sometimes it is the answer itself (how many left over).
- Check with multiplication: 32 remainder 4 means 32 × 6 + 4 should give back 196.
- If the written steps keep going wrong, do the same division with coins or place-value counters: share the tens, exchange the leftover into ones, share again. The written method is a record of that.