Multiplication and Division
Year 6 is where the written methods really come together. Children multiply four-digit numbers by two-digit numbers using long multiplication, and divide four-digit numbers by two-digit numbers using long division, learning to handle the remainder by writing it as a fraction, as a decimal, or by rounding to suit the question. It sounds like a lot, but it is the same column thinking they have built up since Year 4, now stretched to bigger numbers.
Practise Multiplication and Division
Have a guess, even if you're not sure. Get one wrong and we'll show you why, so every miss is a chance to learn.
Timed practice
The same practice, just with a gentle clock. Pick a length and see how many you can answer.
Good to know
Breaking a number into factors
This 3 by 8 array holds 3 x 8 = 24. Splitting a number into a factor pair like this is the first step towards its prime factors, 2 x 2 x 2 x 3.
For grown-ups
Year 6 also looks closely at how numbers fit together: common factors and the highest common factor, common multiples and the lowest common multiple, and breaking a number down into its prime factors. This structure is the reasoning that sits under secondary maths, where simplifying fractions, finding common denominators and working with algebra all lean on knowing how a number is built. The multi-step problems matter just as much, because they ask children to choose the right operations and carry out a method accurately, which is exactly what the rest of maths will keep demanding.
What is in this topic
- Long multiplication of 4-digit numbers by 2-digit numbers
- Long division of 4-digit by 2-digit, with remainders as a fraction, decimal or rounded
- Short division and mental multiplication and division strategies
- Common factors, the highest common factor, common multiples and the lowest common multiple
- Prime factors, breaking a number into its primes
- Multi-step word problems
- Spot multiples fast with the rules of divisibility
How to help at home
By Year 6 the methods matter more than the answers. Help most by slowing down at the layout: a well set-out long multiplication or division almost solves itself, while a cramped one hides the slip that lost the marks.
- Keep the columns straight when setting out long multiplication. For 3725 x 24, multiply by 4 (14900), then by 20 (74500), then add: 14900 + 74500 = 89400. The neat columns are what stop a careless error.
- When long division leaves a remainder, ask what the question wants it as. 4500 divided by 16 gives 281 remainder 4, which is 281 and 4/16 as a fraction, 281.25 as a decimal, or about 281 rounded to the nearest whole.
- Practise highest common factor and lowest common multiple as a pair. For 12 and 18, list factors (12: 1, 2, 3, 4, 6, 12 and 18: 1, 2, 3, 6, 9, 18) so the highest shared one, 6, jumps out, then count up in each to find the lowest shared multiple, 36.
- Talk multi-step problems through before any sums. Underline what is asked, decide the order of steps out loud, then work them one at a time, so the question becomes a short to-do list rather than one big tangle.
Where children get stuck
The commonest long-division wobble is dropping a digit or losing the place value, so 4500 divided by 16 comes out ten times too big or too small. The fix is to write a small estimate first: 16 goes into 45 about twice, so the answer starts in the hundreds and should be near 280. An estimate before the method gives a target to check the real answer against.
The other frequent muddle is mixing up factors and multiples, which makes highest common factor and lowest common multiple feel interchangeable. Anchor it with the words: factors are smaller and divide into the number, multiples are bigger and the number divides into them. So for 12, its factors stop at 12, but its multiples (12, 24, 36) carry on, and that direction tells you which list to write.