Multiplication and Division
Year 5 is a big year for multiplication and division. Children get to know the numbers themselves: multiples and factors, common factors, prime numbers, and square and cube numbers. Alongside this they learn the written methods of long multiplication and short division with remainders, so much bigger calculations stop feeling like a leap.
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
Multiplication as an array
An array lays a multiplication out in rows and columns. This 4 by 6 array holds 4 x 6 = 24, and it shows the factor pair 4 and 6.
For grown-ups
Underneath multiplication and division sits one idea: how numbers are built from smaller ones. Knowing that 24 splits into 4 and 6, or that 51 is really 3 times 17, is the same thinking that later unlocks simplifying fractions and working with algebra. Children also multiply and divide whole numbers and decimals by 10, 100 and 1000, scale facts they already know, and reason about rates and scaling, which keeps these methods tied to real situations rather than to noughts on the end of a number.
What is in this topic
- Multiples, factors, common factors and prime numbers
- Square numbers and cube numbers
- Long multiplication and short division with remainders
- Multiplying and dividing by 10, 100 and 1000
- Multiplication and division word problems
How to help at home
This topic rewards a calm, methodical hand more than speed. The aim is for your child to slow down, work in clear steps and check each answer back, so the bigger calculations stop feeling like a leap.
- When multiplying or dividing by 10, 100 and 1000, talk about digits moving rather than 'adding noughts'. For 7 x 100 every digit shifts two places to the left, giving 700, and for 4500 / 100 it shifts two places back to 45.
- For long multiplication, split the smaller number out loud before writing anything. For 24 x 13, work out 24 x 10 = 240, then 24 x 3 = 72, then add them: 240 + 72 = 312.
- Make square and cube numbers physical. A square number is a number times itself, so 5 squared is 5 x 5 = 25, and a cube number is times itself again, so 3 cubed is 3 x 3 x 3 = 27.
- Practise short division with the remainder spoken aloud. For 74 / 5, ask how many fives fit into 74: that is 14 fives (70) with 4 left over, so the answer is 14 remainder 4.
Where children get stuck
A very common slip is assuming any odd number is prime. Children meet a number like 51, see it is odd, and call it prime, when in fact 51 = 3 x 17. The fix is a quick checklist: try dividing by 2, 3, 5 and 7 in turn, and only call it prime once none of those go in cleanly.
The other frequent wobble is treating a remainder as the end of the thinking rather than something to interpret. After 74 / 5 = 14 remainder 4, ask 'what does the 4 actually mean here?' For sharing 74 sweets between 5 children, each gets 14 and 4 are left over, which keeps the remainder tied to the real question instead of being a leftover symbol.