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Division Facts and Remainders

Sharing equally and identifying what's leftover is an important skill. Like all mathematical concepts, division needs to be explored practically first for children to understand it. Even the term division needs to be explored so that they can relate the phrases of 'sharing' and 'equal groups of' to the same operation.

When you look at division in this way, children begin to learn this mathematical concept in reception. When you ask your child to set the table for dinner, they are multiplying how many knives and forks they need by the number of people eating. They collect the cutlery then divide it into equal groups at the table.

Six sweets shared into two equal groups.

Counting out the sweets in a bag or tube and then sharing them between friends equally, is a good way to show remainders but there are lots of opportunities to demonstrate this in everyday life.

The key to understanding division is recognising it as the inverse operation (the opposite) of multiplication. This sounds obvious but children need to be taught this explicitly and explore this for themselves, to make the connection. I always use use Fact Families Triangles and love the ones produced by Twinkl. Once I've modelled how the triangles work, I ask children to write out all the facts they can see within the triangle.

Fact Family Triangles from

As adults, writing out the facts might seem like a waste of time as they appear obvious to us. However, children often fall into autopilot mode and write examples like the following:

5 x 4 = 20

4 x 5 = 20

4 ÷ 5 = 20

5 ÷ 4 = 20

Rather than showing children their mistakes, I encourage them to use counters to prove each of their statements and identify their mistakes. Experience led learning is so much more powerful in helping children learning and retain what they have learnt.

If you've read any of my blogs before, you will know that I don't advocate rushing onto the next skill too quickly. The National Curriculum in England is fairly fast paced and some children need to spend longer learning each skill before moving on.

The children who have lots of experience in physically sharing quantities and have a good knowledge of times tables succeed in understanding and using the written methods of division. Those that don't struggle and find it confusing.

I hope you have found this useful. Next week, I will be looking at the 'Bus Stop Method' of division otherwise known as the 'Short Method'.

Happy Maths

Joanne Adams


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