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Click to go to TeachersMedia.co.uk: KS 1/2 Maths - Just Division
Division in KS1 and KS2 is the point where many pupils' mathematical confidence either takes root or starts to wobble. Teaching it well means moving carefully between concrete manipulatives, pictorial representations, and abstract symbols — and giving pupils time to see division as a genuinely different operation, not just multiplication backwards.
About this video
Division sits at the top of the four operations in terms of cognitive load. It requires pupils to hold multiplication facts, understand what "grouping" and "sharing" mean, apply place value to multi-digit numbers, and (later) interpret remainders sensibly in context. Rushed teaching produces pupils who can do a bus stop division on demand but can't tell you which of two answers to a real problem makes sense.
The most reliable approach in the UK primary tradition is CPA — concrete, pictorial, abstract. Pupils first divide real objects (sweets shared among children, cubes grouped into towers), then move to visual representations (bar models, number lines, arrays), and only then to written methods. Pupils who skip the first two stages tend to produce right answers to easy questions and wrong answers to anything unfamiliar.
The two mental models of division worth teaching explicitly are sharing (24 shared between 4 people gives 6 each) and grouping (how many groups of 4 fit into 24?). Both give the same numerical answer, but they suit different contexts and different problems. Fluent pupils can move between them.
A sequence that reliably works
- Sharing objects. Real division of real things — sweets, cubes, counters — between real groups.
- Grouping objects. How many groups of 3 can we make from 12 counters? A different mental model, same answer.
- Pictorial: arrays and bar models. Draw a rectangle of 12 dots; how many rows of 3? Bar models for word problems.
- Abstract: fact families. Link division to multiplication (3 × 4 = 12, so 12 ÷ 3 = 4 and 12 ÷ 4 = 3).
- Multi-digit written division. Only when the concept is secure. Bus stop / short division for one-digit divisors.
Discussion prompts
- When your pupils get a division answer wrong, is it typically a calculation error or a conceptual error? What's the difference in what you'd do to help?
- How do you teach pupils to interpret remainders — round up, round down, express as a fraction — in different real contexts?
- What proportion of your division teaching involves manipulatives versus abstract symbols? Is that ratio right for your class?
Try this in your classroom
- For a lesson, start every division problem with cubes or counters. Notice which pupils reach for the manipulatives without prompting and which still don't use them.
- Give pupils a word problem where the answer is 4 remainder 2, in different contexts (buses, pizzas, prizes). Ask which answer makes sense in each context.
- Have pupils create their own division word problem for a specific division fact. Their problems tell you whether they understand what division means, not just how to do it.