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Differentiation in maths

Differentiation means making sure every pupil in the class can learn from the lesson: the ones who find it hard get the support they need, and the ones who find it straightforward are stretched. In primary maths, that used to mean three different worksheets for three ability tables. Many schools now aim for something different: the whole class learns the same thing together, with support and challenge built into one lesson.

This guide covers how to do that in practice, with ideas you can use tomorrow.

Keeping the class together

The National Curriculum in England expects most pupils to move through the content at broadly the same pace. Pupils who grasp a concept quickly should be challenged with richer problems rather than moved on to the next topic, and pupils who aren't yet fluent should consolidate with extra practice before moving on. This is the thinking behind teaching for mastery.

In a lesson, keeping the class together usually looks like this:

• One core task for everyone. Every pupil works on the same idea, for example adding two-digit numbers, but with different amounts of support.
• Small steps. Break a new idea into small steps and check each one with a quick "show me" before moving on.
• Same-day catch-up. A short "keep-up" session later that day with the few pupils who struggled, so they start tomorrow's lesson ready.
• Depth, not speed. Pupils who finish are given harder questions on the same idea, not next week's work.

Manipulatives: concrete, pictorial, abstract

Many schools follow a concrete, pictorial, abstract approach (often shortened to CPA). Pupils first handle real objects, then draw pictures or diagrams, then work with numbers and symbols alone. The useful classroom kit includes:

• Ten frames and counters for numbers to 10 and 20 and number bonds.
• Base 10 (Dienes) blocks and place-value counters for exchanging in column addition and subtraction.
• Bead strings and number lines for counting on and back.
• Multilink cubes for arrays, times tables and bar models.
• Fraction walls and strips for comparing and finding equivalent fractions.

Manipulatives aren't only for pupils who are struggling. Asking a confident pupil to show 52 − 27 with base 10, exchanging a ten for ten ones, often reveals that they know the steps but not why they work. Leave the equipment out on every table so reaching for it isn't a public admission of finding the work hard.

Low threshold, high ceiling tasks

A low threshold, high ceiling task is one every pupil can start but that goes a long way. It lets the whole class work on the same problem, with pupils naturally reaching different depths.

• Key Stage 1: "Find two numbers that add up to 10." Everyone can find one pair. Can you find them all? How do you know you have them all? What about three numbers?
• Lower Key Stage 2: "Find two numbers with a total of 20 and a difference of 4." Pupils can guess and check (12 and 8). Then: what if the total is 30 and the difference is 6? (18 and 12.) Can you find a quick way that always works? (Take the difference away from the total and halve it to get the smaller number.)
• Upper Key Stage 2: "Which numbers from 1 to 20 can you make by adding two or more consecutive whole numbers?" For example, 9 = 4 + 5 = 2 + 3 + 4. Every pupil can find some. Pupils who go far notice that 1, 2, 4, 8 and 16 can't be made, and that each is double the one before.

Scaffolds that come away

A scaffold is temporary support that helps a pupil do something they couldn't yet do alone. The aim is always to remove it. Useful maths scaffolds include:

• a worked example on the board, next to the questions, with each step labelled;
• a part-whole model or bar model drawn for the first question;
• a number line, hundred square or times-table grid to check facts while working on a method;
• sentence stems for explanations: "I know that… so…";
• fewer questions, chosen carefully, rather than the first half of the sheet.

Plan when each scaffold will come away: after three questions, after a "show me" check, or next lesson. Otherwise a support quietly becomes a crutch.

Challenge cards

A challenge card deepens the same learning. Write a few general prompts on cards and pick the ones that fit the lesson:

• Give an example, and an example that nobody else will think of.
• Make up a question with the answer 36. Now make one harder.
• Is it always, sometimes or never true? Prove it.
• Find all the possibilities. How do you know you've found them all?
• Explain the mistake in this answer.

For example, if the lesson is adding two-digit numbers: "Use the digits 2, 3, 4 and 5 once each to make two two-digit numbers. What's the biggest total you can make? The smallest?" The biggest is 95 (for example 53 + 42), because the 5 and 4 need to be tens. The smallest is 59 (for example 24 + 35), with the 2 and 3 as tens. Pupils who spot that any arrangement with the same tens digits gives the same total are reasoning about place value, not only adding.

Puzzles for early finishers

Early-finisher work should be worth doing, not more of the same. Puzzles are ideal because they practise facts while asking pupils to think.

• Honeycomb puzzles. In a Beequation honeycomb, one number is the sum (or product) of two others, and pupils have to find it. The free puzzle pack has sums to 20 and times-table sheets with an answer key, so pupils can check their own work.
• Make your own. Ask early finishers to build a honeycomb for a partner where exactly one number is made from two others. Making sure no other pair works is real, systematic checking.
• The browser game. On a class computer or tablet, Beequation in the browser needs no sign-up and gives a fresh puzzle each time.

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