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Different routes into the same maths

Children in the same class may need different amounts of support with the same idea. One may still count every object, another may use a drawing and another may explain a relationship mentally. Differentiation means responding to that evidence. It need not mean preparing three unrelated lessons.

Keep the mathematical goal clear. For example, “Add by making a ten” allows several routes into 8 + 5. “Complete ten sums” tells you much less about what children are learning. This approach also helps in a multigrade classroom, where independent work and small-group teaching must fit together.

One example, three representations

Objects: make the ten visible

Give the child eight counters on a ten-frame (a card with two rows of five boxes) and five beside it. Ask them to fill the two empty spaces. Three counters remain outside, so the total is 10 + 3 = 13. Check that they can identify the original five as the two moved counters and the three remaining ones.

Use familiar materials such as counters or bundles of sticks. On an abacus, label the place-value columns and use the arrangement the class has been taught. Materials help only when the child understands what each position or group represents.

Pictures: record the bridge

Draw eight marks in a ten-frame and five outside, or draw a number line with a jump of 2 from 8 to 10 and a jump of 3 from 10 to 13. Ask the child to label both jumps. A picture should show the reasoning, not become decoration beside an unexplained answer.

Equations: explain the split

Write 8 + 5 = 8 + 2 + 3 = 13. Ask why the 5 can be replaced by 2 + 3 and why making 10 is useful. A child who can explain this may no longer need a fully drawn ten-frame, but should still be allowed to choose one when needed.

Go deeper without only making numbers larger

A confident child can compare 8 + 5 and 8 + 7. Both first need 2 to reach 10, but their remaining parts differ. They can explain why 48 + 5 = 53: add 2 to reach 50, then add the remaining 3.

Another extension is to find every unordered pair of non-negative whole numbers with total 13. Count zero as allowed and don't count reversed pairs twice. There are seven pairs: 0 + 13, 1 + 12, 2 + 11, 3 + 10, 4 + 9, 5 + 8 and 6 + 7. Ask how the child knows none is missing.

Change the demand from “find an answer” to “compare, explain or prove completeness”. This keeps the class connected to one idea instead of giving early finishers a longer pile of routine sums.

Keep grouping flexible

Group children for a particular need today, not by a permanent judgment about ability. A child secure in addition may need objects for division. Another may understand an idea orally but struggle to copy the notation.

In pairs, give one child the role of explaining and the other the role of checking, then swap. Don't make the quicker child responsible for all the thinking. Ask each child to show one step independently so that the pair's answer does not hide a misunderstanding.

A manageable three-station lesson

• Make. Build bonds and bridge a ten with counters and ten-frames.
• Draw. Record a bridge with labelled jumps, then check against an equation.
• Explain. Compare methods, repair a mistaken split or solve a related example.

Teach the activity and the checking routine before expecting independent work. Keep the station materials familiar and provide a clear help signal. While some children practise independently, work with a small group on the particular step they are missing.

For a multigrade group, retain a shared idea such as equal groups while varying the numbers and recording. Younger children might build three groups of two; older children might use a known fact to explain six groups of eight. Their tasks need not have identical numerical difficulty to share a mathematical conversation.

Remove access barriers separately

Check whether print size, crowded layout, copying, language or an unfamiliar diagram is blocking the work. An oral answer or a larger, clearly spaced page can preserve the mathematical goal. For children with special needs (CWSN), follow the support agreed with the teacher or special educator rather than inventing a new requirement.

Reduce unnecessary writing when the goal is reasoning, but retain enough recording to check the calculation. For example, let a child describe the bridge aloud while pointing to the two labelled jumps. Use accessible worksheet formats where helpful; braille requires the additional checks on the braille page.

Fade support using evidence

Move from a completed ten-frame to a blank one, or from a labelled number line to one the child labels. Let them choose whether they still need the tool. Record a precise observation such as “bridges to ten independently; needs help splitting the second addend”, rather than “low ability”.

Use a short exit question to decide the next lesson. Revisit the missing step, not an entire topic by default. See maths starters for quick prompts and reasoning questions for explanations worth listening to.

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