Some pupils begin calculating as soon as they see numbers, before deciding what the problem asks or how the quantities relate. Teach one consistent process and model the thinking at each stage. Keep the routine visible until the pupil can use it with less support.

A useful structure is: understand, plan, solve, check. Planning here means showing how the quantities relate before choosing a calculation.

1. Understand the problem

Read the problem and identify:

• what is happening;

• what needs to be found;

• which information is relevant;

• the units involved;

• whether there is more than one step.

Ask the pupil to explain the question in their own words. Do not rely on operation keywords. Words such as more, difference or shared can appear in problems with different mathematical structures.

2. Plan: represent the relationship

Choose a representation that makes the known and unknown quantities visible:

• objects;

• a drawing;

• a bar model;

• a number line;

• a table;

• a number sentence.

Label every part. The representation should help choose the calculation, not decorate an answer reached already.

3. Solve

Select a dependable method that matches the relationship. Keep each result connected to what it represents.

For a multi-step problem, record an intermediate result with a label rather than leaving an unexplained number.

4. Check against the question

Ask:

• Have we answered what was asked?

• Is every part complete?

• Are the unit and label included?

• Is the answer reasonable?

• Can it be stated in a sentence?

Checking the calculation alone is not enough if the final result does not answer the problem.

A complete Primary example

Problem: A class has 28 red pencils and 17 blue pencils. The teacher puts 9 pencils into a new tray. How many pencils remain in the original trays?

Understand

We need the number remaining. First find the total, then remove 9.

Plan

A bar model shows 28 and 17 combined, with 9 removed from the total.

Solve

28 + 17 = 45
45 − 9 = 36

Label the intermediate result: 45 pencils altogether.

Check

The final answer is 36 pencils. It is smaller than 45 because 9 were removed, and the unit is pencils.

The important reasoning comes from the relationship between the quantities, not the presence of words such as altogether or remain.

Model the thinking aloud

Say what an experienced problem solver notices:

• “The question asks what remains, but I cannot subtract until I know the total.”

• “This number tells me how many were moved, not how many were there originally.”

• “I will label 45 so I remember what it means.”

• “My answer must be fewer than 45.”

The pupil needs to hear why each decision is made.

Fade the routine

Move from:

• teacher models all four stages;

• teacher and pupil complete each stage together;

• pupil completes a prompt sheet;

• pupil uses four short headings;

• pupil makes a brief independent plan;

• prompts are removed.

Return to the full structure temporarily when a new type of problem creates difficulty.

Common mistakes to avoid

• Choosing an operation from one keyword.

• Underlining every number without deciding whether it is relevant.

• Requiring a bar model for every problem.

• Completing calculations without labelling intermediate results.

• Recalculating without checking the context.

• Removing the routine after one successful example.

• Keeping a long checklist after the pupil can plan independently.

Evidence and further reading

The Education Endowment Foundation’s article on improving mathematical problem-solving describes modelling planning, monitoring and evaluation. Its Improving Mathematics in Key Stages 2 and 3 report provides the wider evidence-informed framework.