A practical guide for UK primary school teachers | KS1 & KS2

Maths isn't just about getting the right answer – it's about understanding why an answer is correct, explaining how we got there and exploring different ways to solve a problem.

Developing mathematical reasoning and problem-solving skills is an important part of the primary maths curriculum, helping children become more confident, independent and flexible thinkers.

But with so much to fit into the school day, finding time for dedicated reasoning and problem-solving activities can sometimes feel like another challenge!

The good news? Building these skills doesn't have to mean planning extra lessons or preparing complicated activities. Small changes to everyday maths teaching can make a big difference.

Here are five simple, practical ways to encourage mathematical thinking in your classroom.

1. Ask "How Do You Know?"

One of the easiest ways to develop mathematical reasoning is to encourage children to explain their thinking, rather than simply giving an answer.

Instead of moving straight on when a child answers correctly, try asking:

• How do you know that's correct?
• Can you explain how you worked it out?
• Why did you choose that method?
• Can you convince someone else that your answer is right?
• Would that always work?
  

These simple questions encourage children to think more deeply about the maths involved.

Quick classroom idea: Display a "How do you know?" question on your maths working wall and make it a regular part of your lessons. Encourage children to explain their answers to a partner before sharing with the class.

2. Let Children Spot the Mistake

Children often enjoy finding mistakes – especially when it's the teacher who's supposedly made one!

Presenting an incorrect calculation or explanation gives pupils the opportunity to identify errors, explain why something is wrong and suggest how to correct it.

For example:

A pupil says that 36 ÷ 4 = 8 because 4 × 8 = 36.

Ask the class:

• Is the pupil correct?
• Where have they gone wrong?
• How could you prove the correct answer?
• What advice would you give them?
  

This approach helps children develop their reasoning skills while reinforcing their understanding of mathematical concepts.

Quick classroom idea: Introduce a weekly "Spot the Mistake" challenge. It could be as simple as displaying an incorrect calculation on the board for children to discuss with a partner.

3. Encourage More Than One Way to Solve a Problem

In maths, there is often more than one route to the correct answer.

Encouraging children to explore different methods helps them become more flexible thinkers and recognise connections between mathematical concepts.

For example, ask children to calculate:

25 × 12

Some might use a formal written method, while others may partition the calculation:

25 × 10 = 250

25 × 2 = 50

250 + 50 = 300

Others might recognise that 25 × 4 = 100, so 25 × 12 = 300.

Discussing these approaches helps children understand that maths isn't always about following one set procedure.

Quick classroom idea: Once children have solved a problem, challenge them to find a second method. Ask: "Which method do you prefer, and why?"

4. Introduce Short Maths Investigations

Maths investigations don't have to take up an entire lesson. Even a five-minute challenge can encourage children to explore patterns, make predictions and test their ideas.

For example:

KS1 challenge: How many different ways can you make 20p using 1p, 2p, 5p and 10p coins?

KS2 challenge: Two whole numbers add up to 20. What is the largest possible product? Can you explain why?

These open-ended activities encourage children to think creatively, work systematically and explain their findings.

They're also ideal for partner work, giving pupils opportunities to discuss their ideas and learn from one another.

Quick classroom idea: Try a "Friday Maths Challenge" – one short investigation each week that children can explore individually, in pairs or as a class.

5. Make Reasoning Part of Everyday Maths Practice

Mathematical reasoning doesn't need to be taught as a completely separate activity. It can be woven into almost any maths lesson with just a few carefully chosen questions.

For example, instead of asking children to simply calculate 48 + 27, try:

• True or false? 48 + 27 is greater than 70. Explain your answer.
• Which is the most efficient way to calculate 48 + 27?
• What happens to the answer if you add 10 to one of the numbers?
• Can you create a different calculation with the same answer?
  

By adding an extra question or two, a straightforward calculation becomes an opportunity for deeper mathematical thinking.

Quick classroom idea: Choose one question from your usual maths lesson and add a reasoning prompt. It doesn't need to take long, but it encourages children to think beyond the answer.

Helping Children Become Confident Mathematical Thinkers

Developing strong reasoning and problem-solving skills takes time, practice and plenty of opportunities to explore mathematical ideas.

The important thing is to create a classroom environment where children feel comfortable explaining their thinking, trying different approaches and even making mistakes.

By introducing small reasoning opportunities into everyday lessons, we can help children develop the confidence to tackle unfamiliar problems and understand the maths behind their answers.

And remember – it's not always about finding the answer quickly. Sometimes the most valuable learning happens when children take time to explain how they got there.