The Five Big Ideas – Fluency

In this feature, Debbie Morgan shares insights and practical advice on how to develop children’s fluency. Discover what fluency really means, why it's essential for mathematical success, and how to embed it across your school.

What do we mean by fluency?

Fluency in maths is often misunderstood as simply recalling facts quickly, but it encompasses much more.

There are three key elements to fluency:

1. Recall and automaticity: the effortless recall of facts, such as number bonds within 10 and times tables facts, and understanding the relationship between these facts.
2. Procedural fluency: being confident and accurate with using procedures and being able to select the most appropriate method for the task at hand.
3. Flexibility and adaptability: the skill of moving between different contexts and recognising connections between them. For example, understanding the concept of ¹⁄₄ in various situations, whether it's a fraction of a shape, a portion of time or a proportion of set of objects.

Why is fluency in maths important, and what are the benefits?

Knowing key facts to automaticity enables you to calculate more efficiently, even when those facts aren't within the times tables that we typically learn or the number bonds to 10. For example, 14 × 5 could be solved by adding the partial products. If you know 10 × 5 and 4 × 5, you can add them together. This is helpful in the real world, such as when scaling up a recipe or working out equivalences.

It can be the key to unlocking the door for some pupils, relieving cognitive load in order to focus more readily on concepts. As Daniel Willingham aptly put it, fluency in a small set of key facts allows students to focus on a wide range of concepts. When children have a strong grasp of basic facts, they can more easily make connections. For example, understanding the relationship between doubling and halving can help pupils grasp the concept of equivalent fractions, such as recognising that ⁶⁄₁₂ is the same as ¹⁄₂.

In the following video, notice how the children are set up to spot a remainder, because they have secured their times tables:

Here is a question from the 2024 Year 6 SATs paper:

Tap/click image to enlarge)

It is likely that some pupils went straight to dividing both numbers by 2, 3, 4, 8 and 9, which would take a very long time.

However, if pupils have developed factual fluency, it becomes a very easy question. The first three can be solved using divisibility rules; you can tick 2 because both numbers are even. You can tick 3 because the digits in each integer add to a multiple of 3. You know if half an even number is even, it is a multiple of 4, and 8 and 9 are within our range of times tables facts, which we've learned to automaticity.

How does it fit into the other Five Big Ideas in Teaching for Mastery?

Tap/click image to enlarge

Fluency plays a critical role in the other Big Ideas. It supports the application of concepts, helps in recognising patterns within variation and eases cognitive load, which is essential for mathematical thinking. I would say that, without fluency, reasoning and problem-solving become significantly more challenging.

How should teachers incorporate fluency into their maths lessons?

TTeachers and maths leads should plan a consistent, school-wide approach to fluency, starting with children in Reception developing subitising skills and exploring the composition of numbers. A system should be put in place so that all staff are aware of the responsibilities for each year group.

Fluency isn't just about rote learning; simply seeing a fact repeatedly and trying to remember it won't be enough for most pupils. Pupils need to understand the ‘why’. Explicitly making those connections will help children understand these facts in depth. For example, knowing that 8 is composed of 5 and 3 will support pupils to learn and connect addition and subtraction facts. They will be able to derive that if 5 + 3 = 8, then 3 + 5 is also 8, and 8 − 5 = 3 or 8 − 3 = 5. People often say, ‘if I know one fact, I get three for free’.

Developing fluency takes time and effort, but the effort is worth the rewards. All pupils need plenty of practice and time dedicated to the retrieval of facts. A child might know it on Tuesday, but have forgotten it by Friday, so they may need opportunities to retrieve it on Wednesday and Thursday.

What are some of the potential barriers that teachers might face?

‘I don’t have the time’
Insufficient practice is often a barrier to fluency. It isn’t always easy, but it is important to make time for both retrieval and application of facts. Find those little pockets of time: even when lining up for assembly, teachers can incorporate a call-and-response activity:

Teacher: ‘9 is made of 5 and…’
Pupils: ‘…4, 5 and 4 make 9.’

‘Some children just can’t learn facts’
It is true that some children find learning facts harder than others; therefore, it is important we remove their anxiety and provide additional support. Some pupils need extra practice or teaching, or you may need to slow down and focus on one fact at a time. Try sending a little pack of cards home to encourage extra practice and build their confidence.

Remember that these strategies can also be beneficial to the whole class. When developing our Mastering Number Programme, we found that gesturing can help to embed facts in the long-term memory for all children, not just for those who are struggling. For example, when learning that 7 × 7 = 49, marking out a square with a hand gesture helps us remember it is a square number.

‘Learning facts isn’t ‘real’ maths’
Teacher mindset can also be a barrier. Often people mistakenly think that learning facts is not as important as learning concepts, so not enough time is spent developing fluency in facts. The Mastering Number Programmes support staff in seeing how to integrate factual and conceptual knowledge.

In summary, what are your top tips for teachers who want to improve their pupils’ fluency?

Schools need a plan for developing fluency across all year groups. There needs to be a systematic approach across the school that works, such as the Mastering Number at Reception/KS1 and KS2 Programmes. I would recommend the DfE guidance, which has a whole strand on fluency, and the Ready-to-Progress criteria, which explains what children should know and learn in every year group. There are also some appendices which could be usefully integrated into a school policy.

Make sure all teachers are aware of what their responsibilities are in their year group, and how it builds on what comes before and prepares for what comes later. Remember that some teachers will need professional development to support them in this, which is where your local Maths Hub can help.

Consider how to support pupils who are finding it harder to develop fluency. All pupils can develop fluency, but some might need extra teaching or practice. Identify those pupils and make sure they get what they need to develop fluency. This will help develop confidence – they'll suddenly feel like they are keeping up with the rest of the class – and it will relieve some cognitive load, freeing them up to access future concepts.

Be aware of the fluency needed to access new learning. When introducing a new topic, make sure that pupils have the prerequisite fluency by checking that the numbers involved are ones that they are already fluent in.

If we spend time developing children’s fluency now, it will make their future learning easier and help them to become confident mathematicians.

Did you enjoy this?

Read our previous Five Big Ideas features:

• Variation
• Representation and Structure
• Coherence.

Coming shortly: an explainer video exploring Fluency in the primary classroom.