Tips and tricks for teaching times tables in KS2
In this blog, Gill Knight, experienced maths leader and teaching for mastery specialist, explains government expectations for times tables, and explores effective and fun ways to teach them.
Times tables in the curriculum
Since the announcement of the multiplication tables check (MTC) for year 4 pupils, emphasis on ensuring that pupils can quickly recall times table facts has increased. The MTC assesses how close pupils are to achieving the national curriculum expectation that all facts up to 12 times 12 will be known by the end of year 4. Schools are committing considerable amounts of time to this, yet many are unclear about the best way of using this time. What is the best way to learn times tables? How can teachers ensure that pupils have the facts they need at their fingertips?
Why learning times tables is important
Much of the maths curriculum in upper key stage 2, key stage 3 and beyond is built on multiplicative reasoning. The pupil who has secure recall of times tables facts will be able to use this knowledge to solve problems, answer questions, make connections and generalise, whereas pupils who need to derive facts (for example, by skip counting on their fingers) won’t have working memory available for that deeper thinking.
For example, when asked to simplify 14/35 , a pupil who knows their seven times table will quickly recognise this to be equivalent to 2/5 , because they will recognise both 14 and 35 as products on the seven times table. If 14 and 35 do not spark that multiplicative connection, they will need to go through a far longer process of identifying a common factor.
‘Knowing your tables’ is also viewed as a benchmark of being good at maths. Pupils who don’t have easy recall often develop the idea that maths is hard. No wonder: by having to work out facts, they are putting in far more effort than those who effortlessly produce the facts they need to solve a problem. However, Jo Boaler reports in her guidance ‘Fluency without fear: research evidence on the best ways to learn math facts’ that the onset of maths anxiety is closely associated with the start of timed testing. In our efforts to ensure that pupils have the facts they need at their fingertips, we need to be careful that we don’t unwittingly cause pupils to become anxious about maths, as this will cause a significant reduction in their available working memory.
Effective ways to teach times tables
Sadly, in my experience, there are no easy shortcuts to knowing times tables. However, there are some simple steps that can be taken to make the process as painless as possible.
Conceptual understanding is key
For fact recall to be secure, it must be built on understanding. The first step is to ensure a child understands what each part of a tables fact represents. There are only three things to understand about a multiplication fact:
- how many groups are there?
- how many are there in each group?
- how many altogether?
A really effective way of embedding understanding of this relationship is to work with counters. Take 10 counters – how many ways can they be split into equal groups? Relate this to the matching multiplication and division facts, showing that if I have 2 groups of 5 and the equation 2 x 5 = 10, the 2 represents the number of groups, the 5 represents how many in each group and the 10 represents how many counters I have altogether.
If the groups stay the same but the equation changes to 5 x 2 = 10 or 10 ÷ 5 = 2 or 10 ÷ 2 = 5, what does each of the numbers in the equation represent now? This can be repeated with any total of counters up to about 20, regardless of the times table a product appears in (so no need to start with 2, 5 or 10 times tables) – any more counters than that and you’ll spend longer organising counters than talking about the maths!
If you have pupils who are struggling to learn their tables, try this exercise with them. You’ll be surprised how difficult children can find it.
Teaching for recall
Teaching for recall is very different to teaching for understanding, so a completely different approach is needed. Sometimes, we talk about owls and parrots: by developing conceptual understanding, we are teaching pupils to become owls, wise and able to think about what they are doing. Parrots, however, repeat what they have been taught. Once conceptual understanding is in place, we need to teach our pupils to be parrots so that they can effortlessly and accurately recall the facts they need.
Decide how to say the facts
The first thing we need to know is that multiplication facts are processed in the same part of our brains as sound patterns and song lyrics. How many times have you heard a song you haven’t heard since you were a teenager, yet you find yourself singing along, word perfect? No effort is needed, and that’s where we want our pupils to be with their recall of multiplication facts. To achieve this, the most important thing is to agree on a consistent way of saying multiplication facts, used by all adults in the school and at home.
Do you say ‘seven times five equals thirty-five’, or ‘seven multiplied by five makes thirty-five’, or ‘seven lots of five is thirty-five’? The possibilities are almost endless. Personally, I favour the shorter the better: ‘seven fives are thirty-five’, as it has a good rhythm, and we’re minimising the amount we’re asking children to remember. But what is crucial is that you have consistency, so that pupils build secure auditory soundbites – decide as a school what it’s going to be. Make sure everyone knows it and sticks to it.
Know who is teaching and learning which facts – and when
Do you have a whole-school overview of when facts are learnt and practised? If you don’t, you run the risk of running out of time in the run up to the MTC, with too many pupils trying to commit too many facts to memory, just for the purposes of the test. Sadly, these hastily learnt facts are often not transferred to long-term memory, and so are quickly forgotten, which leads to ongoing difficulties in year 5 and beyond.
If it’s clear that in autumn term 1, for example, year 4 are learning their 6 times table, then everyone knows that’s the priority and can focus on making sure no child is left behind. The whole class can work together to secure their recall of the 6 times table facts (and related division facts of course). Those who are ready can spot patterns, connections and links – if I know 5 x 6, what else do I know? Games of strategy can be played, which strengthen fact recall.
Which facts do the class find it hardest to recall? Isolate individual tricky facts and make them a daily focus so that all pupils can internalise the sound pattern by repeating them at every opportunity. Are some pupils struggling to recall their 6 times table facts? If so, they can be supported to use strong visual images or concrete resources to secure their conceptual understanding of what the facts represent – if that is missing, recall will always be a problem.
Teach, don’t test
So often, ‘learn your tables’ is set as homework, with an expectation that practice will be done at home and then checked in a weekly tables test. Not only do tests not teach children their tables (if you don’t know them, you aren’t going to be able to find the right answers under the pressure of a test situation), but this approach disadvantages those pupils who do not have support at home. Make it your priority in school to teach the facts, starting with skip counting.
If you’ve never used a counting stick to skip count in different multiples, this video from the Association of Teachers of Mathematics shows you exactly how to do it. If you would rather use a virtual counting stick on your interactive whiteboard, the PowerPoints from FunKey Maths that can be downloaded free of charge from the times tables section are great. Instead of having to hold the stick and take cards on and off, it’s all on the screen so you can point to the products you are focusing on. This is particularly useful when drawing attention to patterns or related facts (for example, helping children towards the generalisation that if I double one of the factors, the product also doubles).
Always say the full fact
Working with a counting stick over several days and questioning children repeatedly about the facts will start to embed recall. When you ask the class a question, be especially careful to ensure that they reply with both the question and the answer. If you ask ‘three fours?’ (whilst pointing to the space on the counting stick), they need to reply that ‘three fours are twelve’. That way, the question and answer are being linked in their minds – if they just reply ‘twelve’, they won’t be building the secure auditory soundbite that will help them to find the right fact when they need it.
My next step would be to give the class a two-minute retrieval quiz on the times table they are learning. Mix multiplication and division, and vary the part of the equation you leave blank for pupils to complete. Make sure the relevant times table is on display in the classroom or on pupils’ desks – if they don’t know the fact, then they aren’t going to learn it by doing a quiz, but being able to read it will support their developing recall.
Marking the quiz together means pupils quickly get feedback on how well they are doing. Repeating this two-minute quiz (ideally daily) will enable pupils to see their progress. Focus on how many more questions they can answer each time. Making progress is motivating – pupils will want to try and beat their previous score. If you have access to an online programme to help children learn their tables, this could be used instead of pencil and paper, but again, focus on progress rather than attainment.
Identify the tricky facts
Some facts will always be harder to learn than others – 12 times anything is often a stumbling block. Which questions on the retrieval quiz are causing the greatest difficulty? Online systems provide data on this (for example, the heat maps in TT Rockstars), so if you have access, make sure that you are using this valuable information.
Take each tricky fact in turn – what hooks or visual images can be used to strengthen recall? For example, if 7 x 9 = 63 is the problem, you could use the distributive law to link this fact to 10 x 7 subtract 1 x 7. What about looking again at the counting stick and seeing where this fact sits in relation to known facts? What visual image could you create for the fact? Chant the fact at every opportunity during the day. Draw attention to how many times and in how many different ways one fact can be found on a retrieval quiz so that pupils realise how easily they can increase their score by learning that one tricky fact.
Can you create a rhyme for a fact? For example: I ate and I ate and was sick on the floor – 8 x 8 = 64.
Look at the patterns in a times table and support children to generalise that even times even equals even, even times odd equals even, but odd times odd equals odd. Why is this? Knowing this will help children to avoid near misses with recall, e.g. nine times seven equals 64 – it’s plausible, sounds right, and is in the right ballpark, but can’t ever be right, which is a trigger to double-check the answer.
What happens to the product if you halve one of the factors? What happens if you double both factors? Why is this? Exploring the multiplication patterns will encourage those who can already recall facts to think more deeply.
Year 4 multiplication tables check (MTC)
It’s not possible to write about learning times tables without mentioning the MTC. Love it or loathe it, it’s part of life in year 4 in English schools. Following a structured programme will enable you to quickly pick up on children who are falling behind so that you can fill in gaps, using the strategies outlined in this blog (whilst small), rather than children needing to learn all facts in a few weeks or months. The National College offers a range of webinars to help with key stage 1 and 2 maths, including resources to help you to prepare for the MTC and improve times table fluency.
My three top tips when preparing for the MTC are as follows:
Tip one – be strategic. Know which facts are most likely to come up and focus on them. Page ten of the DfE assessment framework shows that 6, 7, 8, 9 and 12 times table questions are far more likely to come up than 2, 3, 4, 5, 10 and 11.
Tip two – make sure that children understand why knowing their facts will make maths easier for them in the future. They aren’t just learning their tables for the end of year 4 test. They are learning them because tables are at the root of a huge proportion of future mathematical learning. For example, in the 2023 key stage 2 SATs papers, 77.5% of marks on paper 1, 63% of marks on paper 2, and 57% of marks on paper 3 required multiplicative reasoning. Learning and using times tables don’t stop at the end of year 4.
Tip three – ensure pupils have a sense of achievement. Focus on how much they have learnt and how much progress they have made, not how much they’ve got left to learn.
Show them a grid like this one from the 2020 DfE primary maths guidance that draws attention to the 36 most important facts to learn.
Encourage children to colour in the facts they already know to show them how few they’ve got left to learn.
Look at the patterns in a multiplication square. Identify the line of reflective symmetry made by square numbers and look at the patterns on either side of the line – this highlights the power of knowing the commutative law and using this to reduce the number of facts to be learnt.
Periodically, give children a blank multiplication square and encourage them to work both horizontally and vertically to fill in the facts they recall easily. Over time, they will see the number of unknown facts reducing.
Finally, make it fun!
Gimmicks don’t teach children their tables – a coherent, structured and progressive programme of learning like the one outlined here does. But once the process of securing facts for a times table in long-term memory is underway, you can start to have fun.
One of my favourites is the Maze Game from FunKey Maths. Another great game is Multiplication Wars. Pupils work in pairs with a pack of playing cards (picture cards removed) dealt evenly between them. Both pupils turn their top card over at the same time and the first to shout the (correct) product gets both cards. Who will be the first to have all the cards?
If you have some budget available, there are the times tables cards available to buy from FunKey Maths. They not only provide strong visual images, which support many pupils, but also come with instructions for a range of games which you can play to help children learn their tables, without realising that’s what they’re doing.
Different approaches to learning times tables will work for different pupils – some will have a stronger auditory memory, whilst others might have a stronger visual memory. Some pupils will quickly understand what multiplication facts represent, whilst others will need to keep returning to groups of counters to secure this understanding. Following the strategies suggested in this blog will give all pupils the best possible chance of retaining and recalling these important facts.
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