Creative Ways of Teaching Times Tables

WHITEPAPER BY EDUCATIONCITY

This paper looks to explore the many ways times tables are taught and embedded within schools in order to share practical experiences, which can be applied in any classroom. Within it are many tried and tested formulae, but hopefully some new ideas too!

We all know that times tables are one of the basic mathematical skills children need to progress further in mathematics. It’s this assertion that underlies the new times tables tests to be introduced in England for all Year 6 students as of 2018, which has made times tables teaching a hot topic recently.

It’s universally agreed that practice is key to mastering times tables but how can schools embed these basics whilst keeping the content fresh and the students interested? Is learning by rote the be-all and end-all or can other strategies be more effective for certain types of learners? Read on to find out what we saw from schools around the UK.

Introduction

Table of Contentsii Introduction

1 Counting and the Basics

2 Tips for Learning at Key Stage 1

3 Tips for Learning at Key Stage 2

4 Rote Learning

5 Testing and Assessing Development

6 Homework and Parental Involvement

7 Extra Support

8 EducationCity Tools

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Counting and the Basics

Counting in single digits is one of the first steps towards learning how to multiply.

This is sometimes learnt at home through play, but is generally one of the early areas of focus at Reception/Foundation level. Once mastered, students can look to short cut the process by counting in chunks, which is essentially what multiplication is. Simple counting in steps of 2, 5 and 10 should be conquered by Year 2 and this knowledge built on in successive years as indicated below:

By the end of Year 4, most children should be able to recall any times table instantly, as times tables learnt from Year 2 onwards have been practised continually and so ingrained into the children’s long-term memory. This is usually achieved by giving the children a good understanding of the mechanics of multiplication, then consolidating this understanding and facilitating recall using learning by rote strategies. We look at these strategies later in this paper.

Year 2 2, 5 and 10 times tables

Year 3 3, 4 and 8 times tables

Year 4 6, 7, 9, 11 and 12 times tables

Years 5 and 6 Practice years

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At Key Stage 1, as ever, the focus should be on practical and visual techniques to help the students grasp the basics of multiplication. It's something that doesn’t need to be restricted to the classroom environment either.

• Looking at pairing shoes is often a good starter for children to learn about the 2 times table, and is great as shoes are something every classroom has in abundance!

• Getting into groups of 2s, 3s and 4s to play games in P.E, for example, is a great way to develop the children’s understanding, before moving on to number grids where the children can see the patterns that exist for each times table.

Games are great learning devices at this stage too. Patrick Mainprize, former teacher and Education Lead at EducationCity, used to promote the use of a rabbit hill in his EYFS classrooms. The hill, with numbered burrows, would be

presented as a wall display in his classroom, and students would be asked to pop cards into the burrows which, when multiplied, would make that number. That’s to say, cards 2 and 3 would be inserted into burrow 6, as could 1 and 6.

Tailoring board games to multiplication is also effective. By multiplying the dice values instead of adding them together, children get to practise their times tables, with the added bonus being that the traditional game is speeded up significantly.

Pelmanism, a memory training system devised by the Pelman Institute for the scientific development of mind, memory and personality in London, can also be introduced. It sounds complicated but one game, which adopts Pelmanism, which we’re all familiar with, is laying cards face down and matching pairs from memory.

Tips for Learning at Key Stage 1

Year 2 2, 5 and 10 times tables

Year 3 3, 4 and 8 times tables

Year 4 6, 7, 9, 11 and 12 times tables

Years 5 and 6 Practice years

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Tips for Learning at Key Stage 2

Key learning points to impart in Key Stage 2 are as follows:

• Seeing a times table as repeated addition is useful. For example, 4 x 5 is the same as 5 + 5 + 5 + 5.

• Understanding that times tables are commutative, so that both 5 x 4 and 4 x 5 = 20, is vital to speedy recall as it reduces the ‘amount’ of learning to one third of its original. Simply by understanding this, 169 key facts are reduced to 91.

• Multiplication should be recognised as the inverse of division. The number sentence or calculation 20 ÷ 5 = 4 can be worked out because 5 x 4 = 20.

• Different times tables have different patterns within them, which make learning them much easier. See our table below for some handy explanations:

Times Table Hints

2 x Table Answer is always double the given number

3 x Table Answer always adds up to 3, 6 or 9

4 x Table Answer is double, then double again

5 x Table Answer always ends in 0 or 5

9 x Table Answers always adds up to 9*

10 x Table Answer always is sequence number with 0 on the end

11 x Table Answer is always repeat digits**

* Rule doesn't apply to 11 x 9 **Rule doesn't apply to 11 x 11

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Over and above this, one of the teachers we spoke to, Simrat Mavi, Deputy Head Teacher of St Giles C of E Primary School, advises children should try to “remember near facts. For example, if you remember 8 x 5 = 40, you can work out 8 x 6 = 48 more easily.”

Immersion is also very effective, so it’s an idea to include times tables visually everywhere possible in the children’s daily

environment. Think about creating hallway and classroom displays or murals showcasing multiplication sequences and patterns. This repeated exposure will help to embed times tables into their long-term memory.

Pictorial arrays are visual representations of multiplications, which the viewer can ‘pull apart’ with their eyes, or put together the individual items. Take the example below:

0 1 2 3 4 5 6 7 8 9 10 11 12

1 0 1 2 3 4 5 6 7 8 9 10 11 12

2 0 2 4 6 8 10 12 14 16 18 20 22 24

3 0 3 6 9 12 15 18 21 24 27 30 33 36

4 0 4 8 12 16 20 24 28 32 36 40 44 48

5 0 5 10 15 20 25 30 35 40 45 50 55 60

6 0 6 12 18 24 30 36 42 48 54 60 66 72

7 0 7 14 21 28 35 42 49 56 63 70 77 84

8 0 8 16 24 32 40 48 56 64 72 80 88 96

9 0 9 18 27 36 45 53 63 72 81 90 99 108

10 0 10 20 30 40 50 60 70 80 90 100 110 120

11 0 11 22 33 44 55 66 77 88 99 110 121 132

12 0 12 24 36 48 60 72 84 96 108 120 132 144

White: 90 unique calculations

Pink: Duplicate calculations

Total: 169 calculations

Visual learning often plays a big part in the education of a

SEN student which is where EducationCity

comes in...

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Representations like this are great for students who respond to more creative learning strategies. Lauren Casey is a SEN teacher at Barking Abbey School. “Visual learning often plays a big part in the education of a SEN student which is where EducationCity comes in,” she said. “The times table songs, as well as the games, really support this style of learning.” You can access EducationCity’s wealth of mathematics and numeracy teaching resources through their website, www.EducationCity.com.

Lauren elaborates about teaching methods: “Even though, initially, I thought rote learning would stick best, and even bought a times table CD to play as background music in my lesson whilst we worked on other maths problems, it didn’t. The process within EducationCity’s PlayLive game was essentially the same in terms of the questions, the people you play are different and this was the method that worked.” PlayLive is a competitive mental maths challenge, which pits students from the same year group in a race to answer as many multiplication questions as they can in 60 seconds. You can access PlayLive by logging in to EducationCity, clicking on Maths, choosing your academic year, then PlayLive from the content types, then PlayLive Multiplication.

The visual method of teaching can be developed to include concrete manipulatives as well, meaning that the visual aids are not just pictures on paper, but physical representations of the problems presented. The children can then get their hands in, multiplying and dividing the items. Stimuli such

as counters and multilink cubes work well in school. At home, items such as sweets or toys can be used. “We use blocks and coins to start with to show the concrete nature of the tables and their practical use,” Sarah Cook, teacher at Greyfriars Primary School said, highlighting that this method of teaching works for her. “My lower ability children will go over and over the physical work as many times as they need to. They will do a lot of practical work like putting Play-Doh spots on a ladybird, eggs in nests, and so on”.

We asked our primary school teachers, "What are the main times table teaching strategies you use?"

“We use number families and recall activities such as triangle cards, matching games and Pelmanism. The children are regularly tested on both the technical and the application of times tables.” – Sarah Cook

Deputy Head, Amy Bain said “Games, loop cards, songs, weekly homework of a number family and rapid recall. I try to make it fun and encouraging to improve how fast they can remember.”

Tom Phillips recommended weekly times tables lessons, that are not just confined to the classroom. He’s had success with throwing and catching activities where the children simultaneously chant multiples as well as with balloons bearing multiples on, where the children had to sort them by the times tables they appear in.

Games, loop cards, songs, weekly homework of a number family and rapid recall. I try to make it fun and encouraging to improve how fast they can remember.

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Rote learning refers to the process of learning something via repetition and practice, which leads to memorisation. Camilla Turner, Education Editor of The Telegraph, stated, “An educated person is someone who has knowledge in his or her long-term memory.”

This type of learning leads to instant recall of knowledge by the participant, which is best explained by children reciting and chanting their times tables in order to remember or ‘learn’ them. Eric Kandel won a Nobel Prize in the year 2000 for his work on the subject of memory, in which he proved that repeated stimulus enabled brain cells to grow and make new connections. It can still be tailored to your needs as with anything.

An additional advantage of PlayLive Multiplication is that it gives the child a summary of his/her performance at the end, so that they can understand where they went wrong – bonus! Music and song have long been a part of children’s culture and for years used as a learning aid in the home and at school. Devise ways in which times tables can be heard everywhere; play CDs in class or sing and recite in line to assembly. Straightforward chants can get boring and monotonous, so think about personalising the words and rhymes. Add actions, use instruments, whatever works for your class.

Rote Learning

An educated person is someone

who has knowledge in his or her long-

term memory.

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• On a 1-to-1 basis, read the times tables out loud together. When the child is comfortable proceeding alone, ask them to tap the table. If they are unsure or get an answer incorrect, join in again. Repeat several times, on a regular basis.

• Try reciting the times tables out of order, by pointing to numbers in the sequence on the board.

• Work backwards so your students look to identify the question that could be being asked from the answer. For example, if the answer is 36, what could the question have been? 6 x 6, 4 x 9, 18 x 2? Pre-write the answer on the whiteboard and play Splat!, so that when a student finds the question to the answer, the number gets ‘splatted’ off the board!

• Turn your students into teachers and have them work together to remember their times tables. It’s important to note, we remember 90% of what we teach others, so by children building their own lesson plans, creating songs, presentations and posters they are reiterating multiplications to themselves as well as helping to teach others their times tables.

Rote learning is a method favoured by many teachers and with good reason as it produces successful results on the majority of occasions. However, it is argued children are simply reacting with automaticity, which is voicing an automatic response out of habit.

Children are remembering information rather than learning the information. Many topics require a deeper understanding of how they work and why it all makes sense, which may be the key to training the mind to solve more complex maths problems. “Children are good at learning by rote, but need practical activities and constant application to truly understand what they are doing.” - Sarah Cook is a Teacher and Computing Coordinator at Greyfriars Primary School. When asked what she found most difficult about teaching times tables, Sarah said, “Moving from rote learning to application. My children can learn the song or the chant easily in the majority of cases and can recite them happily, but when asked ‘What’s 2 x 7?’ will look at me with confused faces!”

We asked primary school teachers, "What are your experiences of learning by rote for times tables?" And these were some of the responses:

“Learning by rote has its place, but it must be linked to mixing facts around and using the key facts quickly.” - Vicky Redshaw, Brooke Hill Academy

“I always think there is a balance between rote times tables and active learning. It goes back to different learning types but at some point, we just have to make them stick!” - Amy Bain, Deputy Head Teacher, St. Peter’s R.C. Primary

It is important here to note, as ever, that rote learning doesn’t work for every child. Simrat Mavi, Deputy Head Teacher, St Giles C of E Primary School says, “Some students struggle with mental retention over a period of time therefore need alternative strategies such as multiplication squares”.

Great Activity Ideas

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In 2016, it was announced by Education Secretary Nicky Morgan that all Year 6 students in England are to be tested on their times tables.

At the time, Schools Minister Nick Gibb said, “It is my view that there should be a multiplication check. It was in our manifesto in 2015 that there would be. We think times tables are a very important part of mathematical knowledge.” This makes it more important than ever to learn multiplication well before embarking on secondary education.

“For children in the 1950s, there was an expectation that they should know their times tables,” said Professor Alan Smithers, Director of the Centre for Education at Buckingham University. “This was cast aside in the 1960s - but then we found that we were well behind other countries as international comparisons grew in importance. Now we have gone back, we have come in a full circle really.”

Before the standardised tests (SATs) of KS2, regular testing should be introduced in school in order for the prospect to seem more ‘normal’ when they arrive in Year 6. A good idea is to start off with more informal testing methods, so that they appear less scary to younger

students. “When teaching times tables, I use weekly ‘speed’ testing.” Vicky Redshaw’s experience was true of the majority of the teachers we spoke to.

Great Activity Idea: Turn your weekly test into something the children look forward to. Pick a song (perhaps a genre of music you are looking to introduce them to) and get them to complete as many questions as possible before the track ends.

Great Activity Idea: Organise a shoot-out-style competition. The children form two lines so that the ones at the front can compete against one another and answer the teacher’s quick question. “What’s 5 x 2?” The quicker responder stays in the game, the slower stands down to be replaced by another student, and the numbers playing reduce until there’s a winner.

Top Tip: To further boost those children who are performing particularly well, award them with ‘Ask Me!’ badges. The other children should then be encouraged to ask these students quick-fire times tables so they can showcase their knowledge and enjoy their new-found kudos!

Testing & Assessing Development

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As with every aspect of learning, it’s important that it’s reinforced positively in the home where possible.

Parents and carers should be encouraged to get involved with different teaching strategies and by creating their own games. For parents with children in KS1, this may simply involve playing board games at home with their families or incorporating basic counting into their daily lives by counting paving stones or similar. For parents with children in Key Stage 2, it may include involving their children in more complex counting, such as working out change at the supermarket.

When it comes to those years when students are learning times tables at school, parents can continue to support their children by playing games with stacks of coins and packs of sweets. Packs of cards offer lots of opportunities for multiplication too. Firstly, take out the aces and

kings, and give jack a value of 11, the queen a value of 12. Draw out two cards and ask the child to multiply the numbers together.

Another great resource is EducationCity’s Home Access which allows children to access the fun and engaging activities they access at school at home to reinforce the work they are doing in the classroom. One of our subsequent sections focuses on these resources and how EducationCity can help in both the classroom and at home.

Homework & Parental Involvement

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Additional support should be given to those children who may find mathematics difficult. This could mean extra time being dedicated to the area, or working with students in smaller groups where a more targeted approach can be taken to reflect their needs.

We hear from a Special Educational Needs (SEN) teacher and how she uses different teaching methods with her students to produce the best results.

Lauren Casey is a SEN teacher and said, “Trying to teach SEN students the times tables are at times a minefield. Often, some students can grasp the ‘simple’ times tables that other students won’t; but, on occasion, some students grasp the more difficult times tables and cannot fathom the ‘simple’ ones. They struggled with the fact that the same pattern isn’t apparent for all the times times and kept asking me why this was the case.”

Deputy Head Amy Bain suggested that: “We always try a range of strategies to meet the different learner types as well as showing the children there are different ways to learn.”

Vicky Redshaw, another of the teachers we contacted, agreed that a multitude of strategies should be presented to the child: “I employ all the different strategies for each learner, so they can use different strategies for different times tables.” As she said, these may be used exclusively or in conjunction with other ways of learning.

Extra Support

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Teaching times tables can be a complex and sometimes daunting experience.

Practice is critical, as outlined before, and this is where EducationCity, the award-winning teaching, learning and assessment resource can come in helpful. Founded in 1999, the company has been dedicated to developing new ways of delivering curriculum content. Created by educationalists and loved by children worldwide, EducationCity is proven to engage children and improve their attainment.

You can find engaging, educational and curriculum-linked content on EducationCity, which aims to support students aged 3 to 12 years old and their teachers. The resource offers a multitude of activities to support the learning and assessment of times tables, which are structured to address national learning objectives. The resources are accessible anytime, anywhere and allow teachers to plan in advance, set students work and assess their progress. In addition to mathematics, it covers English, science, computing, French, Spanish and learning English as an additional language.

Times tables songs are a favourite of many already using EducationCity, including Mrs Redshaw from Brooke Hill Academy in Oakham, who’s been telling us all about how she uses them in her classroom. Mrs Redshaw said, “Always looking to make learning fun, I turn to EducationCity to help me. Covering the 2 – 12 times tables the multiplication songs make for fun and engaging class participation and work great as an introduction to the subject. Including friendly characters alongside great graphics and enjoyable songs – the children won’t realise they are learning.” Amy Bain is also a fan: “We LOVE the sing-along songs. The 12 times table song is my favourite - and the children know it!” Tom Phillips agrees. He said, “Children love the songs and we’ve made them available for homework and for the children to use at home.”

EducationCity also offers times tables challenges testing multiplication and division both separately and alone. Their Mental Maths Topic Tool is customisable and focuses on testing times tables. “I start my children with the songs, and then use a Topic Tool to demonstrate the activity,” said

EducationCity Tools

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Sarah Cook. Perhaps the most popular aspect of the EducationCity resources is the PlayLive Maths feature. Students race to answer as many questions as they can in 60 seconds. Sarah Cook continues, “The children use PlayLive to practise at home after completing homework activities that match the table we are focusing on. I like being able to set the same thing we have done at school so that they can have it reinforced at home.”

Lauren Casey works with SEN students and explains, “One day, I introduced them to PlayLive – something clicked and this became the greatest tool at my disposal. Students wanted to play this every Maths lessons, as well as at break time – there was even a PlayLive competition happening every lunchtime! After a few weeks (spending 5 to 10 minutes on PlayLive every Maths lesson) I gave the students a times tables test – the results were so much better than before”.

Friendly competition is a teaching strategy in itself, as some students really come into their own when pitched against others. Vicky Redshaw added, “PlayLive is popular when the children are able to battle against other learners around the world.” The interactivity is similar to that which children are familiar with in leisure time computer games.

We have previously marked the importance of testing and continually assessing a student’s progress with their times table learning. EducationCity’s SuccessTracker allows teachers to individually monitor children’s scores and keep a track of development whilst getting to grips with multiplication.

We LOVE the sing-along songs. The 12 times table song is my favourite - and

the children know it!

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Children need mathematics skills, this cannot be argued against. Grasping times tables leaves them prepared for National Curriculum testing in KS2 and stands them in good stead for further mathematical learning.

This knowledge is then transferable to real-life ‘grown up’ situations, where quick mental maths and multiplication knowledge proves itself invaluable. Making this obvious to children from the outset will emphasise the importance of learning multiplication facts now, which benefit them in later life.

Making links with other areas of mathematics and logic helps both teacher and child to break down the sheer amount of number facts into manageable chunks. Recognising that multiplications are commutative in value, as mentioned before can ‘cut down’ what is left to learn by two thirds. An overall view of times table learning seen in this way makes the whole task less daunting and more feasible.

Rote learning and regular practice are still fantastically effective in ingraining times tables into children’s minds, while visual and physical stimuli work well as illustrative aids to show children how multiplication works. Music and singing are traditionally

used to help students memorise multiplication facts.

Tabs must be kept of children’s learning to assess their development and help identify which strategies are working for individual children. This knowledge can be fed into teaching plans and shared with children’s parents and carers to tailor subsequent teaching to the child’s specific needs.

We hope by reading our Creative Ways to Teaching Times Tables paper, you’ve either found some new ideas to try or just been reassured that you’re already following best practice.

To conclude, not all mathematics and academic development is centred around learning times tables. However, children with a strong grasp of multiplication have the strongest foundations on which to develop their mathematical understanding. As always, a combination of strategies is required to embed learning, which in this case, seems to be both a mix of techniques for learning styles and learning by rote.

Conclusion

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About The AuthorEducationCity is an award-winning online teaching, learning and assessment resource, used in schools in over 75 countries around the world.

Founded in 1999, it has over 15 years’ experience of supporting teachers to teach times tables, and has developed a whole range of content to do this. This includes Learn Screens to introduce the mathematical concepts, Activities to reinforce knowledge, and Topic Tools to help students practise their skills. It has also developed a PlayLive Maths challenge dedicated to multiplication to encourage the speedy recall of multiplication facts, as well as problem-solving Activities where the students have to put their knowledge of times tables to practical use.

All these resources have been created by its in-house Education Team with the support and input of many teachers in the field. The team would like to take this opportunity to thank these teachers here, along with those that also helped create this document. Your feedback and practical insights are very much appreciated.

To see EducationCity’s resources for yourself, please go to: www.educationcity.com/free-trial for a no obligation, 21 day free trial for your school.

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