Times tables matter - working towards multiplication mastery

Times tables matter

Times tables matter and multiplication facts are non-negotiable basic building blocks that will serve you well, but only if they are learned well in the first place.  Times tables should be ‘BFF’ lifesavers but for many people they are like a Moriarty-standard nemesis.   

Every education minister hates times tables… mostly because they aren’t good at recalling them. They tend to be easy prey for TV and radio presenters who are always keen to fire a multiplication at them during an interview. That multiplication salvo tends to be a “What’s 7x8?” or a “8x9?” and flustered, stuttering and sweaty-browed politicians normally upend themselves by giving an incorrect answer.   

(Politician Tip: remember the sequence 5678 for 7x8 = 56)

Schools have always put tremendous effort and resources into getting children to have instant recall of their times table facts and rightly so. Being fluent in calculation and knowing times tables by heart are a maths essential and an ‘educational entitlement’. 

Knowing the times tables (and their associated division facts) supports mathematical learning and understanding and those children who have a strong grasp of them tend to be more self-assured when learning new concepts. In an ideal world, every pupil will start secondary school with a fluent, accessible and automatic knowledge of their tables.

But how well do children really know them?

A few years ago, Caddington Village School in Bedford used an app to generate data on which times tables their children found the hardest to do.

A total of 60,000 questions across 232 children in years 5-8 were analysed and results revealed that the hardest was 6 x 8 (pupils got wrong 63% of the time), followed closely followed by 8x6, 11x12, 12x8 and 8x12. 

Other research has found that the top ten most difficult facts for 9-10 year olds to learn are 6x9, 7x8, 7x6, 8x6, 4x8, 4x9, 7x9, 7x7, 6x7, 4x7. Clearly multiplication facts are not equally difficult to learn and the predominance of the numbers 6,7,8 and 9 indicate that’s where we should channel our energies.  

Multiplication ‘on-demand’ is not easy and for many of us, expecting to have an instant and accurate answer can be stressful. Not knowing your times tables doesn’t mean you aren’t ‘good at maths’ but it can pummel self-confidence and lead to maths anxiety.  

The Facts

Based on research evidence, there is no established order for teaching the tables although the National Curriculum states that children should learn, with recall, the multiplication facts for the 2s, 5s and 10s in Year 2, then the 3s, 4s and 8s in Year 3 and finally know all facts to 12×12 (and corresponding division facts) by the end of Year 4. This is a big ask. 

It is commonly agreed that the process of learning tables should begin with children building up a table using concrete apparatus, moving on to a pictorial representation, then symbolising the two types of table (e.g. 1x2 = 2, 2x1 = 2) and then practising the tables both in written and oral forms.  

Tip: focus on the easy facts (x0, x1, x2, x5, x10) and build on these

One suggested order for learning multiplication tables is 2,0,1,10,5,4,8,9,3,6,7. Starting with the easy facts for 1,2,10 and 5 emphasises how useful doubling and halving can be.  
 
Multiplication facts are just facts which are stored in the memory and if they are not used regularly then they are less conspicuous. Practising times tables is therefore paramount but with so many facts to learn where do we start?

A table square for the 0x to 10x facts has 121 facts for multiplication (and 121 for division). A blank times table square can look formidable but if the simple facts for 0, 1, 2, 5 and 10 are completed then there are only 36 facts left and 6 of these are easy too as they are the squares 32, 42, 62, 72, 82, 92. The remaining 30 facts we can get down to 15 facts due to the commutative property of ab = ba. Of course, children need to know their 11s and 12s too. The 11’s are easy enough and for 12s, children can easily learn 10× plus 2×, such as 12×4 = 40+8 = 48.

Multiplication facts are much more valuable when known separately, rather than only as part of a list. It is important to arm children with the self-reliance and the mental strategies to figure out 8x7 from a closely related key fact, such as 7x7 or 4 x 7, or 8x5. These strategies need to be taught, discussed, compared and practised. Rather than see these as ‘tricks’, regard these strategies as essential written and mental calculating strategies. 

For example, doubling and halving are key skills. The 2x, 4x and 8x tables can be generated by repeated doubling. The 10x table is easy to memorise and gives the 5x table by halving. The 6x table is double the 3x table. The 9x table can be related to the 10s by subtracting from 10, such as 7x9 = 7x10 – 7. Strategies using fingers and the sum of the digits of multiples of 9 will also help in learning the multiples of 9. This leaves the 7x table but most of the multiples of 7 will have already been encountered in the other tables.      

The good news then is that you don’t have to know all the multiplications facts to know your times tables but doing them daily definitely helps. 

Multiplication Mastery  

Although learning tables by rote is by far the best method for speed and efficiency, accurately reciting the times tables doesn’t mean children ‘know’ them. Children who claim to know all their tables only have a superficial understanding of them. 

It is therefore crucial that children go deeper and understand what the numbers mean and how to apply their knowledge in a maths problem. Planned experiences and activities for learning about multiplication must be sequenced and ordered in order to support progression and real understanding. 

Many teachers use the CPA approach (Concrete-Pictorial-Abstract) approach to underpin knowledge, understanding and skills. This basically involves giving children a better chance of creating a long term memory, based on manipulation of physical resources and constructing images before or alongside the abstract e.g. the facts written as numbers;  7 x 8 = 56.

Multiplications have to have a real-life purpose so look for opportunities to use them when problem-solving when shopping or using recipes.

For many maths experiences to be effective children need to be able to work with and manipulate practical materials. Such apparatus represents a concrete model of the mathematical concept. For multiplication mastery, children should encounter the same concepts in many different contexts to help them identify and describe common patterns and relationships. 

Apparatus for developing mastery of the concept of multiplication could include:  

• A variety of real objects to sort and count, e.g. counters, beans, shells
• Interlocking cubes, e.g. multilink
• Cuisenaire rods
• Base-10 equipment, e.g. Dienes
• Number lines and grids (marked and unmarked)
• Washing lines and 0-100 number cards with pegs
• Money 
• Pegboards and pegs
• Pictures
• Arrays
• Multiplication number grids (for number sequences and pattern spotting)

‘See’ the maths

To develop number sense and times table proficiency, children to be able to ‘see’ the maths in different representations and have the language to describe their own thinking. Mental image activities which encourage this include children closing their eyes and mentally moving groups of objects or small arrays of dots. Number lines and grids can be imagined and movements and patterns on them described. Precision in the use of language is important if we are to reach shared understandings so we need to make sure that children know the right vocabulary to use when talking about multiplication. For example, 4 x 6 = 24. The 4 and 6 are factors of 24 and 24 is a multiple of 4 and 6.  

Combined with the hands-on resources above there are many other exciting ways to help children make connections when learning their times tables such as:

• listening and singing to times tables songs 
• playing games like Fizz Buzz, Tables Bingo etc.
• playing multiplication and division ‘Snap’ type games
• using flash cards with missing numbers 
• playing with loop cards 
• using dice games
• using playing cards, dominoes and darts
• using graphing tables  
• interacting with Venn and Carroll diagrams
• making Spidergrams 
• using ‘Jym’ cards (jog your memory cards)
• designing fun mnemonics, e.g. use phrases which sound like numbers (sticky floor = 64, plenty more = 24 etc) 
• promoting ‘Personal Best’ multiplication timed races 

When exploring multiplication and division facts, teaching should include a balanced range of experiences that ensure children consolidate and extend their learning. Where possible they should be integrated into every lesson too.

According to Nick Tiley-Nunn in his book, ‘How To Teach Primary Maths’, when we are teaching times tables then it’s a good idea to SMASH them to pieces. By this he means:

Short and sweet – spend approximately 5 minutes on a times table related activity every day.

Mix it up – ensure that children can recall their multiplication facts forwards, backwards and jumbled up so they can work out related division calculations. 

Arrangement – represent numbers in as many ways as possible (e.g. arrays, patterns etc)

Stir and stimulate – encourage variety, movement and competition through times tables circuit training (make several stations where pupils use times tables to solve questions each station requiring physical activity)

Hammer away – consistent practise and plenty of repetition to develop resilience and perseverance.    
  
It’s worth remembering, times tables is a ‘long game’ and children need to go through several learning stages over many years before they can understand them. 

Learning the multiplication facts are essential as they make a very large contribution to numeracy and underpin our maths system like counting, number bonds and place value. If children can get a firm grasp of their times tables then they have a solid arithmetical foundation for future problem-solving. 

And finally….

The real secret to learning times tables and getting them to ‘stick’ comes through hard work but work filled with special ingredients: jokes, giggles, movement, puzzles, music games, team work and novelty. If we can fill times tables with fun, curiosity, surprises and memories then we are giving children every chance of growing maths muscles who can answer 7x8 without dissolving into tears.  

For lots of engaging times tables practice, see Rising Stars Skills Builders books – try a free sample now!       

References:
Tiley-Nunn, N. (2014) How To Teach: Primary Maths. Glasgow: Independent Thinking Press.