Thanks to our maths advisor Caroline Clissold for this jam-packed article all about the new multiplication check and how to help children develop number fluency and fast recall from Reception through to Year 6.
The new multiplication check
In January of this year the government announced that all children will be tested on their multiplication tables in Year 6. They will be expected to know all facts up to 12 x 12 and will be tested using an on-screen check. These checks will be piloted to about 3,000 children this summer before being rolled out across all schools in England next year.
Many children struggle to be as fluent as they should be in their recall of multiplication facts and the corresponding division facts. It is crucial that they have a good grasp of these because it will affect their ability to problem solve. If children are working on a problem and need a multiplication fact which they don’t know, they have to move away from the problem to work out the fact. This often causes them to lose track of where they are in the problem.
In my work with teachers, a common complaint is that the children ‘don’t know their tables!’ According to the National Curriculum they should know them all by the end of Year 4. This is nothing new. The National Numeracy Strategy expected that children should know all multiplication and corresponding division facts to 10 x 10 by the same age.
At the moment Year 6 teachers tend to have to do a lot of ‘catch up’ work because a lot of children have not gained a deep understanding of what they have been taught in previous years. Hopefully, with mastery now being high profile in education, things will improve. In the meantime, how can we help children gain fluency in the multiplication and division facts that they need to know?
I have been thinking a great deal about this and have shared my thoughts with some of the teachers I work with, both in schools and on courses. They seem to think they make sense and are beginning to try them out, so I will share them with you!
Establishing fluency from an early age
In Reception children count in ones and then tens. Towards the end of Reception they could begin to learn their multiplication facts for one and ten using their fingers to help them, for example, showing their fingers one at a time and saying one multiplied by one equals one, two multiplied by one equals two and so on. This would be helpful in setting the pattern of future multiplication tables. Obviously the children would need to understand the concept of multiplication as adding groups of a particular number, which is something that would help them develop an understanding of what is happening when we count in steps of different sizes. The one times table is not commonly taught in our schools. It is in higher performing jurisdictions, such as Shanghai. I was a little nervous at suggesting this to Reception teachers, as I am not an Early Years expert, but those I worked with said that it made sense to give it a try.
Moving up to Year 1
In Year 1, they could continue learning their multiplication facts for one and ten and then begin their fives and twos. They will have counted in steps of these sizes, so again by using their fingers to help them they can begin to learn the facts. The national curriculum expects children to solve one-step problems involving multiplication and division, by calculating the answer using manipulatives, pictorial representations and arrays. Why not focus on multiplying by the facts they are learning? In that way they can immerse themselves in these facts and remembering them will become easier. So if they are learning their facts for two, use manipulatives, visual representations and arrays to multiply everything by two until they are fluent in recalling the facts. You could also include displaying pictograms where each symbol represents two and explore these with the children. You could begin with two when the children are working on half in fractions. It is really helpful to know these facts when they are finding half of different numbers.
If we make connections between the different areas of maths, like multiplication, division, fractions and pictograms, the children will spend more time focussing on the facts they need to know. When they know their facts for two, move onto facts for five in the same way. You may even consider fours when they work on quarters. Fours are simply doubling twos.
One key concept in multiplication which can help children with their multiplication facts is commutativity. If they understand this, they will understand that when they know one fact they automatically know a second one. Year 1 children need to be introduced to commutativity as soon as they solve problems involving multiplication. Arrays are ideal for this. They help the children develop a deep understanding of this fairly quickly. When exploring arrays I always ask the children to say the commutative statements together, for example, ‘six multiplied by five equals 30 and five multiplied by six equals 30 because multiplication is commutative’. They can do this well!
Recalling facts in Year 2
In Year 2, they should continue to rehearse recalling facts for multiplication by 1, 2, 5, 10 and 4 if appropriate. Regular short sharp bursts of this will help. Children need to work on thirds in fractions, so it would be helpful to learn the facts for multiplication by three and focus on the sharing model of division. Again, multiply everything by three and display pictograms where symbols represent three. I would have a week or two dedicated to thirds and sharing and also multiplication and division by three so that these concepts link together. Of course, you will need to emphasise commutativity again.
This principle could continue throughout Years 3 and 4. Very often textbooks and worksheets ask the children to complete random sets of calculations. They will have numbers that are multiplied by 6, then 4, then 7 and so on. If we just focus on one multiplier, the children will stand a better chance of embedding the facts for that multiplier into their memories.
Mastery at Key Stage 2
In Year 3, if the children have been taught using a mastery approach, they should have mastered halves, thirds and quarters by now and be ready to move onto other fractions. It makes sense to look at sixths (half of thirds), eighths (half of quarters) and possibly twelfths (half of sixths). Initially focus on one fraction, say, sixths and learn the multiplication facts for six which are just double those for three. They will need to spend some time multiplying and dividing all numbers by six, looking at pictograms with symbols representing six and bar graphs with divisions increasing in sixes and also reinforcing commutativity. You could do the same thing for the facts when multiplying by eight, which are double those of four and maybe towards the end of the year, when they are fluent with multiplying by six you could begin multiplying by 12. The children will still need to rehearse and consolidate the other facts that they have learned previously. This could be done at the beginning of the mathematics lesson when the children are ‘warming up.’
By Year 4, the only multiplication facts that they won’t have focussed on are those for seven, nine and eleven. To help them learn these, focus on sevenths, ninths and elevenths when dealing with fractions and multiplying and dividing numbers by these three.
By Year 5 – Bingo, they will know the multiplication and division facts to 12 x 12! They need a time of rehearsal and consolidation of all facts and the opportunity to find the appropriate fractions. They can then work on answering sets of calculations which ask them to multiply and divide by a variety of multipliers.
Why not consider this approach in your school and see if it makes a difference?
Multiplication clocks – time to practise!
With this activity, I start with pointing at all the hour numbers in turn, the children tell me what the product is when multiplied with whatever multiplier we are working on, in this case eight. I then randomly point at numbers, frequently revisiting those that they don’t instantly recall. I then focus on division facts. The pattern is important, some children will need that to help them absorb the division facts into their memories.
I also use a pendulum (three interlocking cubes on a piece of string). I swing the pendulum and the class count in steps of, for example, three from zero to 36 and back to zero. We repeat this for sixes from zero to 72 and back to zero. I then split the class in half. As the pendulum swings to the right, the half on that side count in threes. As it swings to the left the half on that side count in sixes. Then everyone counts in threes as the pendulum swings to the right and in sixes when it swings to the left. The concentration on their faces is brilliant! After some practice they can do this. After all it is simply thinking about the three facts and doubling for the six facts. I would usually start with fives and tens and then twos and fours!
Get in touch!
Let us know of any effective and enjoyable ideas that you have for teaching, rehearsing and reinforcing multiplication facts and corresponding division facts. Tweet @risingstarsedu with your suggestions and we will include the best ones in our next maths newsletter!
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