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How do you get students to use times tables fluently?

February 23, 2018

 

Quick answer: help them to see the patterns within, and connections between, different sets of multiples.

 

A quick search on Google for times tables will present a page of sites offering times tables games, and great fun can be had playing these while consolidating the multiplication facts at the same time.

 

However, some pupils won't enjoy these games so much because they have not assimilated the facts. Some will need to add seven six times when working out 7 x 6. Others need to start from 1 x 6 and recite this, followed by 2 x 6, 3 x 6, 4 x 6, 5 x 6 and 6 x 6 until they reach the point in the multiple table that they need.  

 

The hundred grid is a great place to start when looking at multiple patterns. Some pupils, even when proficient at reciting multiplication facts, have never explored the links between the multiples of three, six and nine. A number line is also effective at showing the links for example, when jumping between twos then fours, then eights on the same line.

 

Some recent articles, when discussing the forthcoming statutory times tables test in England, have referred to the 144 facts that pupils need to learn. A quick perusal of the image above shows that there are actually far fewer facts to learn since the multiplication grid displays the symmetry due to the commutative rule which states, for example, that 3 x 4 equals 4 x 3. If a pupil is not sure about the multiples of 7 and therefore stumbles at 5 x 7, they can just use 7 x 5 to give them the answer. Everything above the red line is reflected below the line. Pupils can play games with half grids so that they get used to swapping the numbers for the same result.

 

The multiplication grid is also useful for connecting the multiplication and division facts since the dividend can be found within the grid as the bottom right entry in an array, such as 56, which has 7 rows and 8 columns or 8 rows and 7 columns. So 56 divided by 7, or 56 split into 7 rows results in 8 in each row.

 

Getting pupils to construct their own multiplication grid is useful for spotting patterns. First the rows containing the multiples of 1, 2, 5 and 10 are easily filled. They then double the multiples of 2 to get the multiples of 4 and then double again to get the multiples of 8. After this, they return to complete the multiples of 3, and double this for multiples of 6. Multiples of 9 have their own pattern when written down consecutively which leaves the multiples of 7. Pupils could use the relationship with the multiples of 6 as in the following examples : 7 x 5 = 6 x 5 + 1 x 5 and 7 x 4 = 6 x 4 + 1 x 4. This can be shown visually using arrays.

 

The array is a powerful visual tool for multiplication since pupils can see how a number is built up. Most pupils are familiar with multiples of 1, 2, 5 and 10 so if a pupil is working out 6 x 8 and they have had plenty of practice with arrays, they can see this as 5 rows of 8 (or 8 x 5) plus another row of 8. Similarly, when working out multiples of 9 such as 9 x 7, they can work out 10 rows of 7 and reduce this by one row of 7.    

 

Once pupils have spent time exploring multiple patterns and connections, they can be challenged in groups, perhaps against a timer to see how many ways they can solve a calculation such as 7 x 8. This activity allows those who struggle to assimilate the facts to see that there are lots of ways in which facts can be worked out from other known facts.

 

So don't ditch the consolidation activities such as games and songs but use them as regular reinforcement once pupils are more confident that they can work out facts when needed.

 

 

For an engaging, interactive resource that covers all of the ideas above and includes games and visual images, click this link.

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