Q. In a previous column you mentioned that you had researched the learning of multiplication tables. What would you consider the most appropriate way to introduce multiplication tables?
A. I strongly advocate encouraging the recognition of patterns within multiplication tables and using mental methods for finding answers. Pupils will occasionally wish to add or subtract based on another table fact, but methods involving "counting on" do not encourage engaging in the fun of manipulating the numbers, which leads to a depth of understanding.
For some pupils, "counting on" has negative consequences, as they may miscount and build incorrect relationships between certain number facts.
Why should we sing our times tables when there is real beauty to be had in numeric relationships?
Before you begin teaching tables, make sure pupils understand addition and subtraction. I start with the 11 times table. I can hear the general chorus, "but it isn't in the curriculum". In my research I found that 80 per cent of primary teachers were teaching up to and including the 12 times table. I can only guess that the reason the strategy begins with the 2 times tables is because 2 is a small number to count on, thus encouraging a "counting on" strategy.
So how to introduce the 11 times table? I had a lively lesson with a very dyslexic seven-year-old last week. I began the session with an arrangement of 4 groups of 11 dots.
I circled one group and asked Jenny to count them. Then I told her there were 11 in each of the other groups. I asked her how many were there altogether. The look on her face said it all, dismay at having to count all those dots. Just as she began counting them, I asked her if she would like to learn a quicker way to find out how many dots were there altogether. She instantly smiled. She knew that I would have a "trick" up my sleeve.
I circled each of the groups so she could clearly see that there were 4 groups. I wrote this as an addition sum, 11 + 11 + 11 + 11. I told her there was a shortcut for "4 lots of 11" and that we had a special sign for this. I showed her the multiplication symbol "x". We talked about how this sign was different from the addition sign.
The next step was to help her recognise the pattern in the 11 times table.
We did this by counting on a number rope. I asked her to count 11 along the rope, circling the answer. Then I asked her to count along another 11 and she finished on 22. We circled this number.
I asked how many lots of 11 she had counted and showed her, with a single line, that there was 1, then 2 lots of 11. I wrote this as a multiplication beside the number rope, emphasising 1 lot of 11 is 11, and 2 x 11 = 22.
I asked if she could guess the number that we would finish on if we counted another 11. I wrote down her response: 28. Of course, we ended up on 33.
(In the past, I have found pupils have difficulty counting and moving, so I place my finger on the rope and move forward while they count.) Again, I went through 1 x 11 = 11, 2 lots of 11 is 22 and 3 x 11 = 33. However, this time I underlined the 1 and 11, the 2 and 22, and the 3 and 33.
The next time, when I asked her where we would be after another lot of 11, she correctly said 44, with a satisfied smile on her face. The correct response doesn't always happen as quickly as this. However, I have always found that we have the pattern by the end of the rope. To see if she understood what is meant by multiplication, I asked her a range of questions about the 11 times table, using groups of dots, as in the first diagram. Finally, I suggested she practise her 11 times table using PerfectTIMES (for details visit www.perfect-times.co.uk).
* If you would like a PowerPoint version of this lesson please email me Wendy Fortescue-Hubbard is a teacher and game inventor. She has been awarded a three-year fellowship by the National Endowment for Science, Technology and the Arts (NESTA) to spread maths to the masses.
Email your questions to Mathagony Aunt at firstname.lastname@example.org Or write to TES Teacher, Admiral House, 66-68 East Smithfield, London E1W 1BX