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You can't take a table square into an exam
This may a controversial topic when it comes to calculator use. Do you use them to support your groups with some of the number topics or do you give your students a times table square?
Finding Factors
There are times in teaching when we as teachers have to make decisions about how to support the students in our classes. I have often been asked to teach a year 7 group about factors and multiples and in the earlier years of my career I most definitely would have put a times table square on every table but often found this just added another barrier to their learning rather than supporting their understanding. Pupils have to look for the number in the grid in as many places as they can and then read the factors from the outside. Numbers have to be carefully chosen so that all the factors are less than 12, for example even numbers over 24 automatically do not work as the factor pair with 2 is over 12.
Instead I decided to teach the pupils to use a calculator to find factors.
To find the factors of 18 I asked the pupils to type 18 divided by 1 and press equals (execute) depending on the calculator.
Pupils got a an integer value and I explained this meant that 1 divided exactly into 18 so 1 was a factor of 18 along with 18.
We repeated this calculation with 2 and 3 with both values returning an integer answer so 2 and 3 (and 9 and 6) are factors of 18.
I took the opportunity here to show students how to use the left arrow to replay a calculation and just delete the 1 and replace with the 2. This was then be repeated for 3.
I was then also able to talk to students about being systematic with their calculations.
"If we have divided by 1, then by 2, and then by 3, the next number we should divide by is 4".
I saw the pupils type it in and immediately got their puzzled faces looking back.
"What did you get I asked?"
Amongst the various responses of "It didn't work", "Something went wrong" etc I did get pupils saying "a fraction" and even "nine over two" plus some that said 4.5."
This led to a discussion about how if the answer is not an integer then the number we were dividing by was not a factor.
We then tried 5, and found that was also not a factor.
We tried 6 and found the answer was 3 but we had already written both those numbers so we did not to go any further. We have found all the factors of 18.
After this we tried some more numbers and pupils did lots of independent practice. They soon discovered that they did not need to divide every number by 1 and that 1 was a factor of every number. Many did not need to divide by 5 as they knew the rule of divisibility for 5.
What this method allowed was a a lot of questions to be completed and pupils spotting patterns and rules themselves. The calculator was a tool they had never used before in a lesson about factors and now they understood what a factor was.
The TA that had supported the lesson, spoke to me at the end about how she would have expected pupils to be doing this lesson without a calculator. So I asked her how she would have supported the pupils who could not do their times tables and of course she expected the pupils to be given a times tables square. Once I said "But you can't take a times tables square into an exam, so I have given them a tool to work out the answers in 2 of their GCSE papers" she started to see the method in the madness.
Using the calculator to find multiples
For most pupils in year 7 the concept of multiples is one they understand, they may just get a bit confused between a factor and a multiple. Pupils can quickly pick up that all they have to do is keep adding the same number, but this can become a chore if they just have questions in a book or on a worksheet to complete.
Instead show the pupils how to use the answer button as talked about in my last blog to do repeated addition. You could even get pupils to compete to find as many multiples in a minute to practise this techniques to demonstrate that multiples never stop.
I'm not sure whether this blog will convince all of you, maybe some of you have never even thought about this way of using calculators for these topics, but maybe some will give it a go.
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