Factors can be tricky to grasp, but visual aids and a catchy slogan will prime pupils for progress, says Leila Murray
Confusion between key vocabulary in maths is sometimes difficult to unravel: "multiple", "product" and "factors" are all associated with multiplication, but which is which? By using visual apparatus and a catchy slogan, all can become clear.
I got pupils to build "factor towers" using multi-sensory number plates, so they could see the factors then move on to more complicated challenges.
I explained to them that we were going to use our number plates to work on factors, defining these as numbers that divide exactly into another number without leaving a remainder. I wanted to create a memory aid, so as a factor "goes into" the number, our slogan became: "If they 'Guzinta', then that means they must be a factor."
I asked the children to arrange 12 counters into as many arrays (lines of equal length) as they could: 1x12, 2x6, 3x4. These were all the factors of 12. We then worked with other visual representations that showed this even more clearly. They made 12 out of the 10 and 2 number plates and covered it with the 2-plates, which fitted exactly six times.
I then asked them: if twos fit exactly six times, what would happen if we covered the 12 with sixes? They investigated with the 6-plates, which proved the relationship.
I started with simple factors, so the children felt confident with the method before moving on to more challenging factors. I then set up a differentiated investigation.
Using the plates to find patterns, I asked which numbers have six factors? Two? Five? An odd number of factors? The children recorded what they found out, moving away from the equipment towards using mental methods as their confidence grew.
In the plenary, we found that all numbers with two factors were prime numbers because they could only be divided by themselves and one other number.
We took this one step further and talked about prime factors. I explained that every number can be made up of factors that are prime numbers. The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24. The prime factors of 24 are 2 and 3, and these numbers can be used to make 24: 2 x 2 x 2 x 3=24.
This lesson was successful because it made vocabulary explicit and it showed pupils what a factor looks like.
Leila Murray is deputy head at Meridian Primary School in East Sussex.