At school I always found mathematics easy, and fluency with numbers came easy to me, as a consequence I find it hard to understand how students can come to secondary school and not be flent with manipulating the number system, especially the integers.
Earlier this week I asked a KS3 student to tell me how many 20s were in 120. In answer to this they said seven and when I asked how they arrived at this they counted up in the following way: 20,40,60,80,91,102,120. I later went back to them and asked them to count up in 20s and they gave me the same list of numbers. I am struggling to explain this and wondering about the following:
- Why did they count up in this way?
- Is there anything special about the numbers 91 and 102?
- What barriers are there that mean they haven’t developed this number processing fluency?
- How can we develop this?
- Can we tackle this quickly?
- How can we develop the fluency so that the student recognises that 120/20 can simply be calculated by working out 12/2?
I’d love to know your thoughts on these questions, or anything else for that matter.