Today during a year 10 lesson, students were faced with a calculation: 81 – 45 during a worded problem. They reached the answer 36. One student was waiting for the other students to reach their answer and he said “All of the numbers are in the 9 times table”

We stopped to look at why that was and we came to the conclusion that if you had 9 nines and you subtract 5 nines then you are left with 4 nines. Students explored which calculations this worked for and they summarised that two numbers that are in the same times table had a difference that was also in that times table.

I then went home thinking about generalisations and how this isn’t always apparent

I want students to notice that when you subtract multiples of the same number then the difference is also a multiple of that number.

I then hope to move onto 3 and 3 squared and how you cannot simplify this.

I think the slide below is a little complicated but i want students to compare the two ideas.