Sometimes I like to do a quick starter with my groups where they are just playing with numbers and which isn’t related to the work of a particular lesson.
One day last week I decided I wanted a starter that I could use across all abilities and year groups. I remembered the following problem that I had recently read on Dan Meyer’s (@ddmeyer) blog here:
- Choose three consecutive whole numbers and add them. Write your sum on the board. What do you notice?
I chose to use this problem as it seems simple but can revel lots about the nature of numbers. The only modification I made was to restrict the numbers that could be chosen to be less than or equal to 50 – I did this to make the arithmetic manageable.
I was very happy with the response I got to this problem from all of my groups, they were all engaged with thinking about what they could say about the results, especially once they had come and written them on the whiteboard.
I found this task good for the lower attaining KS3 as a way of getting them to practice mental / written addition methods and to have a look at how to tell if a number is divisible by 3 or not. With the higher attaining students it led on to a discussion of knowing something and how to rigorously show it using algebra. We also discussed how it doesn’t matter how the consecutive numbers are labelled, we will always get a sum that is divisible by 3.
Overall I think this activity benefited my students and that it was a valuable thing to do, which I will try to repeat in future. Of course, having to plan one activity that can be used with all classes is a nice bonus in terms of planning time!