One of those classic investigations that gets forgotten about all too easily. So much scope for generalising at different levels.
The fact that all odd numbers can be expressed as sum of two consecutive numbers is probably the first thing that will be established. But why is this the case? And can students express this as a generalisation, first in the form of concise words and then algebraically?
The beauty of this is that there are then many other layers of things to discover, right down to a generalisation explaining which numbers cannot be expressed as a sum of consecutive numbers. And maybe even a proof.
This nRich page gives away some of the answers.
Thanks to Alan Parr for reminding me about it with this excellent blog post:
The All I Can Throwers – Sessions with Den and Jenna. #1 – Consecutive Numbers
I liked the look of this Nrich task thinking that my Year 7s, who have shown some appetite for investigative tasks, would enjoy it.
It’s a great task, but like so many investigations, you really need to have a go at it first yourself. I did it with my daughter (Yr7) and we took nearly an hour to find the 3×3. And I was trying pretty hard! Interestingly the 4×4 was much easier. Here are our combined efforts!
It’s going to be critical how I introduce / explain the task, so I will create a notebook file to help with this.
I have also created a worksheet as I feel that my class will need a bit more scaffolding on this task. I now know that I will encourage them to move onto the 4×4 if they get fed up with the 3×3.
I’ll update this post tomorrow once I have taught the lesson.