I made this years ago, but just realised it is not on this blog.
It contains snippets of bits of maths from 500BC up to the present day to adorn your classroom or corridor. The focus is on interesting, but accessible maths rather than historical completeness! Mostly inspired by the excellent Alex’s Adventures in Numberland (Alex Bellos) as well as Number Freak (Derrick Niederman)
Best printed A3 in colour. Here is the whole thing as a pdf, and here as a word doc
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
Something that has never come naturally to me in the classroom is establishing and following routines. I’m not drawn to following routines myself. Before I was a teacher my work had very few routines in it. But I’ve seen how effective routines can be in developing good classroom management at all ages. So it’s something I know I need to work at.
Whilst there are lots of brilliant and inspiring ideas out there, a few of which I have tried, I think coming up with your own ideas in this area means they are more likely to stick and become, well, routine. So here’s something I’m going to introduce from next term.
The one person talking could be the teacher, or another student. You should be actively listening and thinking about what they are saying and what it means. It is simple – if someone else is talking and you then start talking over them, it’s highly disrespectful, even if it is about the work.
There will be something specific that I want you to discuss and I’ll tell you how long you have to discuss it. Make sure everyone gets a say and that you don’t chat about irrelevant stuff that doesn’t help your learning.
Sometimes all we need is a little nudge in the right direction. See if you can help each other before asking the teacher. It needs to be quiet enough so that everyone else can concentrate on their own work, so use a whisper if you need to discuss something.
There will be a specific reason why I want to be sure that this is your own work, e.g. during a rest or a piece of work I want to mark to assess your understanding.