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Extension 1

These activities come from the marvellous people at Nrich, a website that can be reached here.

Some of these activities may take more time than you have at the end of one session, in which case make sure that you come back to them and complete them the next day.  I'd love to see your thinking on these activities, so please send me pictures of what you've worked out.

This activity is slightly adapted from the activity that appears on the Nrich site.

Button-up Some More

This question is about finding relationships between numbers – an extension of our work on number sequences.  The key to extending your own learning, is to answer the final question – can you predict the number of ways of buttoning up a coat with five or six buttons?  To extend yourself further, write a simple mathematical explanation of how you would work out the answer to any number of buttons.

Part A: My coat has three different buttons.
Sometimes, I do them up starting with the top button.  Sometimes, I start somewhere else.
How many ways can you find to do up my coat?
How will you remember them?
Do you think there are any more?  How do you know?
Part B: I have a jacket which has four buttons.
Sometimes, I do the buttons up starting with the top button. Sometimes, I start somewhere else.  
How many different ways of buttoning it up can you find?

Explaining your reasoning

Look back at the number of different ways you found for buttoning up three buttons and four buttons.
Can you predict the number of ways of buttoning up a coat with five buttons?
Six buttons ...?  
This problem was inspired by an idea from Bernard Murphy.