Conjecturing and generalising

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...

Who said that adding couldn't be fun?

Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?

This big box adds something to any number that goes into it. If you know the numbers that come out, what addition might be going on in the box?

Can you work out the irrational numbers that belong in the circles to make the multiplication arithmagon correct?

How would you create the largest possible two-digit even number from the digit I've given you and one of your choice?

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?