Conjecturing and generalising

Imagine flipping a coin a number of times. Can you work out the probability you will get a head on at least one of the flips?

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

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

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

How can you change the area of a shape but keep its perimeter the same? How can you change the perimeter but keep the area the same?

Can you find rectangles where the value of the area is the same as the value of the perimeter?

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

I'm thinking of a rectangle with an area of 24. What could its perimeter be?