Conjecturing and generalising

How many rectangles can you see? Are they all the same size? Can you predict how many rectangles there will be in counting sticks of different lengths?

Ayah conjectures that the diagonals of a square meet at right angles. Do you agree? How could you find out?

If you take four consecutive numbers and add them together, the answer will always be even. What else do you notice?

Investigate the different ways that fifteen schools could have given money in a charity fundraiser.

I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?

Watch the video of Fran re-ordering these number cards. What do you notice? Try it for yourself. What happens?

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?