Conjecturing and generalising

problem
Charitable pennies

Age

7 to 14

Challenge level

Investigate the different ways that fifteen schools could have given money in a charity fundraiser.
problem
Terminating or not

Age

11 to 14

Challenge level

Is there a quick way to work out whether a fraction terminates or recurs when you write it as a decimal?
problem
Neighbourly addition

Age

7 to 14

Challenge level

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

Age

7 to 11

Challenge level

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

Age

7 to 11

Challenge level

Does this 'trick' for calculating multiples of 11 always work? Why or why not?
problem
Digit addition

Age

5 to 11

Challenge level

Try out this number trick. What happens with different starting numbers? What do you notice?
problem
Unexpected ordering

Age

5 to 7

Challenge level

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

Age

5 to 14

Challenge level

This task encourages you to investigate the number of edging pieces and panes in different sized windows.
problem
Triangle or no triangle?

Age

5 to 7

Challenge level

Here is a selection of different shapes. Can you work out which ones are triangles, and why?
problem
Name that triangle!

Age

7 to 11

Challenge level

Can you sketch triangles that fit in the cells in this grid? Which ones are impossible? How do you know?