Conjecturing and generalising

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?
problem
Polygon rings

Age

11 to 14

Challenge level

Join pentagons together edge to edge. Will they form a ring?
problem
Bundles of cubes

Age

7 to 11

Challenge level

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?
article
Mastering mathematics: the challenge of generalising and proof

This article for primary teachers discusses how we can help learners generalise and prove, using NRICH tasks as examples.