Conjecturing and generalising

problem
Strange bank account

Age

11 to 14

Challenge level

Imagine a very strange bank account where you are only allowed to do two things...
problem
Snake coils

Age

7 to 11

Challenge level

This challenge asks you to imagine a snake coiling on itself.
problem
Walking the squares

Age

7 to 11

Challenge level

Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
problem
Perimeter possibilities

Age

11 to 14

Challenge level

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

Age

14 to 16

Challenge level

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
article
Train spotters' paradise

Dave Hewitt suggests that there might be more to mathematics than looking at numerical results, finding patterns and generalising.
problem
Summing geometric progressions

Age

14 to 18

Challenge level

Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?
problem
Making spirals

Age

7 to 11

Challenge level

Can you make a spiral for yourself? Explore some different ways to create your own spiral pattern and explore differences between different spirals.
problem
Constructing triangles

Age

11 to 14

Challenge level

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

Age

16 to 18

Challenge level

Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.