Visualising and representing

problem
Colour wheels

Age

7 to 11

Challenge level

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
problem
Folded A4

Age

11 to 14

Challenge level

What shapes can be made by folding an A4 sheet of paper only once?
problem
An unusual shape

Age

11 to 14

Challenge level

Can you maximise the area available to a grazing goat?
problem
Rolling around

Age

11 to 14

Challenge level

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?
problem
A square in a circle

Age

7 to 11

Challenge level

What shape has Harry drawn on this clock face? Can you find its area? What is the largest number of square tiles that could cover this area?
problem
Inside seven squares

Age

7 to 11

Challenge level

What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?
problem
Special numbers

Age

11 to 14

Challenge level

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?
problem
Dotty triangles

Age

11 to 14

Challenge level

Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?
problem
Squares, squares and more squares

Age

11 to 14

Challenge level

Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?
problem
Taking steps

Age

7 to 11

Challenge level

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.