Working systematically

problem
Triangles all around

Age

7 to 11

Challenge level

Can you find all the different triangles on these peg boards, and find their angles?
problem
Right angles

Age

11 to 14

Challenge level

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
problem
Triangles in circles

Age

11 to 14

Challenge level

Can you find triangles on a 9-point circle? Can you work out their angles?
problem
Late again

Age

5 to 7

Challenge level

Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
problem
Nineteen hexagons

Age

5 to 7

Challenge level

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?
problem
Cuisenaire counting

Age

5 to 7

Challenge level

Here are some rods that are different colours. How could I make a yellow rod using white and red rods?
problem
Arrangements

Age

7 to 11

Challenge level

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?
problem
Stars

Age

11 to 14

Challenge level

Can you work out what step size to take to ensure you visit all the dots on the circle?
problem
Isosceles triangles

Age

11 to 14

Challenge level

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
problem
Efficient cutting

Age

11 to 14

Challenge level

Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.