Working systematically

problem
Teddy Town

Age

5 to 11

Challenge level

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
problem
Watch your feet

Age

7 to 11

Challenge level

I like to walk along the cracks of the paving stones, but not the outside edge of the path itself. How many different routes can you find for me to take?
problem
Halloween investigation

Age

7 to 11

Challenge level

Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?
problem
Penta place

Age

7 to 11

Challenge level

Penta people, the Pentominoes, always build their houses from five square rooms. I wonder how many different Penta homes you can create?
problem
Let's investigate triangles

Age

5 to 7

Challenge level

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?
problem
Maze 100

Age

7 to 11

Challenge level

Can you go through this maze so that the numbers you pass add to exactly 100?
problem
Making cuboids

Age

7 to 11

Challenge level

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?
problem
Round and round the circle

Age

7 to 11

Challenge level

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
problem
Counting on letters

Age

11 to 14

Challenge level

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?
problem
Bean bags for Bernard's bag

Age

7 to 11

Challenge level

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?