Exploring and noticing

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
Sticky triangles

Age

7 to 11

Challenge level

Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
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
Calendar capers

Age

11 to 14

Challenge level

Choose any three by three square of dates on a calendar page...
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?
problem
It's all about 64

Age

7 to 11

Challenge level

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
problem
Train carriages

Age

5 to 11

Challenge level

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?
problem
Great squares

Age

7 to 11

Challenge level

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.
problem
The great tiling count

Age

7 to 11

Challenge level

Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.