Exploring and noticing

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

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

In this section from a calendar, put a square box around the 1st, 2nd, 8th and 9th. Add all the pairs of numbers. What do you notice about the answers?

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

Have a go at this 3D extension to the Pebbles problem.

How many ways can you find of tiling the square patio, using square tiles of different sizes?

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?

Here is your chance to investigate the number 28 using shapes, cubes ... in fact anything at all.