Conjecturing and generalising

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.

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.