Exploring and noticing

Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

Imagine a machine with four coloured lights which respond to different rules. Can you find the smallest possible number which will make all four colours light up?

Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?

You are organising a school trip and you need to write a letter to parents to let them know about the day. Use the cards to gather all the information you need.

Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?

A task involving the equivalence between fractions, percentages and decimals which depends on members of the group noticing the needs of others and responding.

A task which depends on members of the group noticing the needs of others and responding.

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?