Creating and manipulating expressions and formulae

problem
Robert's spreadsheet

Age

14 to 16

Challenge level

Robert noticed some interesting patterns when he highlighted square numbers in a spreadsheet. Can you prove that the patterns will continue?
problem
How do you react?

Age

14 to 16

Challenge level

To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
problem
Simplifying doughnut

Age

14 to 18

Challenge level

An algebra task which depends on members of the group noticing the needs of others and responding.
problem
Algebra match

Age

11 to 16

Challenge level

A task which depends on members of the group noticing the needs of others and responding.
problem
Partly painted cube

Age

14 to 16

Challenge level

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?
problem
Divisible expression

Age

14 to 16

Challenge level

Can you show this algebraic expression is divisible by 4?
problem
Christmas chocolates

Age

11 to 14

Challenge level

How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?
problem
How much can we spend?

Age

11 to 14

Challenge level

A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?
problem
Sweeping satellite

Age

16 to 18

Challenge level

Derive an equation which describes satellite dynamics.
problem
Calculus countdown

Age

16 to 18

Challenge level

Can you hit the target functions using a set of input functions and a little calculus and algebra?