Estimating and approximating

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

My measurements have got all jumbled up! Swap them around and see if you can find a combination where every measurement is valid.

There are nasty versions of this dice game but we'll start with the nice ones...

Here's a chance to work with large numbers...

Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?

How many ways can you find to put in operation signs (+, −, ×, ÷) to make 100?

See how the motion of the simple pendulum is not-so-simple after all.

The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?