Estimating and approximating

Analyse these beautiful biological images and attempt to rank them in size order.

Examine these estimates. Do they sound about right?

How might you use mathematics to improve your chances of guessing the number of sweets in a jar?

Looking at small values of functions. Motivating the existence of the Taylor expansion.

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

Build up the concept of the Taylor series

Work out the numerical values for these physical quantities.

Estimate these curious quantities sufficiently accurately that you can rank them in order of size

There are four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?

Work in groups to try to create the best approximations to these physical quantities.