How could you estimate the number of pencils/pens in these pictures?

This activity challenges you to decide on the 'best' number to use in each statement. You may need to do some estimating, some calculating and some research.

Who said that adding, subtracting, multiplying and dividing couldn't be fun?

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

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

Here is a chance to play a version of the classic Countdown Game.

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

This challenge is a game for two players. Choose two of the numbers to multiply or divide, then mark your answer on the number line. Can you get four in a row?

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?

Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?

Dicey Operations for an adult and child. Can you get close to 1000 than your partner?

Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.

Get some practice using big and small numbers in chemistry.

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?

An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.

Investigate the effects of the half-lifes of the isotopes of cobalt on the mass of a mystery lump of the element.

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

Work out the numerical values for these physical quantities.

In this twist on the well-known Countdown numbers game, use your knowledge of Powers and Roots to make a target.

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

From the information you are asked to work out where the picture was taken. Is there too much information? How accurate can your answer be?

Practise your skills of proportional reasoning with this interactive haemocytometer.

How many generations would link an evolutionist to a very distant ancestor?

Work with numbers big and small to estimate and calulate various quantities in biological contexts.

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

Build up the concept of the Taylor series

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

Can you deduce the pattern that has been used to lay out these bottle tops?

Make an estimate of how many light fittings you can see. Was your estimate a good one? How can you decide?

Find the exact difference between the largest ball and the smallest ball on the Hepta Tree and then use this to work out the MAGIC NUMBER!

Mr. Sunshine tells the children they will have 2 hours of homework. After several calculations, Harry says he hasn't got time to do this homework. Can you see where his reasoning is wrong?

Bluey-green, white and transparent squares with a few odd bits of shapes around the perimeter. But, how many squares are there of each type in the complete circle? Study the picture and make. . . .

Can you work out how many of each kind of pencil this student bought?

Which is larger: (a) 1.000001^{1000000} or 2? (b) 100^{300} or 300! (i.e.factorial 300)

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?