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Broad Topics > Calculations and Numerical Methods > Estimating and approximating

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Count the Crayons

Age 5 to 7 Challenge Level:

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

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Discuss and Choose

Age 5 to 11 Challenge Level:

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.

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Dicey Operations

Age 11 to 14 Challenge Level:

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

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Nice or Nasty

Age 7 to 14 Challenge Level:

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

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Back Fitter

Age 14 to 16 Challenge Level:

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?

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Countdown

Age 7 to 14 Challenge Level:

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

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The Not-so-simple Pendulum 1

Age 16 to 18 Challenge Level:

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

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Four Go

Age 7 to 11 Challenge Level:

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

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Little Man

Age 5 to 7 Challenge Level:

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?

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Sissa's Reward

Age 11 to 14 Challenge Level:

Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...

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Four Go for Two

Age 7 to 11 Challenge Level:

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

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Dicey Operations for Two

Age 7 to 11 Challenge Level:

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

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Nice or Nasty for Two

Age 7 to 11 Challenge Level:

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

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Big and Small Numbers in Chemistry

Age 14 to 16 Challenge Level:

Get some practice using big and small numbers in chemistry.

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Biology Measurement Challenge

Age 14 to 16 Challenge Level:

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

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Does This Sound about Right?

Age 11 to 14 Challenge Level:

Examine these estimates. Do they sound about right?

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Counting Sweets

Age 7 to 14 Challenge Level:

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

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Branching Processes and Extinction

Age 16 to 18 Challenge Level:

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

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Cobalt Decay

Age 16 to 18 Challenge Level:

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

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Approximately Certain

Age 14 to 18 Challenge Level:

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

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Big and Small Numbers in Physics

Age 14 to 16 Challenge Level:

Work out the numerical values for these physical quantities.

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Power Countdown

Age 14 to 16 Challenge Level:

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

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Today's Date - 01/06/2009

Age 5 to 11 Challenge Level:

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

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Using the Haemocytometer

Age 14 to 16 Challenge Level:

Practise your skills of proportional reasoning with this interactive haemocytometer.

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Time to Evolve

Age 14 to 16 Challenge Level:

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

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More or Less?

Age 14 to 16 Challenge Level:

Are these estimates of physical quantities accurate?

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Big and Small Numbers in Biology

Age 14 to 16 Challenge Level:

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

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Big and Small Numbers in Physics - Group Task

Age 16 to 18 Challenge Level:

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

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Building Approximations for Sin(x)

Age 16 to 18 Challenge Level:

Build up the concept of the Taylor series

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What Do Functions Do for Tiny X?

Age 16 to 18 Challenge Level:

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

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Building Patterns

Age 7 to 11 Challenge Level:

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

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Shedding Some Light

Age 7 to 11 Challenge Level:

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

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The Magic Number and the Hepta-tree

Age 7 to 11 Challenge Level:

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!

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Back to School

Age 7 to 11 Challenge Level:

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?

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Squaring the Circle

Age 11 to 14 Challenge Level:

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. . . .

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Whole Numbers Only

Age 11 to 14 Challenge Level:

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

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Growing

Age 16 to 18 Challenge Level:

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

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What's My Weight?

Age 7 to 11 Short Challenge Level:

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?