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Very Old Man

Stage: 5 Challenge Level:

Is the age of this very old man statistically believable?

Stirling Work

Stage: 5 Challenge Level:

See how enormously large quantities can cancel out to give a good approximation to the factorial function.

CSI: Chemical Scene Investigation

Stage: 5 Challenge Level:

There has been a murder on the Stevenson estate. Use your analytical chemistry skills to assess the crime scene and identify the cause of death...

Diamonds Aren't Forever

Stage: 5 Challenge Level:

Ever wondered what it would be like to vaporise a diamond? Find out inside...

Big and Small Numbers in Physics

Stage: 4 Challenge Level:

Work out the numerical values for these physical quantities.

Smoke and Daggers

Stage: 5 Challenge Level:

We all know that smoking poses a long term health risk and has the potential to cause cancer. But what actually happens when you light up a cigarette, place it to your mouth, take a tidal breath. . . .

Global Warming

Stage: 4 Challenge Level:

How much energy has gone into warming the planet?

Scale Invariance

Stage: 5 Challenge Level:

By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.

Making More Tracks

Stage: 5 Challenge Level:

Given the equation for the path followed by the back wheel of a bike, can you solve to find the equation followed by the front wheel?

Taking Trigonometry Series-ly

Stage: 5 Challenge Level:

Look at the advanced way of viewing sin and cos through their power series.

Powerfully Fast

Stage: 5 Challenge Level:

Explore the power of aeroplanes, spaceships and horses.

Bessel's Equation

Stage: 5 Challenge Level:

Get further into power series using the fascinating Bessel's equation.

What Salt?

Stage: 5 Challenge Level:

Can you deduce why common salt isn't NaCl_2?

Reaction Rates!

Stage: 5

Fancy learning a bit more about rates of reaction, but don't know where to look? Come inside and find out more...

Big and Small Numbers in Chemistry

Stage: 4 Challenge Level:

Get some practice using big and small numbers in chemistry.

Robot Camera

Stage: 4 Challenge Level:

Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?

A Rational Search

Stage: 4 and 5 Challenge Level:

Investigate constructible images which contain rational areas.

Designing Table Mats

Stage: 3 and 4 Challenge Level:

Formulate and investigate a simple mathematical model for the design of a table mat.

Alternative Record Book

Stage: 4 and 5 Challenge Level:

In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.

Big and Small Numbers in the Physical World

Stage: 4 Challenge Level:

Work with numbers big and small to estimate and calculate various quantities in physical contexts.

Genetic Intrigue

Stage: 5

Dip your toe into the fascinating topic of genetics. From Mendel's theories to some cutting edge experimental techniques, this article gives an insight into some of the processes underlying. . . .

Stage: 5

Read about the mathematics behind the measuring devices used in quantitative chemistry

Big and Small Numbers in the Living World

Stage: 3 and 4 Challenge Level:

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

Clear as Crystal

Stage: 5 Challenge Level:

Unearth the beautiful mathematics of symmetry whilst investigating the properties of crystal lattices

Escape from Planet Earth

Stage: 5 Challenge Level:

How fast would you have to throw a ball upwards so that it would never land?

A Different Differential Equation

Stage: 5 Challenge Level:

Explore the properties of this different sort of differential equation.

Geometry and Gravity 1

Stage: 3, 4 and 5

This article (the first of two) contains ideas for investigations. Space-time, the curvature of space and topology are introduced with some fascinating problems to explore.

Chance of That

Stage: 4 and 5 Challenge Level:

What's the chance of a pair of lists of numbers having sample correlation exactly equal to zero?

The Invertible Trefoil

Stage: 4 Challenge Level:

When is a knot invertible ?

Problem Solving: Opening up Problems

Stage: 1, 2, 3 and 4

All types of mathematical problems serve a useful purpose in mathematics teaching, but different types of problem will achieve different learning objectives. In generalmore open-ended problems have. . . .

Peeling the Apple or the Cone That Lost Its Head

Stage: 4 Challenge Level:

How much peel does an apple have?

Sextet

Stage: 5 Challenge Level:

Investigate x to the power n plus 1 over x to the power n when x plus 1 over x equals 1.

Eight Ratios

Stage: 4 Challenge Level:

Two perpendicular lines lie across each other and the end points are joined to form a quadrilateral. Eight ratios are defined, three are given but five need to be found.

Two Regular Polygons

Stage: 4 Challenge Level:

Two polygons fit together so that the exterior angle at each end of their shared side is 81 degrees. If both shapes now have to be regular could the angle still be 81 degrees?

Stage: 4 and 5 Challenge Level:

Some of our more advanced investigations

Building Approximations for Sin(x)

Stage: 5 Challenge Level:

Build up the concept of the Taylor series

9 Hole Light Golf

Stage: 1, 2, 3, 4 and 5 Challenge Level:

We think this 3x3 version of the game is often harder than the 5x5 version. Do you agree? If so, why do you think that might be?

Trig-trig

Stage: 4 and 5 Challenge Level:

Explore the properties of combinations of trig functions in this open investigation.

Take Ten Sticks

Stage: 3 and 4 Challenge Level:

Take ten sticks in heaps any way you like. Make a new heap using one from each of the heaps. By repeating that process could the arrangement 7 - 1 - 1 - 1 ever turn up, except by starting with it?

Witch's Hat

Stage: 3 and 4 Challenge Level:

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

Perfect Eclipse

Stage: 4 Challenge Level:

Use trigonometry to determine whether solar eclipses on earth can be perfect.

Odd Stones

Stage: 4 Challenge Level:

On a "move" a stone is removed from two of the circles and placed in the third circle. Here are five of the ways that 27 stones could be distributed.

Track Design

Stage: 4 Challenge Level:

Where should runners start the 200m race so that they have all run the same distance by the finish?

There's Always One Isn't There

Stage: 4 Challenge Level:

Take any pair of numbers, say 9 and 14. Take the larger number, fourteen, and count up in 14s. Then divide each of those values by the 9, and look at the remainders.

Snookered

Stage: 4 and 5 Challenge Level:

In a snooker game the brown ball was on the lip of the pocket but it could not be hit directly as the black ball was in the way. How could it be potted by playing the white ball off a cushion?

Number Chains

Stage: 5 Challenge Level:

Find all the periodic cycles and fixed points in this number sequence using any whole number as a starting point.

Spokes

Stage: 5 Challenge Level:

Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.

Twizzles Venture Forth

Stage: 4 Challenge Level:

Where we follow twizzles to places that no number has been before.

What Do Functions Do for Tiny X?

Stage: 5 Challenge Level:

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