Resources tagged with: Investigations

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There are 55 results

Broad Topics > Thinking Mathematically > Investigations

Advanced Investigations

Age 14 to 18
Challenge Level

Some of our more advanced investigations

A Rational Search

Age 16 to 18
Challenge Level

Investigate constructible images which contain rational areas.

Sextet

Age 16 to 18
Challenge Level

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

Spokes

Age 16 to 18
Challenge Level

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

Trig-trig

Age 16 to 18
Challenge Level

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

Eight Ratios

Age 14 to 16
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

Age 14 to 16
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?

Stirling Work

Age 16 to 18
Challenge Level

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

Bessel's Equation

Age 16 to 18
Challenge Level

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

Building Approximations for Sin(x)

Age 16 to 18
Challenge Level

Build up the concept of the Taylor series

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.

Taking Trigonometry Series-ly

Age 16 to 18
Challenge Level

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

Chance of That

Age 16 to 18
Challenge Level

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

Spirostars

Age 16 to 18
Challenge Level

A spiropath is a sequence of connected line segments end to end taking different directions. The same spiropath is iterated. When does it cycle and when does it go on indefinitely?

Track Design

Age 14 to 16
Challenge Level

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

Few and Far Between?

Age 16 to 18
Challenge Level

Can you find some Pythagorean Triples where the two smaller numbers differ by 1?

Scale Invariance

Age 16 to 18
Challenge Level

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

Clear as Crystal

Age 16 to 18
Challenge Level

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

Reaction Rates!

Age 16 to 18

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

The Power of Dimensional Analysis

Age 14 to 18

An introduction to a useful tool to check the validity of an equation.

What Salt?

Age 16 to 18
Challenge Level

Can you deduce why common salt isn't NaCl_2?

Genetic Intrigue

Age 16 to 18

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. . . .

Inspect Your Gadgets

Age 16 to 18

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

Big and Small Numbers in the Physical World

Age 14 to 16
Challenge Level

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

Electromagnetism

Age 16 to 18

Read all about electromagnetism in our interactive article.

Perfect Eclipse

Age 14 to 16
Challenge Level

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

Big and Small Numbers in the Living World

Age 11 to 16
Challenge Level

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

Smoke and Daggers

Age 16 to 18
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. . . .

Alternative Record Book

Age 14 to 18
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 Chemistry

Age 14 to 16
Challenge Level

Get some practice using big and small numbers in chemistry.

Robot Camera

Age 14 to 16
Challenge Level

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

Designing Table Mats

Age 11 to 16
Challenge Level

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

Diamonds Aren't Forever

Age 16 to 18
Challenge Level

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

Global Warming

Age 14 to 16
Challenge Level

How much energy has gone into warming the planet?

Witch's Hat

Age 11 to 16
Challenge Level

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

Very Old Man

Age 16 to 18
Challenge Level

Is the age of this very old man statistically believable?

There's Always One Isn't There

Age 14 to 16
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.

Geometry and Gravity 1

Age 11 to 18

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.

Peeling the Apple or the Cone That Lost Its Head

Age 14 to 16
Challenge Level

How much peel does an apple have?

Problem Solving: Opening up Problems

Age 5 to 16

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. . . .

The Invertible Trefoil

Age 14 to 16
Challenge Level

When is a knot invertible ?

A Different Differential Equation

Age 16 to 18
Challenge Level

Explore the properties of this different sort of differential equation.

Which Twin Is Older?

Age 16 to 18

A simplified account of special relativity and the twins paradox.

More Bridge Building

Age 16 to 18
Challenge Level

Which parts of these framework bridges are in tension and which parts are in compression?

Mach Attack

Age 16 to 18
Challenge Level

Have you got the Mach knack? Discover the mathematics behind exceeding the sound barrier.

Making More Tracks

Age 16 to 18
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?

Escape from Planet Earth

Age 16 to 18
Challenge Level

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

Powerfully Fast

Age 16 to 18
Challenge Level

Explore the power of aeroplanes, spaceships and horses.

Snookered

Age 14 to 18
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?

Operating Machines

Age 16 to 18
Challenge Level

What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?