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Resources tagged with Investigations similar to Model Solutions:

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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. . . .

Global Warming

Age 14 to 16 Challenge Level:

How much energy has gone into warming the planet?

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.

A Different Differential Equation

Age 16 to 18 Challenge Level:

Explore the properties of this different sort of differential equation.

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.

Taking Trigonometry Series-ly

Age 16 to 18 Challenge Level:

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

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.

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?

Modelling Assumptions in Mechanics

Age 16 to 18

An article demonstrating mathematically how various physical modelling assumptions affect the solution to the seemingly simple problem of the projectile.

The Power of Dimensional Analysis

Age 14 to 18

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

Big and Small Numbers in Chemistry

Age 14 to 16 Challenge Level:

Get some practice using big and small numbers in 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.

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.

Building Approximations for Sin(x)

Age 16 to 18 Challenge Level:

Build up the concept of the Taylor series

Bessel's Equation

Age 16 to 18 Challenge Level:

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

Few and Far Between?

Age 14 to 18 Challenge Level:

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

Mach Attack

Age 16 to 18 Challenge Level:

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

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.

Big and Small Numbers in Physics

Age 14 to 16 Challenge Level:

Work out the numerical values for these physical quantities.

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.

Peeling the Apple or the Cone That Lost Its Head

Age 14 to 16 Challenge Level:

How much peel does an apple have?

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. . . .

Age 16 to 18

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

Twizzles Venture Forth

Age 14 to 16 Challenge Level:

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

What Salt?

Age 16 to 18 Challenge Level:

Can you deduce why common salt isn't NaCl_2?

Diamonds Aren't Forever

Age 16 to 18 Challenge Level:

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

Clear as Crystal

Age 16 to 18 Challenge Level:

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

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.

9 Hole Light Golf

Age 5 to 18 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?

Designing Table Mats

Age 11 to 16 Challenge Level:

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

Trig-trig

Age 14 to 18 Challenge Level:

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

Age 14 to 18 Challenge Level:

Some of our more advanced investigations

Chance of That

Age 14 to 18 Challenge Level:

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

Very Old Man

Age 16 to 18 Challenge Level:

Is the age of this very old man statistically believable?

More Bridge Building

Age 16 to 18 Challenge Level:

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

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 ?

Odd Stones

Age 14 to 16 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.

Bent Out of Shape

Age 14 to 18 Challenge Level:

An introduction to bond angle geometry.

Perfect Eclipse

Age 14 to 16 Challenge Level:

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

Take Ten Sticks

Age 11 to 16 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?

A Rational Search

Age 14 to 18 Challenge Level:

Investigate constructible images which contain rational areas.

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.

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?

CSI: Chemical Scene Investigation

Age 16 to 18 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...

Which Twin Is Older?

Age 16 to 18

A simplified account of special relativity and the twins paradox.

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.

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?