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#### Resources tagged with Investigations similar to Random Squares:

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Challenge level:

### 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?

### 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.

### Global Warming

##### Stage: 4 Challenge Level:

How much energy has gone into warming the planet?

### Taking Trigonometry Series-ly

##### Stage: 5 Challenge Level:

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

### 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.

### Very Old Man

##### Stage: 5 Challenge Level:

Is the age of this very old man statistically believable?

### More Bridge Building

##### Stage: 5 Challenge Level:

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

### Big and Small Numbers in Physics

##### Stage: 4 Challenge Level:

Work out the numerical values for these physical quantities.

### Building Approximations for Sin(x)

##### Stage: 5 Challenge Level:

Build up the concept of the Taylor series

### Stirling Work

##### Stage: 5 Challenge Level:

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

### 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.

### 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.

### Big and Small Numbers in Chemistry

##### Stage: 4 Challenge Level:

Get some practice using big and small numbers in chemistry.

### 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. . . .

### The Power of Dimensional Analysis

##### Stage: 4 and 5

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

### Mach Attack

##### Stage: 5 Challenge Level:

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

### Modelling Assumptions in Mechanics

##### Stage: 5

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

### Diamonds Aren't Forever

##### Stage: 5 Challenge Level:

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

### Which Twin Is Older?

##### Stage: 5

A simplified account of special relativity and the twins paradox.

### 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.

### 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.

### What Salt?

##### Stage: 5 Challenge Level:

Can you deduce why common salt isn't NaCl_2?

### 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?

### 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.

### Twizzles Venture Forth

##### Stage: 4 Challenge Level:

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

### 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.

### Peeling the Apple or the Cone That Lost Its Head

##### Stage: 4 Challenge Level:

How much peel does an apple have?

### 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: 5

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

### Clear as Crystal

##### Stage: 5 Challenge Level:

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

### A Rational Search

##### Stage: 4 and 5 Challenge Level:

Investigate constructible images which contain rational areas.

### 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. . . .

### Few and Far Between?

##### Stage: 4 and 5 Challenge Level:

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

### The Invertible Trefoil

##### Stage: 4 Challenge Level:

When is a knot invertible ?

##### Stage: 4 and 5 Challenge Level:

Some of our more advanced investigations

### Trig-trig

##### Stage: 4 and 5 Challenge Level:

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

### What Do Functions Do for Tiny X?

##### Stage: 5 Challenge Level:

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

### 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. . . .

### 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?

### Operating Machines

##### Stage: 5 Challenge Level:

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

### 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.

### Spokes

##### Stage: 5 Challenge Level:

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

### Bent Out of Shape

##### Stage: 4 and 5 Challenge Level:

An introduction to bond angle geometry.

### 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?

### Robot Camera

##### Stage: 4 Challenge Level:

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

### Designing Table Mats

##### Stage: 3 and 4 Challenge Level:

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