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#### Resources tagged with Investigations similar to Retracircles:

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### 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?

### A Rational Search

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

Investigate constructible images which contain rational areas.

### 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 ?

### 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. . . .

### Spokes

##### Stage: 5 Challenge Level:

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

### 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?

### 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...

### 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?

### Spirostars

##### Stage: 5 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

##### Stage: 4 Challenge Level:

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

### 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.

### 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.

### 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.

### 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?

### What Salt?

##### Stage: 5 Challenge Level:

Can you deduce why common salt isn't NaCl_2?

### 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.

### 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. . . .

### Diamonds Aren't Forever

##### Stage: 5 Challenge Level:

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

### Mach Attack

##### Stage: 5 Challenge Level:

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

### Designing Table Mats

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

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

### 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...

### The Power of Dimensional Analysis

##### Stage: 4 and 5

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

### Clear as Crystal

##### Stage: 5 Challenge Level:

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

### Carbon Footprints

##### Stage: 4 Challenge Level:

Is it really greener to go on the bus, or to buy local?

### 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.

### Bent Out of Shape

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

An introduction to bond angle geometry.

### Perfect Eclipse

##### Stage: 4 Challenge Level:

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

### 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.

### 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

### Robot Camera

##### Stage: 4 Challenge Level:

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

### Escape from Planet Earth

##### Stage: 5 Challenge Level:

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

### 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.

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

##### Stage: 4 Challenge Level:

How much peel does an apple have?

### A Different Differential Equation

##### Stage: 5 Challenge Level:

Explore the properties of this different sort of differential equation.

### 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?

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

Some of our more advanced investigations

### Twizzles Venture Forth

##### Stage: 4 Challenge Level:

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

### 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.

### 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?

### Spiroflowers

##### Stage: 5 Challenge Level:

Analyse these repeating patterns. Decide on the conditions for a periodic pattern to occur and when the pattern extends to infinity.

### 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.

### Trig-trig

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

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

### 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?

### Taking Trigonometry Series-ly

##### Stage: 5 Challenge Level:

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