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Future Morph careers quest

Future Morph Careers Quest was developed for students attending one of the the Big Bang science fairs. In the activity, students question exhibitors about aspects of their work and how they had chosen their particular career.

Whilst developed for an exhibition context, the resources can suggest questions for...

The Overlapping Circles

Carom Maths provides this resource for teachers and students of A Level mathematics.

In this activity the equations of the lines, which are formed at the points of intersection of three circles, are explored and an Autograph file is used to show what happens when the equations of the circles are added...

Repunits

Carom Maths provides this resource for teachers and students of A Level mathematics.

A repunit, which stands for repeated unit, is a number like 11, 111, or 1111 that contains only the digit 1 and extends to number bases other than base ten. This presentation challenges students to prove that any repunit...

Siders

Carom Maths provides this resource for teachers and students of A Level mathematics.

A motif, seen on the floor of a cafe, prompts an investigation into whether or not it is possible to use the kite shapes to form an exact polygon and leads to some interesting discoveries.

The resource is designed to...

Buffon's Needle

Carom Maths provides this resource for teachers and students of A Level mathematics. This presentation introduces an explanation and a simulation of Buffon's Needles experiment, that yields an approximation for π, before developing the experiment further by asking what would happen if the shape of the needles were...

Curves of Constant Width

Carom Maths provides this resource for teachers and students of A Level mathematics.

This presentation introduces the Reuleaux Triangle and shows how to construct a curve which has a constant width, as well as Barbier's Theorem and the Isoperimetric Inequality. Three dimensional shapes are also investigated...

Multiple-free Sets

Carom Maths provides this resource for teachers and students of A Level mathematics.

In this activity a set of numbers is referred to as multiple free if there is no pair of numbers in the set such that one is a multiple of the other and the challenge is to find the largest multiple free set from the first...

Descent

Carom Maths provides this resource for teachers and students of A Level mathematics.

This activity explores an example of the Descent method. This method was popularised by the famous mathematician Pierre de Fermat...

Wallpaper Patterns

Carom Maths provides this resource for teachers and students of A Level mathematics.

Wallpaper patterns all have one thing in common; they are all produced by repeating a single fundamental tile by translation, that one basic rule gives rise to a range of possible patterns, each with their distinctive...

Ergodic Mathematics

Carom Maths provides this resource for teachers and students of A Level mathematics.

Ergodic maths is a fairly new branch of mathematics which concerns itself with repeated processes and some of the basic theorems are introduced here.

The activity is designed to explore aspects of the subject which...

The Distribution of Prime Numbers

Carom Maths provides this resource for teachers and students of A Level mathematics.

In this activity the distribution of prime numbers, proved by Hadamard and de la Vallée Poussin in 1896, is investigated using an Excel spreadsheet program, Autograph and the Prime Number Theorem.

The resource is...

Infinity

Carom Maths provides this resource for teachers and students of A Level mathematics.

This presentation highlights the concept of infinity and its implications, as well as introducing the mathematician Georg Cantor and the arguments relating to infinity that he came up with.

The resource is designed to...

Hyperbolic Geometry

Carom Maths provides this resource for teachers and students of A Level mathematics.

This presentation introduces Euclid's axioms and theorems and provides historic information on the development of geometric principles, as well as discussing hyperbolic geometry. A link to Non-Euclid software, from Joel...

The Propositional Calculus

Carom Maths provides this resource for teachers and students of A Level mathematics.

This presentation challenges students to use the rules they have been given to develop a logical system and deduce theorems which prove that the system is complete and consistent and introduces the idea of truth tables to...

The Mandelbrot Set

Carom Maths provides this resource for teachers and students of A Level mathematics.

This presentation explores the Mandelbrot Set, a topic from Chaos Theory, which involves complex numbers and the Argand diagram. Following a set of rules, students use a spreadsheet to establish if complex numbers, on the...

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