Sampling and Hypothesis Testing Using the Normal Distribution
These Making Statistics Vital resources are produced for those studying the S2 Module of A Level Statistics provide practical experience of sampling techniques and highlight the importance of using suitable sampling procedures. Sampling – Students are given 100 natural numbers and are asked to estimate the mean by taking…
The Normal Distribution
These Making Statistics Vital resources are provided for those studying the S2 Module of A Level Statistics and present students with the opportunity to investigate problems, which require a different approach to those questions usually posed, on the topic of the Normal Distribution. The coffee problem – poses the problem…
Binomial Distribution
This Making Statistics Vital resource consists of independent activities, covering aspects of this area of statistics for those studying the S1 Module of AS Level Statistics. The tasks are designed to encourage students to apply their knowledge of binomial distributions to solve challenging problems, giving them the opportunity to…
Exploring Data
This Making Statistics Vital resource consists of a number of independent activities, covering many aspects of this area of statistics. Students have practical opportunities to explore and develop further their knowledge and understanding of statistical measures and their application. Worldwide statistics - students explore the…
Vectors Introduction
This interactive resource, produced by the University of Leicester, is designed to enable students to explore vectors, beginning with the definition of a vector followed by the algebra of vectors and the scalar product. The opening slides of the presentation explain the difference between scalar and vector quantities followed…
Transformation of Shapes
This interactive resource, produced by the University of Leicester, is designed to enable students to explore transformations of shapes including translation by a vector, stretches, rotations around a point, reflection in the axes and reflections in the lines y=x and y=-x. The first activity draws a parallelogram which is translated…
Transformation of Functions
This interactive resource, produced by the University of Leicester, is designed to enable students to explore transformations of functions including translations, stretches, reflection in the axes and rotations. The first activity uses function notation to explore translations parallel to the x axis and translations parallel…
The Exponential Function
This interactive resource, produced by the University of Leicester, is designed to enable students to explore the nature of the exponential function and to explore the derivative of the exponential function. An introduction page sets out some basic information about exponential functions leading to a definition of the exponential…
Quadratic Equations
This interactive resource, produced by the University of Leicester, is designed to enable students to explore what is meant by a quadratic equation, the meaning of the coefficients of a quadratic equation and to be able to solve quadratic equations. An introduction page gives examples of where quadratic equations can be found…
Differentiation Exercise
This interactive resource, produced by the University of Leicester, is designed to enable students to explore the differential function of a polynomial and conclude by forming a generalisation. An instruction page explains to students that they should draw a polynomial. Then by sliding the slider the gradient of the curve is plotted,…
Shelter for the World
This resource pack introduces the concepts of shelter and shelter deprivation around the world to students in Key Stage Two. It highlights the challenges people face in their daily lives when their homes do not provide adequate shelter. It linked to the curriculum areas of design and technology, geography and PSHE and promotes thinking…
The Cross-ratio
Carom Maths provides this resource for teachers and students of A Level mathematics. This presentation looks at the theorem of cross-ratio, of four complex numbers, which is of great interest in a field of mathematics known as projective geometry and has an ancient history. The activity is designed to explore aspects of the…
Could Pi Be 3?
Carom Maths provides this resource for teachers and students of A Level mathematics. This presentation investigates the value of π in different types of geometry and provides a link for students to experiment with Hyperbolic geometry. The classic definition of a distance function, or metric, is given and a version of the Manhattan…
Cyclotomic Polynomials
Carom Maths provides this resource for teachers and students of A Level mathematics. Cyclotomic polynomials are explained in this presentation, which uses a regular polygon to illustrate the complex roots of unity and establish which of those are primitive, before demonstrating some intriguing algebra. The activity is designed…
Zeroes of a Recurrence Relation
Carom Maths provides this resource for teachers and students of A Level mathematics. The Fibonacci sequence is an example of a linear recurrence relation (LRS). A matrix is used to calculate future terms, as well as running the sequence backwards to see how many zeroes appear. Algebra is used to prove the maximum number of zeroes…
Triominoes
Carom Maths provides this resource for teachers and students of A Level mathematics. This presentation shows how, when placing triominoes onto a chessboard, there is always one empty square. An algebraic proof is developed to show that the empty square will always appear in the same location, or in one of its rotations. The…
Elliptic Curves
Carom Maths provides this resource for teachers and students of A Level mathematics. This presentation uses the fact that 1729 is the smallest number that can be expressed as two cubes in two different ways to introduce the topic of Elliptic curves, which are used more and more in the field of number theory. The activity is…
The ABC Conjecture
Carom Maths provides this resource for teachers and students of A Level mathematics. This presentation begins by introducing students to the technique used to find the radical of an integer before progressing to the ABC conjecture, which is recognised by mathematicians as being an important unsolved problem in number theory. The…
Triangle Centres
Carom Maths provides this resource for teachers and students of A Level mathematics. A triangle can have more than one centre and this presentation demonstrates the application of vectors, in three different situations, to show that the circumcentre, the centroid and the orthocentre of a triangle are indeed positioned at the centre…
Hikorski Triples
Carom Maths provides this resource for teachers and students of A Level mathematics. This presentation demonstrates how the interesting idea of Hikorski triples was developed from writing a GCSE Equations worksheet in 2002. The triples are identified as (p, q, pq+1/p+q). The activity is designed to explore aspects of the subject…
Quadratic Reciprocity
Carom Maths provides this resource for teachers and students of A Level mathematics to explore aspects of the subject which may not normally be encountered, to encourage new ways to approach a problem mathematically and to broaden the range of tools that an A Level mathematician can call upon. This presentation on Quadratic reciprocity…
Inversion
Carom Maths provides this resource for teachers and students of A Level mathematics. This presentation begins with a reminder of some transformations of the plane before introducing the less well known transformation of Inversion. Students are able to experiment with an Autograph file to explore this concept and the Steiner Chain…
The Logistic Map and Chaos
Carom Maths provides this resource for teachers and students of A Level mathematics. This presentation provides a spreadsheet, which models a population of mice, and allows students to vary the input and thus change the behaviour of the model. There are some surprising discoveries to be made when the results are analysed. The…
V, S and E
Carom Maths provides this resource for teachers and students of A Level mathematics. There are six ways to write the total edge length, total surface area and volume of a cube, or cuboid, in order of size. This presentation challenges students to find a cube for each order. Autograph files are provided to help with this problem. Thw…
The Four Colour Problem
Carom Maths provides this resource for teachers and students of A Level mathematics. Colouring maps, so that no two countries sharing a border are shaded with the same colour, is the focus of this presentation, which includes both the history and mathematical proofs to this problem. This activity is designed to explore aspects…
Conics
Carom Maths provides this resource for teachers and students of A Level mathematics. This presentation introduces the Conics and provides a Geogebra file for students to explore how, by changing the eccentricity of a curve, the locus of a point is altered. They are also challenged to vary the constants of an equation to see how…
What Are You Implying?
Carom Maths provides this resource for teachers and students of A Level mathematics. This presentation provides students with an opportunity to explore their own grasp of logic and introduces a logical tautology called Modus Tollens. This activity is designed to explore aspects of the subject which may not normally be encountered,…
Tangles
Carom Maths provides this resource for teachers and students of A Level mathematics. This presentation describes the concept of Tangles, which were the idea of John Conway. Students are given some rules from which they create the tangle representing 2/5, before creating their own tangle numbers for others to untangle. The activity…
Pearl Tilings
Carom Maths provides this resource for teachers and students of A Level mathematics. This presentation explores the effect of placing a single tile into an existing pattern which tessellates, referred to as a pearl tiling. New descriptions and notation are introduced and questions regarding regular polygons, polyominoes, and quadrominoes…
Mapping a Set to Itself
Carom Maths provides this resource for teachers and students of A Level mathematics. In this presentation students are given a function and explore the mapping of natural numbers, as well as being challenged to find the inverse function. A link to the online encyclopaedia of integer sequences is provided for students to check…
The Game of Life
Carom Maths provides this resource for teachers and students of A Level mathematics. The Game of Life is a simulation of how a population might grow, if subject to a few simple rules. Initially students try the rules out for themselves on squared paper, before following a link to a computer program that shows the patterns which…
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 Argand diagram, are within…