Topic | Level | Resource | Description |
Algebra | KS3 | To build the concept of bisection, this quiz goes a step further than ‘guess again’ – each team gets 3 guesses which they are told are either too high or too low before they submit a final answer. Regardless of their sense of the size of the thing (from largest ship to fastest animal), those who can best narrow down their range will do best in general. | |
Algebra | GCSE | A complete description of the method required for GCSE trial and improvement questions, including a worked example (plus ‘My thinking…’ notes), and examples of GCSE questions to try. | |
Algebra | GCSE | The New York Times ran an article which complained of a lack of sufficient information to deduce the number of sales and the number of rentals of a movie when they knew the cost of each, the total revenue and the total number of transactions. Enter: simultaneous equations. | |
Algebra | KS3 | Solving equations by means of function machine notation and reversing operations. | |
Algebra | KS3 | With a choice of either a 1 or 2 step function machine, this generates random rules linking an input and output for learners to guess. | |
Algebra | KS3 | A simple version of the classic pick-up game, Nim. You play against the computer at 3 levels of difficulty with a customisable number of starting objects, and the aim is to avoid being the last player to take an object. | |
Algebra | KS3 | Designed to ease students into the use of algebra to describe rules – grids of numbers inherently contain patterns (adding 8 as you go down diagonally to the right, etc) depending on the way they are generated. This worksheet requires students to identify these rules, spot patterns and apply rules in algebraic form. | |
Algebra | KS3 | Designed to bridge between describing sequences term by term and generating a general term. Useful for a group which is already familiar with generating a sequence from an nth term rule, or for a more advanced class to derive the method themselves. | |
Algebra | KS3 | An alternative version of the investigation into mobile phone contracts – with a given up-front charge and a certain amount per month, which contract gives the best deal for a particular phone? Incorporates formulae to derive and use. Full solutions attached. | |
Algebra | GCSE | A mind-map of Foundation GCSE algebra topics followed by a selection of questions on each of the topic areas. Full solutions included. | |
Algebra | GCSE | Starting with a fill-in-the-blanks table of square numbers, and moving on to quadratics with no x term (all with whole number solutions). Includes full solutions. There is also an extension worksheet attached, still with quadratics without an x term but this time requiring more manipulation and calculators (and one has no solutions). | |
Algebra | KS3 | A sequences and nth term investigation based on square tile patterns. Involves a linear and a (simple) quadratic sequence. | |
Algebra | GCSE | The next level up from Tile Patterns, this investigation looks into the number of small cubes in a larger one which have 3 faces showing, 2, 1 or none. Involves sequences and nth term, a linear, quadratic and cubic sequence. | |
Algebra | KS3 | A fully worked method for finding the nth term of a quadratic sequence. | |
Algebra | Other | An open-ended investigation into the number sequences found within Pascal’s triangle. Designed to be used by a group who can make conjectures, test and prove them with minimal input from the teacher. Includes a large Pascal’s triangle to enable students to easily investigate patterns such as Sierpinski’s triangle. | |
Algebra | KS3 | The problem is very simple – how many squares are there on a chessboard? however, this includes 2 by 2 squares, 3 by 3, etc. | |
Algebra | KS3 | Demonstrating the principles of removing the same thing from both sides using a coins in cups analogy. | |
Algebra | KS3 | Using the analogy of matches and matchboxes, this worksheet uses diagrams to reinforce the concept to allow solving of equations with x on both sides. | |
Algebra | KS3 | Designed for students to work on with a laptop, to develop a rudimentary understanding of some key Excel formulas at the same time as getting a feel for basic financial planning. | |
Algebra | KS3 | Designed to come at the concept of algebra from a more intuitive direction. Using Excel formulas, students effectively perform substitution, interpreting cell references as variables. | |
Algebra | KS3 | Allows the user to construct an equation with x on both sides to be displayed in the form of balancing scales. Boxes representing x can be removed one by one from each side, and weights representing numbers can also be removed, to illustrate how to simplify an equation. Includes a more widely applicable interactive solver for use with negatives. | |
Algebra | KS3 | A customisable worksheet where you can input your own coefficients and preferred solutions and both a question and answer sheet will be generated automatically. | |
Algebra | KS3 | Completely customisable random equation generator. Click for a new equation, then click to go through the stages of solving, including explanations. | |
Algebra | GCSE | Demonstration of changing the subject of a formula. To be used with Changing the Subject worksheet | |
Algebra | GCSE | Examples of formulae to rearrange, making each term the subject. Includes solutions. | |
Algebra | GCSE | Combining volume formulae to find a formula for the volume of a newly created 3D shape. | |
Algebra | GCSE | Using constant acceleration suvat equations to prove results about firing a gun into the air. | |
Algebra | GCSE | Proving that the volume of certain shapes can be found exactly using simpson’s rule. | |
Algebra | GCSE | Generates a completely customisable series of double brackets and quadratics (toggle view either one or both) for printing or on-screen use. | |
Algebra | GCSE | Notes on how to quickly and easily factorise a range of different quadratic expressions (with a single x squared term), including questions as well as notes. Full solutions included. | |
Algebra | GCSE | A summary of the main competencies required by the higher GCSE involving quadratics – forming, solving, completing the square to find max/min, graphing and rational expressions. Includes examples. | |
Algebra | GCSE | Worked example question with a given quadratic describing ballistic motion. | |
Algebra | KS3 | Combining area and algebra by providing simple algebraic expressions as side lengths for rectangles whose area and perimeter are to be calculated in terms of x. | |
Algebra | KS3 | Type in a hidden message to have the morse code version appear on the screen. Decoder by the side to help solve the puzzle. | |
Algebra | GCSE | This requires some careful thought and the application of algebra (only linear equations, but the element of problem solving makes it quite a tricky one). | |
Algebra | KS4 | A problem involving a quadratic expression to the power of another. Only requires knowledge of solving quadratics by factorising and rules of indices, but is a bit sneaky. Comprehensive solutions included, as well as an informative graph. | |
Algebra | GCSE | A numerical introduction to the concept of the difference of two squares, using a trick the author spotted back when he was trying to learn his times tables as a kid. Also shows the geometric connection (the actual squares) and leads on to a series of multiplying out brackets and factorising questions. Full solutions included. | |
Algebra | GCSE | A series of increasingly complex questions on solving quadratics by factorising. Starting with taking out a single term, then double brackets with no negatives, then mixed, then disguised quadratics (that is, compound functions such as even powered quartics). Full solutions included. | |
Algebra | KS3 | Set up to work from the powerpoint, this simple game requires players to remove either 1 or 2 objects in turn, with the last player to remove an object losing. The winning strategy (which is relatively easy to work out) leads nicely into a study of linear sequences. | |
Algebra | GCSE | Worked example of finding the nth term of a quadratic sequence. | |
Algebra | GCSE | Covers key terminology, common forms (eg factorised, completed square) and a couple of examples of applications. | |
Algebra | KS3 | A variety of questions on sequences, building up from continuing a linear sequence to spotting term to term rules to finding and using nth terms. Includes full solutions. | |
Algebra | GCSE | Simplifying, adding, subtracting, multiplying and dividing algebraic fractions. Includes examples, comparisons with common numerical techniques and full solutions. | |
Algebra | KS3 | Carefully laid out structure with boxes to fill in, designed to reinforce the use of the balancing method. (What happened between lines 2 and 3 to this equation?) Goes from 1 step all the way to x on both sides problems. Varying levels of scaffolding throughout. | |
Algebra | GCSE | Examples and questions including using completed square quadratics to solve equations and to find maximum or minimum values. | |
Algebra | GCSE | Extension work on linear inequalities requiring students to consider how to break a three part inequality into parts. Scaffolded and includes full solutions. | |
C1 | A-Level | A simple optimisation problem based on a quadratic (so it can be solved by sketching a curve or completing the square). | |
C1 | A-Level | Pupils have to produce a simplified astronomical model of the order of jupiter’s moons and their equations of motion – requires circle equations. | |
C1 | A-Level | To accompany the above activity – gives the solution equations. | |
C1 | A-Level | Beginning by proving why the ratio of an A4 sheet approximates to 1:√2, and moving on to a simple folding exercise which leads to a problem involving surds. Includes multiplying brackets such as (1+√2) together. | |
C1 | A-Level | Accompanying PowerPoint – proving some results based on the ratio of A4 sheets. | |
C1 | A-Level | Shows a graph (and the equation) of the quadratic generated by a focus and directrix. The focus and directrix can be altered and the graph of the parabola is automatically updated. | |
C1 | A-Level | For use when introducing calculus – using the intuitive understanding of differentiation as the gradient of a line. Uses an embedded GeoGebra applet to allow modification. | |
C1 | A-Level | Beginning with gradient, a clear colour-coded sheet walking students through estimating the gradient of the standard quadratic graph, then looking for a pattern or rule. A good way to understand the concept of the slope of a curve. | |
C1 | A-Level | Thorough introduction to integration including exercises, exam questions and examples of applications. Includes full solutions. | |
C1 | A-Level | A neat introduction to integration using the concept of reversing differentiation: students have to reverse-engineer an original expression and try to derive a general rule for polynomials. | |
C1 | A-Level | A helpful booklet detailing all the main facts, techniques and formulae that are required for the Core 1 exam, but not provided in the formula book. Valuable for revision or as an additional resource during teaching of the module. | |
C1 | A-Level | Designed to fit on a single side of A4 (still readable when shrunk to A6 size as a pocket-sized revision card), this summarises all the key results, facts and formulae from the AQA Core 1 Mathematics module. For more in-depth revision, see the C1 Not-Formula Book. | |
C2 | A-Level | Designed for students to use at home, taking advantage of the graphical calculator function of Google search, to investigate the effect of various changes to a function. Includes the four main transformations; translations and stretches in the x and y direction, with extension questions on reflections. | |
C2 | A-Level | A problem involving arithmetic series. One person’s starting salary is lower but increases faster than that of another. Calculate how long it will be till one salary overtakes the other, and – crucially – how long until total earnings are balanced. | |
C2 | A-Level | A description of the three main paradoxes of Zeno, by way of an introduction to infinite sums. Can be used when beginning geometric series, and asks the student to refute the arguments. | |
C2 | A-Level | Introduction to the idea of summing to infinity using geometric series, with screenprints from Buffer (see below), followed by three examples of shapes created by an infinite iteration but with finite area and perimeter, to be found by applying geometric series formulae. Also includes ball bouncing problem. | |
C2 | A-Level | This is designed to illustrate the link between video buffering and geometric progressions. An infinite sum can be more easily visualised in the context of a common phenomenon – customisable times and buffer delays. | |
C2 | A-Level | A look at currency conversion rates and how geometric series can be used to examine the effect of repeated buying and selling. Uses the nth term formula and logarithms, but no knowledge of the sum or infinite sum formulae is required. | |
C2 | A-Level | Somewhat far-fetched problem based around the combination of percentage increases and decreases, producing a maths problem requiring use of Geometric Series formulae as well as logarithms. Includes solutions. | |
C2 | A-Level | Using the concept of geometric series to solve a theoretical problem about gender bias. If families keep having kids until they have a son, then stop, what will the eventual proportions of boys and girls be? | |
C2 | A-Level | Not an activity, just some musings into what it would be like if an unlimited athlete took a (suitably modified) bleep test. Involves geometric series calculations and lots of comparitive speeds. | |
C2 | A-Level | Why is a baked bean can that shape? Assuming a cylindrical form is best, what dimensions are optimal for the best surface area to volume ratio? This requires some basic calculus with negative indices. | |
C2 | A-Level | Similar to the Baked Bean presentation, this is a worksheet that goes through the process of optimising the surface area to volume ratio for a cylinder. Includes fully worked solutions. | |
C2 | A-Level | Using different values for the curved and flat surfaces of an oil drum, this worksheet calculates the optimal dimensions to minimise cost of materials. | |
C2 | A-Level | For expansions of the form (a + b)^c this will give the expansion to the x^10 term. Deals with negative and fractional powers, too. This is made in Excel 2007, and contains macros. | |
C2 | A-Level | A short question asking for missing values in a compound interest scenario. Some can be found simply by applying powers, or by rooting, but to reverse exponentiation it is necessary to use trial and error (until logarithms are introduced). Good starter activity. | |
C2 | A-Level | An early introduction to logarithms, designed to demonstrate how they build upon the concept of multiplicative counting, and includes a range of carefully crafted questions which test the understanding, primarily, of index rules. Ideal for extension GCSE, or to tackle before getting onto the rules of logarithms. | |
C2 | A-Level | Revision-style sheet covering the basics of logarithms and their associated rules. | |
C2 | A-Level | To accompany Introducing Logarithms booklet. | |
C2 | A-Level | Intuitive introduction to logarithms and the logarithmic scale, full of examples and mini thought-experiments to help students grasp the value of using logarithms. Includes questions and solutions. | |
C2 | A-Level | Booklet aimed at developing a deeper understanding of logarithms, including how they are used to solve specific problems, what the most commonly used bases are and why, a neat example involving working out the number of digits in the largest known prime. | |
C2 | A-Level | A 2-page summary of the key skills required by the Core 2 module. Listed under chapter headings, with space for students to indicate their level of understanding. For use when revising and identifying areas of weakness. | |
C2 | A-Level | A collection of some of the trickier past paper questions from AQA MPC2. Approximately 2 hours’ worth (around 100 marks), with one version that includes hints as well as mark schemes included at the end. | |
C2 | A-Level | A helpful booklet detailing all the main facts, techniques and formulae that are required for the Core 2 exam, but not provided in the formula book. Valuable for revision or as an additional resource during teaching of the module. | |
C2 | A-Level | Designed to fit on a single side of A4 (still readable when shrunk to A6 size as a pocket-sized revision card), this summarises all the key results, facts and formulae from the AQA Core 2 Mathematics module. For more in-depth revision, see the C2 Not-Formula Book. | |
C3 | A-Level | A step-by-step worksheet which leads you through the derivation of e (Euler’s number) as the limit of a series. Based on the concept of compound interest paid yearly, monthly, weekly, daily, etc, the number e gives a limit the overall income cannot exceed. | |
C3 | A-Level | A GeoGebra generated applet embedded in a web page – by changing the angle of a point on the unit circle, the ratios of sin, cos and tan are generated (and shown on a concurrent graph). | |
C3 | A-Level | A graph of the trigonometric function y=sin(x), but with the option to modify elements of it to demonstrate common graph transformations. y = a sin(bx + c) + d. | |
C3 | A-Level | Some increasingly challenging questions involving stretches and translations in the x and y direction, reflections in the axes and then modulus function transformations, including compound transformations. Includes full solutions. | |
C3 | A-Level | A trigonometry problem involving manipulation of sec cosec cot functions and solving a (simple) trig quadratic equation (requiring a modified solution range). Good plenary question incorporating skills from trig identities and trig equations topics. | |
C3 | A-Level | Parts, Substitution, Inspection and Standard Results. Includes examples of each, and a break down of how to use (including parts twice, ‘backwards’ substitutions, etc). | |
C3 | A-Level | An activity on the C3 topic of volumes of revolution. The task is to calculate the volume of a dome built as a partial sphere. Set on the most likely base of human extra-terrestrial settlement, Jupiter’s moon Europa, the dome is to be a prototype home. Includes solutions. | |
C3 | A-Level | Volumes of revolution question, involving some manipulation of functions and an element of problem solving – how much water would the Jodrell Bank satellite dish hold? Includes solutions. | |
C3 | A-Level | Can be used as an accompaniment for Europa – is a useful calculator which utilizes formulae derived from Volumes of Revolution as well as some simple iterations on a cubic equation to calculate the volume for a given size of sphere-slice, or vice versa. | |
C3 | A-Level | Allows the user to input functions and have Excel calculate approximations using the Mid-Ordinate, Trapezium and Simpson’s Rule, illustrating the difference between the three, and customisable for different limits and for different numbers of ordinates (up to 100 strips). | |
C3 | A-Level | An overview of the three main numerical integration methods described in AQA Core 3: Trapezium rule, Mid-ordinate rule and Simpson’s rule. The rules are compared, represented graphically and their respective accuracy / error terms investigated. | |
C3 | A-Level | An alternate version of the 2014 AQA Core 3 A-level paper, with questions designed to be similar but sufficiently different to work well as a second bite at the cherry for students who have already attempted the real thing. Includes full solutions. | |
C3 | A-Level | A helpful booklet detailing all the main facts, techniques and formulae that are required for the Core 3 exam, but not provided in the formula book. Valuable for revision or as an additional resource during teaching of the module. | |
C3 | A-Level | Designed to fit on a single side of A4 (still readable when shrunk to A6 size as a pocket-sized revision card), this summarises all the key results, facts and formulae from the AQA Core 3 Mathematics module. For more in-depth revision, see the C3 Not-Formula Book. | |
C4 | A-Level | A brief illustration of the proof of the compound angle formula for cos(A-B). A similar idea can be used to prove sin(A+B), etc. | |
C4 | A-Level | A series of questions on exponential growth and decay, on the subject of the rabbit population of Australia. | |
C4 | A-Level | Based on the Otzi man discovered preserved by a glacier, this worksheet uses the principle of exponential decay to investigate the concept of carbon dating. | |
C4 | A-Level | A population prediction based on the UK colonizing the Moon, using principles from exponential growth. | |
C4 | A-Level | A 2-page summary of the key skills required by the Core 4 module. Listed under chapter headings, with space for students to indicate their level of understanding. For use when revising and identifying areas of weakness. | |
C4 | A-Level | A helpful booklet detailing all the main facts, techniques and formulae that are required for the Core 4 exam, but not provided in the formula book. Valuable for revision or as an additional resource during teaching of the module. | |
C4 | A-Level | Designed to fit on a single side of A4 (still readable when shrunk to A6 size as a pocket-sized revision card), this summarises all the key results, facts and formulae from the AQA Core 4 Mathematics module. For more in-depth revision, see the C4 Not-Formula Book. | |
D1 | A-Level | This step-by-step demonstration shows the method for applying Prim’s algorithm to a matrix (module D1). By clicking through with the arrow, each stage of the algorithm is illustrated. The sheet can be printed out for students to follow along. | |
D1 | A-Level | A (correct) table of driving distances between major English and Welsh cities. Includes a map. Designed to be used with Prim’s algorithm for matrices to find a minimum spanning tree. | |
D1 | A-Level | Based on the excellent board game, Ticket to Ride Europe, this is a worksheet on graph theory, requiring the application of Minimum Spanning Tree algorithms and Dijkstra’s algorithm. Includes comprehensive solutions. | |
D1 | A-Level | Some thorough notes on the mathematics behind the Travelling Salesman Problem, and a thorough example / question involving the 8 largest cities in England. By finding upper and lower bounds for every city (ideally this task is shared between a group), students find high confidence solutions. Full solutions (including complete analytical results for true best case solution) are attached. | |
D1 | A-Level | Can Thor take on Agent Smith? Is Wolverine a match for Princess Elsa? Use this match-up to introduce the idea of matchings. Students will probably come up with the idea of a bipartite graph on their own, but there is just enough complexity for an adjacency matrix to look useful. Match the hero with the task. | |
D1 | A-Level | A brief summary of the algorithms encountered in the AQA Decision 1 A-level module, including examples of their purpose and applications. | |
D1 | A-Level | Designed as an activity to go alongside the algorithms chapter of Decision 1, this is an application of Euclid’s algorithm for finding the highest common factor of two numbers written in Python. Students read the code and have it explained line by line, then implement an optimisation using modular residues. | |
D1 | A-Level | Notes on the key terminology of graph theory for Decision 1. Includes words like: simple, connected, complete, tree, spanning tree, walk, trail, path, cycle, Eulerian, Hamiltonian. Includes diagrams and notes on specific algorithms that link to each concept (such as Chinese Postman for Eulerian trails). | |
D1 | A-Level | A set of details for each of the sorting algorithms covered in Decision 1, including an overview of the algorithm, its relative efficiency, a full worked example and full details of the process. Includes bubble, shuttle, shell and quick sort. | |
D1 | A-Level | A game for three groups designed to encourage efficient manual sorting – three teams compete to put a list of 8 names in order. | |
D1 | A-Level | An exmaple using the 8 largest cities in England. Find the minimum spanning tree linking them all. | |
D1 | A-Level | A helpful booklet detailing all the main facts, techniques and formulae that are required for the Decision 1 exam, but not provided in the formula book. Valuable for revision or as an additional resource during teaching of the module. | |
D1 | A-Level | This takes a little while to trace compared to standard Decision 1 algorithms, but it is elegantly simple for what it does, which is create ludicrously accurate values for pi after only a very few iterations. | |
D2 | A-Level | A slightly silly example introducing critical path analysis, analysing the process of swapping the battery in a phone. What actions should be performed first? Where could time be saved? Where is the bottle-neck? Lots of clear illustrations and full solutions. | |
D2 | A-Level | What better introduction to game theory and those confusing matrices than actually playing a game? A couple here I made up, which can later be analysed in more detail to determine which player should have consistently come out on top, why certain strategies worked well, and what the best thing to do would have been. | |
FP1 | A-Level | Details of the standard results for 30, 45 and 60 degrees along with graphs of the three main trig functions and a description of how the symmetries (rotation and reflection) and the period of the graph can yield all solutions. | |
FP1 | A-Level | A bit of background on the history of different types of number. The answer to ‘why do we learn about imaginary numbers if they aren’t real?’ is, of course, that it never stopped us with any other made up number systems, from negatives to fractions to surds, etc. All are the result of You can’t… But what if we could? | |
FP1 | A-Level | Designed to introduce simple transformation matrices for students who may not have come across matrices at all previously. Involves reflections and rotations, and describes how to multiply a matrix by a position vector, a series of position vectors or even another transformation matrix. Solutions included. | |
FP1 | A-Level | An independent investigative task designed to be completed by students at home using Excel or a similar spreadsheet. It builds the concept of a sequence tending towards a limit while also developing confidence in manipulating spreadsheet formulae. | |
FP1 | A-Level | A complex number problem that can be solved using only the most basic definitions, making it suitable for an introduction to i. However, the solution includes content from other topics such as geometric series, allowing a more elegant solution. | |
FP1 | A-Level | Uses real results from a Physics damped oscillation experiment and requires students to convert an exponential curve to a linear function in order to estimate constants involved. | |
FP1 | A-Level | Explanation of the three key numerical methods, along with analogies to USA-Mexico gun-runners. | |
FP1 | A-Level | Details of some of the basic 2 by 2 transformation matrices, along with brief details of how they work. Includes reflections in the axes and lines y=x and y=-x as well as 90 and 180 degree rotations about the origin. | |
FP1 | A-Level | A helpful booklet detailing all the main facts, techniques and formulae that are required for the Further Pure 1 exam, but not provided in the formula book. Valuable for revision or as an additional resource during teaching of the module. | |
FP2 | A-Level | Applying proof by induction to the nth term of the Fibonacci sequence. Involves square rooting a surd, but walks you through the process. Includes solutions. | |
FP2 | A-Level | Converts from rectangular (a+bi) form to polar and exponential form. Also gives the rectangular form for a given value of the modulus and argument of a complex number. Includes a small Argand diagram to illustrate the number on the complex plane. | |
FP2 | A-Level | An introduction to Euler’s Formula and Euler’s Identity. Precursors: basic complex number theory and familiarity with the polar form. Maclaurin’s series is introduced for the proof, but a prior knowledge is not required. | |
FP2 | A-Level | Explanation – with key results – of the method behind turning powers of trig functions (sine and cosine) into expressions involving just multiple angles and vice versa. One of the applications of De Moivre’s theorem, this sheet also includes examples of the identities up to the sixth power. | |
FP2 | A-Level | Applying the exponential form of a complex number to the problem of powers involving complex numbers. Includes solutions. | |
FP2 | A-Level | A 2-page summary of the key skills required by the Further Pure 2 module. Listed under chapter headings, with space for students to indicate their level of understanding. For use when revising and identifying areas of weakness. | |
Geometry | KS3 | Six different photos (a mini, a lava-flow, a box, a water-tower, a high-jumper and the oval office) need to be cut out and matched first with the appropriate units (eg temperature in degrees celsius or area in square metres) and then with the correct number. Solutions included. | |
Geometry | KS3 | A basic unit conversion calculator, illustrating the link between centi-, milli- and kilo- for litres, metres and grams. | |
Geometry | KS3 | A table of the common metric units of distance, weight and capacity. Blank columns for students to fill in common conversions (eg 10mm=1cm) and examples of things which would be measured in these units. | |
Geometry | KS3 | Values are given for various common quantities (thickness of an iphone, weight of a cow) but the unit names need to be chosen by the student. All units are metric. Solutions included. | |
Geometry | KS3 | Gives a brief overview of both the metric and the imperial system of measurements, some examples of when we still use imperial in the UK, then details of conversions with some simple questions. | |
Geometry | KS3 | A number of conversions between metric and imperial length measurements. Conversions are included on the sheet, and photographs of the various items for each question. | |
Geometry | KS3 | Illustrations of parallel and perpendicular lines followed by line and angle properties of common quadrilaterals. | |
Geometry | KS3 | Fact cards from the powerpoint above. Can be used in conjunction with the flow-chart activity below. | |
Geometry | KS3 | Examples of flowcharts, designed to be used as an introduction to classifying shapes (such as the quadrilaterals, using fact cards above). | |
Geometry | KS3 | A series of questions in message box form to be answered with a Yes or No, done by means of a simple macro. Includes a diagram of the program used, in flow-chart form. For teaching flow charts and/or quadrilaterals. | |
Geometry | KS3 | Designed in Geogebra, and embedded as an applet in a web page, you can move each of the 6 quadrilaterals around by their corners – they will always remain constrained according to their properties. | |
Geometry | KS3 | A customisable triangle with ray lines through each vertex to a moveable point of enlargement, and its image, enlarged by a customisable scale factor. Uses GeoGebra (free: geogebra.com). | |
Geometry | GCSE | A grid with a shape to enlarge by scale factor -0.5. Note that this is more challenging than a positive integer enlargement, and is intended as an extension piece. Full solutions included. | |
Geometry | KS3 | Input the correct 2d translation vector to move the blue square to the position of the red square. | |
Geometry | KS3 | A simple introduction to similar and congruent triangles. Students use the fact that similar shapes may be enlargements, but congruent shapes can only be translations, reflections or rotations of one another. | |
Geometry | KS3 | Four shapes to translate using vectors (including negatives) to represent horizontal and vertical motion. Drawn on a grid, and incorporating an extension section (asking about the reverse translations) and full solutions. | |
Geometry | KS3 | An introduction to the concept of a vector describing a set of directions. Students draw out a path following instructions, then generate more efficient instructions. Develops into addition of vectors. | |
Geometry | KS3 | Allows the user to move an object’s corners and observe the effect of a reflection. Can move the object through the line, etc. Uses GeoGebra (free: geogebra.com). | |
Geometry | KS3 | Brief introduction to rotational symmetry with pictures of car manufacturer’s badges. | |
Geometry | KS3 | A customisable shape which may be rotated about a variable point by a variable angle. Uses GeoGebra (free: geogebra.com). | |
Geometry | KS3 | A dozen or so pages covering the fundamentals of point and direction of rotation for multiples of 90 degrees on co-ordinate grids. | |
Geometry | GCSE | A summary of the key methods to follow when applying Pythagoras’ theorem, including when to use it and common errors. | |
Geometry | KS3 | A few slides with examples of escher tessellation. | |
Geometry | KS3 | With angles clearly marked and labelled, this tesselation neatly demonstrates how any quadrilateral can be tessellated. | |
Geometry | GCSE | Why do the sun and moon look the same size? A couple of problems involving similar triangles. | |
Geometry | KS3 | Pupils attempt to accurately make a particular angle on the board, or guess the angle given. Click to show the angle formed. Uses GeoGebra (free: geogebra.com). | |
Geometry | KS3 | This is a thorough introduction and proof of all the key angle rules. Starting with why we split a full turn into 360 pieces, and working through basic rules and parallel lines to finally prove results about triangles. | |
Geometry | KS3 | The 5 most common angle rules, and an introduction to angles in a polygon by splitting into triangles. | |
Geometry | KS3 | Demonstrates the angle properties of triangles. Uses GeoGebra (free: geogebra.com). | |
Geometry | KS3 | A collection of triangles where missing angles must be found using sum of angles in a triangle and isosceles and equilateral properties. | |
Geometry | KS3 | Demonstrates the angle properties of parallel lines. Uses GeoGebra (free: geogebra.com). | |
Geometry | KS3 | Just pictures of some regular and irregular polygons for use when investigating interior and exterior angles by measuring. | |
Geometry | GCSE | A series of questions on interior and exterior angles of regular and irregular polygons. Solutions included. | |
Geometry | GCSE | 3 to a page rules of interior, exterior and centre angles for regular and irregular polygons. | |
Geometry | KS3 | Presentation describing how to measure bearings from one point to another, reverse bearings and how to pinpoint a location from two bearings. See accompanying worksheets below. | |
Geometry | KS3 | A range of worksheets, including introductory work, homework sheets and investigative work involving maps, as well as how to pinpoint a location from two bearings. See accompanying powerpoint above. | |
Geometry | KS3 | Four points with bearings to measure between them. Useful for getting lots of practice with acute, obtuse and reflex bearings, and a good starting point for explaining why opposite directions have bearings 180 degrees apart. | |
Geometry | GCSE | Students plot a course on the map linking points A and B, then use the scale and accurate angle measurements to write descriptions of each leg of the journey. Using Bearings Vectors Conversion spreadsheet these can then be compared to the actual displacement of B from A to give an overall error on their construction. | |
Geometry | GCSE | To accompany Bearings Course Plotter (but can be used for a variety of bearings or vectors calculations). Takes as input the magnitude and direction of a vector and gives North and East components. This allows calculation of, for instance, the relative error of a set of instructions when compared to the overall displacement. | |
Geometry | GCSE | A word problem requiring accurate interpretation and plotting of positions using bearings. The situation involves taking readings of a moving ship from a moving ship, triangulating with a lighthouse and predicting the course of the vessel you’re observing. Full solutions and diagrams included. | |
Geometry | GCSE | An on-screen triangle all-in-one calculator, which allows you to input values and then apply formulae such as the sine rule and the cosine rule to calculate missing measurements. | |
Geometry | GCSE | Estimate the number of people in a large group photo by using right-angle trigonometry to calculate the area of the (roughly) triangular space. | |
Geometry | GCSE | A pair of problems involving angles and the properties of a rectangle and an equilateral triangle. | |
Geometry | GCSE | Calculates the distance to the horizon based on height above the surface of the planet (includes standard results for known planets and the moon, as well as the option for custom radii). Uses Pythagoras, and includes a worksheet | |
Geometry | GCSE | Accompanying presentation illustrating the method for finding the distance to the horizon, using Pythagoras’ Theorem. To be used with Horizon.xls | |
Geometry | GCSE | Currently the tallest building in the world, the Burj Khalifa, has the interesting property that, due to its height and the speed of the elevators, one can view the sunset twice. Do the maths with this worksheet. Involves Pythagoras. | |
Geometry | KS3 | A gradual introduction to midpoints of line segments. Involves plotting some coordinates, finding midpoints from the graph then discovering the method. Final section uses the result that joining the midpoints of the sides of any quadrilateral always gives a parallelogram. Includes solutions. | |
Geometry | GCSE | Questions on finding midpoints and lengths of line segments, followed by an introduction to an investigation. Joining the midpoints of any quadrilateral (as shown in the worksheet) forms a parallelogram. | |
Geometry | GCSE | For use when first encountering right-angled trigonometry. Using the sine ratio, triangles with 30, 45 and 60 degree angles for investigating the ratio. | |
Geometry | GCSE | A short task which makes a good early trigonometry question, only requiring the sine ratio to calculate the hypotenuse of a triangle, and Pythagoras’ theorem. The problem involves estimating the length of cable on the Golden Gate bridge. | |
Geometry | GCSE | Full colour detailed examples of the three different variations of a simple right-angled trigonometry problem (finding the ‘easy’ side, the other side or the angle). | |
Geometry | GCSE | Right-angled trigonometry. Allows the user to dynamically alter the width and height of a right-angled triangle, choose a trigonometric identity to investigate and observe the link between side length ratios and angle. | |
Geometry | GCSE | To be used in conjunction with an inclinometer (angle measurer) and trundle wheel. Walks students through the steps of using right angled trigonometry to estimate the height of objects such as trees or buildings. | |
Geometry | GCSE | Investigation questions involving the 4:1 rule of ladder safety. | |
Geometry | GCSE | Gives a brief description of Archimedes’ method for approximating pi, and provides a method for doing a similar thing (but with right-angled trigonometry). Students follow instructions to form right angled triangles, and use sin and tan ratios to generate an estimate. Includes diagrams and full solutions. | |
Geometry | GCSE | This handy tool allows the teacher to generate Pythagoras questions quickly and easily. A click on the shape generates a new problem; a couple of toggle buttons allow you to change parameters (integer/any answers, hypotenuse/any side unknown). | |
Geometry | GCSE | Explanation of one method for generating Pythagorean triples, written in the form of an independent investigation. Useful for extension of Pythagoras’ Theorem. | |
Geometry | GCSE | A series of problems which involve Pythagoras’ Theorem. Ranging from a hiker to picture frames, area of a kite and what you could fit in a pringles tube, and including full solutions. Good independent problem solving tasks, can be cut to A5 size. | |
Geometry | GCSE | Details of when and how to use each of the various techniques required for the GCSE. Pythagoras, right angled trigonometry, non-right angled trigonometry (including Sine rule, Cosine rule and area of a triangle). | |
Geometry | KS3 | A revision-style sheet outlining the fundamental loci. | |
Geometry | KS3 | A large presentation, intended to span a number of lessons, covering a given distance from a fixed point and from a line, equidistance between 2 points or lines, and introducing an investigation involving a rope around a corner. | |
Geometry | KS3 | A series of problems for learners to solve by obeying the constraints and observing the resultant shapes. | |
Geometry | KS3 | Demonstrates how a pair of equal circles produces an exact perpendicular bisector. Uses GeoGebra (free: geogebra.com). | |
Geometry | KS3 | Demonstrate how a pair of equal circles exactly bisects an angle. Uses GeoGebra (free: geogebra.com). | |
Geometry | KS3 | A series of questions, with extension parts, requiring the application of construction techniques and loci knowledge. | |
Geometry | KS3 | This spreadsheet provides randomly generated rectangles or irregular shapes made from squares, and displays the area and perimeter on demand. | |
Geometry | KS3 | Create your own shapes, and have excel automatically calculate the area and perimeter (toggle button to show/hide). | |
Geometry | GCSE | A wide selection of interesting problems and investigations requiring the use of loci. Some are more straight-forward, but require the use of circle formulae. Others are more complex, and develop a better understanding of the implications of loci and construction results. | |
Geometry | KS3 | Investigates the relationship between the perimeter and the area of a rectangle. One sheet allows the user to fix the perimeter while varying the side lengths, and the othe sheet fixes the area while varying side lengths. The resulting perimeter/area will be shown below, and the optimal shape can be determined. | |
Geometry | KS3 | A 20-second clip demonstrating where the formula for the area of a triangle comes from using cardboard. | |
Geometry | KS3 | A more complicated formula, but can still be demonstrated with a bit of cardboard and some cutting and moving. | |
Geometry | KS3 | A similar idea to the triangle video- cut a piece off one side and stick it on the other to make a rectangle. | |
Geometry | KS3 | Diagrams and formulae for the area of a rectangle, triangle, parallelogram and trapezium. (3 to a page) | |
Geometry | KS3 | A square grid overlaying a map of the british isles, this is designed to be used as an area estimation activity to come up with a ballpark figure for the size of the country. | |
Geometry | KS3 | Designed for group work for younger learners, this is an extended task which requires the application of compound area knowledge to calculate the amount of wood required to build a shack. | |
Geometry | KS3 | Accompanying presentation for Shack worksheet – gives dimensions and details of how to calculate area. | |
Geometry | KS3 | New dimensions are given to the displayed shape at the click of a button, and the answer (and working) displayed as required. | |
Geometry | GCSE | Some examples (plus solutions) for more complicated applications of sector and segment rules. | |
Geometry | KS3 | A series of questions (with attached answer sheet) testing area calculations for a variety of compound shapes. | |
Geometry | KS3 | Can you work out the area of the overlap between these two identical equilateral triangles? 3 different variations. | |
Geometry | KS3 | A computer-based homework. Students record the dimensions of a cuboid from home, then calculate the surface area and volume. As soon as they enter these values into the appropriate boxes the computer will tell them if they are correct or not. Once complete, the sheet can be printed off or emailed directly to the teacher. | |
Geometry | KS3 | Generates random integer side-lengths for a cuboid and give step-by-step working for surface area calculations. | |
Geometry | KS3 | An accompanying presentation illustrating the method for calculating surface area. | |
Geometry | KS3 | An investigation into optimal surface area for cuboids with a fixed volume. Full solutions (including all whole number results for the cuboid of volume 900 cubic centimetres) are included. | |
Geometry | KS3 | Designed to accompany 3 different sizes of Kelloggs Corn Flakes boxes, this worksheet (including solutions) requires students to find volume and surface area by measurement and calculation, then use their figures to compare both value for money and cardboard-use efficiency. | |
Geometry | GCSE | This rather tricky problem requires only Pythagoras’ theorem and some basic algebra to solve. All is explained in the presentation. | |
Geometry | GCSE | Two problems involving compound area, including circles. With worked solutions included. | |
Geometry | KS3 | Instructions explain how to produce what appear to be two identical triangles from the same set of cut-out shapes, but one has a greater area than the other. | |
Geometry | GCSE | Known as Curry’s paradox, this simple collection of shapes seemingly goes together to form two identical triangles… with different areas! For full functionality, also download the embedded video. | |
Geometry | GCSE | Curry’s paradox – embedded video for presentation. | |
Geometry | KS3 | The Penrose triangle (aka the impossible triangle – not to be confused with Curry’s paradox) is a 2D drawing of an impossible 3D shape. This presentation includes a photograph of a 3D model which, from one angle, resembles the impossible triangle. It also illustrates the steps required to draw your own. | |
Geometry | GCSE | Use the density of new-fallen snow and of snowball snow to calculate the size of the field needed to make this snowball. | |
Geometry | KS3 | A standalone spreadsheet which can be used directly by the student. It calculates the area of a polygon for a given perimeter and vice versa, allowing you to change the number of sides and also comparing with a circle. Includes questions. | |
Geometry | GCSE | A series of questions involving upper and lower bounds for a room which is to be painted. Use the upper bound of the area to find out how much paint to buy, then the lower bound to find out how much you might have left over. Includes solutions. | |
Geometry | KS3 | A guided investigation into the A4 (ISO 216) paper system. Students measure paper, look for patterns between A5, A4, A3, etc and discover the root 2 ratio between the sides. An additional part goes into detail on how the A0 paper size was chosen (the area is exactly a square metre) and what equations to solve to generate it. | |
Geometry | KS3 | Predrawn circles on a (roughly) centimetre-square grid. Students estimate the area of the circles by counting the squares within. This can then be compared to the result found using pi. | |
Geometry | KS3 | Estimate the area of a circle by counting squares, then answer the questions below to come up with an estimate for pi, and the formula for the area of a circle. | |
Geometry | KS3 | Introducing the fundamentals of compass construction – drawing a circumscribed shape by following instructions. Includes examples of circle art, and instructions for a 6 pointed star as well as a dodecagon. | |
Geometry | KS3 | Full colour key points and questions on circles. All questions involve finding the circumference from either a radius or diameter, of objects from a 2p coin to Stonehenge. Includes full solutions. | |
Geometry | KS3 | A fill-the-blanks worksheet where students need to work out the two missing elements from radius, diameter and circumference (and guess which planet names might be missing from the table, too). Requires use of circle formulae, but since no numbers are above 9 figures shouldn’t require standard form. Solutions included. | |
Geometry | KS3 | An illustration of the derivation of the circle area formula, using increasingly small slices of a circle formed into an approximate rectangle. | |
Geometry | KS3 | Using Tolstoy’s story of a man who was promised the area of land he could walk around in a day, this sheet is a slightly more interesting way of presenting the basics of circle area and circumference. Includes questions. | |
Geometry | KS3 | Requires knowledge of the circumference of circles. Uses the dimensions of a penny-farthing’s wheels and the radius of the Earth to find out how many wheel revolutions it would take to circle the globe. | |
Geometry | KS3 | Aerial photo of Colorado showing circular irrigation. Includes questions on the effect of increasing the length of the boom (radius) on the area covered. | |
Geometry | GCSE | Taking semicircular bites out of a larger semicircle, testing application of circle area calculations, but also including an algebraic aspect at the end for advanced gcse level – must be able to sketch quadratics for this bit. | |
Geometry | GCSE | A couple of circle area problems introducing the idea of fractions of a circle in the form of sectors. | |
Geometry | Other | This spreadsheet calculates the area enclosed by three circles of variable radius. The values can be altered, and the resulting calculation – as well as the formula derived for the purpose – is demonstrated. | |
Geometry | KS3 | A handful of questions to test estimation skills and build an appreication of cubic centimetres. Objects ranging from a teaspoon to a bathtub. | |
Geometry | KS3 | Various cuboid buildings with given dimensions to find the volume, culminating in the elephant building as an extension. | |
Geometry | KS3 | A practical application for volume and surface area calculations – a fuel tank in the shape of compound cuboids is being built. How much will it cost? Includes scale drawing examples. | |
Geometry | GCSE | Uses volume of a cylinder knowledge to calculate the volume of a hula hoop crisp. | |
Geometry | GCSE | Giving details of Native American dugout canoe dimensions, this worksheet requires the student to calculate the volume of half a hollow cylinder. The extension question gives the density and asks for the weight of the canoe. | |
Geometry | GCSE | Three different sets of 6 cards each – one metals, one other construction materials and one other stuff – for students to arrange in order of density. Did you know that glass is about as dense as granite? Or that butter floats, but only just? Answers (including actual densities) also included. | |
Geometry | Other | A short experiment, carried out in non-laboratory conditions, to determine how much snow you would need to melt for a pint of water. Can be used as an introduction to density. | |
Geometry | GCSE | Using information on the density of snow and the formula for the volume of a sphere, we can work out how much this massive snowball weighs. | |
Geometry | GCSE | A short starter problem on density. Gives the density of packed snow, the diameter of the snowball pictured and the volume of a sphere and asks for the weight of the snowball. | |
Geometry | GCSE | Using the density of wrought iron and a few key facts and figures about the Eiffel Tower, we calculate exactly how high the resulting cuboid would be if the entire metal structure were melted down into a cuboid with the same base area as the base of the Eiffel Tower. | |
Geometry | GCSE | Given the density, price and current world reserves of gold, students are required to calculate various things using the density formula. Involves cube rooting to find the side-length of a cube of known volume. | |
Geometry | GCSE | A slightly more complex version of All the Gold – this alternative requires the student to calculate the radius of a sphere from its volume (formula given). How big would a solid sphere of all the world’s gold be? | |
Geometry | GCSE | A compound problem involving some percentage change as well as calculating the volume of a prism and using density to calculate mass. | |
Geometry | GCSE | A worksheet involving calculations surrounding the Great Pyramid of Giza. Partly to do with volume (of a pyramid) and also density and weight, along with some problem solving skills. | |
Geometry | GCSE | To accompany pyramid.pdf, this gives solutions and answers for the problems on the Pyramid sheet. Requires use of volume and density formulae. | |
Geometry | GCSE | Using density, weight and volume calculations, these figures should enable to estimate the number of pencils required to keep one person afloat. Turns out it’s cheaper to buy a jet-ski. | |
Geometry | GCSE | A worksheet using the concepts of volume and area scale factors to draw conclusions about temperature regulation in babies. Calculates surface area to weight ratio. | |
Geometry | GCSE | Investigation of surface area and volume scale factors. A good introduction to non-linear scale factors by experiment with different cuboids. | |
Geometry | GCSE | A self-checking homework task. Enter answers and the spreadsheet tells you if they are correct. This homework uses non-linear scale factors to calculate values based on volume and surface area of a cuboid. | |
Geometry | GCSE | Photos of a full-size canoe and a 1/4 scale model, along with questions involving length (linear), area and volume scale factors. | |
Geometry | GCSE | A short worksheet on non-linear scale factors linking the Eiffel Tower with the Las Vegas replica. The replica is half the size, therefore uses a quarter of the paint and weighs an eighth of the real thing. Includes solutions. | |
Geometry | GCSE | A couple of questions on converting between volume and area scale factors in order to solve problems. | |
Geometry | GCSE | This is a Similar Shapes problem taken from the film The Englishman Who Went Up A Hill But Came Down A Mountain, requiring the calculation of the volume of a cone as a proportion of a similar cone twice the height. Includes solutions. | |
Geometry | GCSE | The volume of a cone formula can be used in conjunction with trigonometry to calculate either the weight of a pile of sand (or grain, etc) from the dimensions or the dimensions of the cone given the quantity and the angle of repose. This is simply a calculator for the problem. | |
Geometry | GCSE | An in-depth worksheet requiring the use and understanding of density as it relates to the story of Archimedes and the golden crown. | |
Geometry | GCSE | From racing snails to Voyager 1, details of distances and times are given, and speed must be calculated. This only requires use of the formula for speed without rearrangement, but the varying units of measurement add a level of challenge. Solutions included. | |
Geometry | GCSE | Animated web page demonstrating the link between the formulae for volume of these three shapes. | |
Geometry | GCSE | A comprehensive presentation of the major circle facts and theorems, beginning with naming the parts of a circle and ending with geometric proofs of the theorems. | |
Geometry | GCSE | Students may use this as a guide for discovering or verifying the circle theorems. Uses free software GeoGebra and the sheet describes the key tools they will require. | |
Geometry | GCSE | A webpage containing a geometry applet allowing the user to play around with circles in order to get to grips with the main circle theorems. | |
Geometry | GCSE | Worded descriptions of the circle theorems with space below to draw the relevant diagram onto a circle. | |
Geometry | KS3 | On the surface a simple rearrange the pieces activity, but putting these shapes together to make a T shape is surprisingly challenging. This file includes a print-out sheet and on-screen shapes to move and rotate. | |
Geometry | GCSE | Problem involving vectors which works towards proving why the midpoints of the sides of any quadrilateral join to make a parallelogram. | |
Geometry | KS3 | An accompaniment to an origami cube activity – photographs of each stage, set on a loop. | |
Geometry | Other | An introduction to the Reuleaux Triangle, instructions on how to construct that and other regular shapes of constant width using compasses, extension questions involving perimeter and diameter (comparing to circles) and a description of how to construct irregular versions. | |
Geometry | GCSE | Clear descriptions and examples, including explanation of the formulae in terms of a fraction of the area or the circumference, followed by a range of questions and full solutions. | |
Geometry | GCSE | Key circle facts and theorems written out, with diagrams, followed by a number of past GCSE questions along with hints (which theorems might be useful) and solutions. | |
Geometry | GCSE | This worksheet is more of a guided proof, for students who might be curious about where the cone surface area formula comes from. It’s nice how the formula drops out by comparing circles. | |
Geometry | GCSE | A brick barbecue, the Eiffel tower and a shipping container full of gold. Three classic density problems with nice illustrations and full solutions. | |
Geometry | GCSE | By sandwiching a circle between an inscribed and circumscribed hexagon, then using some Pythagoras and right angled trigonometry, it is possible to put upper and lower bounds on the value of pi. Gives pi as between 3 and 3.46. A 100 sided shape would give pi accurate to 3 decimal places. | |
Geometry | GCSE | Calculating the length of the Indy 500 racetrack using the circle circumference formula, then using this information to calculate how fast a lap should be based on certain given information. Full solutions included. | |
Geometry | KS3 | Based around isometric drawing, but includes questions on volume and surface area. | |
Geometry | GCSE | A self-differentiated worksheet making use of the monopoly board format to present a few questions on the three main types of angle that can be identified within parallel lines. Full solutions included, along with extension section. | |
Geometry | KS3 | Name the common quadrilaterals, identify their properties, use a flow chart and decide which ones qualify as more than one (eg a rhombus is also a kite, a square is also a rectangle). | |
Geometry | GCSE | Extension work on surface area and volume – what happens to the surface area to volume ratio of a shape such as a cube or a sphere when it is sliced in half? What about a cylinder? How many ways are there to slice these shapes into two congruent halves? | |
Geometry | KS3 | Introduction to the concept and units of measurement for volume followed by questions involving the volume of real compound shapes such as buildings. | |
Geometry | KS3 | Calculating the area of the Adidas logo stripes using the formula for the area of a trapezium, followed by some problems involving cost of paint. | |
Geometry | KS3 | Describes the concept of area as a 2-D measure, gives some examples of common units and key techniques for a range of common shapes, followed by a series of compound area questions. | |
Geometry | GCSE | A detailed presentation on the main 3D shapes including formulae for surface area and volume, and nets. | |
Geometry | GCSE | Calculating the area of a polygon using trigonometry. | |
Geometry | KS3 | A comprehensive booklet of key construction techniques complete with clear illustrations, true measurement diagrams and questions for students. Includes full solutions. | |
Geometry | KS3 | Finding the volume and surface area of cornflakes boxes using real measurements, then using this information to solve problems. | |
Geometry | GCSE | A collection of problems that require the use of cosine rule, along with full solutions. | |
Geometry | KS3 | A detailed worksheet that leads students through the process of measuring a cuboid of their own, then calculating both the volume and the surface area. | |
Geometry | GCSE | A nice introduction to the concept of density, using common or well known objects and giving plenty of practice calculating density from a given volume and mass. Solutions included. Lots of pictures. | |
Geometry | KS3 | Loads of questions on enlargement, carefully scaffolded and building up throughout the booklet to lead students from making shapes bigger to using points of enlargement, fractional scale factors and even considering area scale factors in relation to length scale factors. | |
Geometry | KS3 | A nice application of speed distance time to thunderstorms. Using the speed of sound (and the assumption that light is crazy fast), students gradually work through the questions to find a method for predicting how far away a thunderstorm must be based on the gap between lightning and thunder. | |
Geometry | KS3 | Lots of questions involving loci, starting with straightforward concepts and gradually building up from there. Written in the form of successive mini investigations punctuated with key ideas, this covers the locus of points a fixed distance from a point, a line, a shape, equidistance, bisectors and overlapping regions. Full solutions and all designed to be done on the sheet with diagrams and space available for drawing. | |
Geometry | KS3 | A quick introduction to the Reuleaux triangle – the simplest regular shape of constant width. This shape shares many properties with a circle, but somehow manages 3 corners at the same time. Nice and easy to construct (the intersection of three equal circles), calculating area or perimeter requires use of segment area and arc length. | |
Geometry | KS3 | Beginning with rotating a single vertical or horizontal arrow from the origin by a multiple of 90 degrees, and progressing to rotation of 2D shapes from any point on the plane, this booklet gradually builds in difficulty. Complete diagrams and full solutions included. | |
Geometry | KS3 | A clear colourful introduction to surface area of cuboids using a cereal box. Students calculate the area of each face on the diagram (3D image and net both given), then find the total surface area. Solutions included. | |
Geometry | KS3 | Detailed explanation of surface area including examples, then a number of questions with clear diagrams, some with squares showing and some without. Full solutions included. | |
Geometry | GCSE | A proof of sine rule based on the area formula for a triangle, followed by examples and explanation, and a section on the ambiguous case. | |
Geometry | GCSE | Formulae given for various common 3D shapes, then an explanation of an open investigation for students to complete involving finding a common household object, measuring it, calculating both area and volume, then finding the surface area to volume ratio. For best results, students should compare three different sizes of the same type of shape, or three different shapes around the same volume. Works well in class to compare a whole group’s results, then come up with conjectures and ideas about SA:V ratio. | |
Geometry | KS3 | Detailed explanation of volume for cuboids including examples, then a number of questions with clear diagrams, some with squares showing and some without. Full solutions included. | |
Graphs | KS3 | Place your ships, then input co-ordinates (1st quadrant) to select a square. | |
Graphs | KS3 | In addition to the logic puzzle within this clip, it can be used with the Distance-Time graphs presentation to link with that topic. | |
Graphs | KS3 | Cut-outs to use when solving the Simpsons Logic Puzzle (see related video). | |
Graphs | KS3 | A description of a journey is to be converted to graph form. | |
Graphs | KS3 | To accompany the Distance-Time graphs worksheet. | |
Graphs | GCSE | A real-life distance-time graph of a journey into Sweden, travelling on foot, by train, by ferry, by bus and hitch-hiking. | |
Graphs | GCSE | To accompany the worksheet, this includes the same distance-time graph. | |
Graphs | KS3 | This spreadsheet is intended to demonstrate the links between y=mx+c graphs and everyday situations. | |
Graphs | KS3 | A sequences problem requiring the use of a graph (see accompanying worksheet). Is it better to have your pocket money increase by £2 a week, £5 a week or to double every week? | |
Graphs | KS3 | Accompanying worksheet – includes graph for students to fill in to determine when the doubling sequence overtakes the other two. | |
Graphs | KS3 | An investigation into mobile phone contracts – with a given up-front charge and a certain amount per month, which contract gives the best deal for a particular phone? Includes tables to complete as well as graphs to draw to compare. Full solutions attached. | |
Graphs | KS3 | An introduction to y=mx+c form, recognising lines, drawing lines with or without a table of values. Introduces the idea of parallel line gradients. Can be used in conjunction with Grapher.xls. | |
Graphs | GCSE | An comprehensive easy-to-use interface allows the user to change the equations of two straight lines, set them to be perpendicular or parallel, find any points of intersection, and more. | |
Graphs | GCSE | Accompanying worksheet – shows the lines from the above spreadsheet along with questions. Students need to write down the equations of the lines, identify highest and lowest gradients and y-intercepts, as well as identifying parallel and perpendicular lines. | |
Graphs | GCSE | A list of the key skills required to master straight line graphs up to GCSE level. Includes GCSE grades and shows progression through drawing a straight line from an equation through to finding the equation of a line from any point and the gradient (or parallel / perpendicular to a given line). | |
Graphs | GCSE | Examples of use of the parabola, how to draw a quadratic graph (including finding max or min from completing the square) and an introduction to the concept of a focus. | |
Graphs | GCSE | Allows the user to change the variables of a quadratic (either in standard polynomial form or in completed square form), and generate its graph. The range of x values to be graphed is also customisable. | |
Graphs | GCSE | Colour-coded examples and method for solving quadratic equations using graphical methods. Involves drawing a quadratic graph and linear graphs and reading off points. | |
Graphs | KS3 | A standalone spreadsheet task for pupil use – it allows the user to edit the speed and direction of a projectile and graphs the resulting parabola, also giving values for the resulting range and maximum height reached. Task sheet requires the student to answer using the tools given, and hopefully to think about the consequences of changing angles – how the same speed can give different ranges, how the same speed can give the same range with two different angles, optimal conditions, etc. | |
Graphs | GCSE | Relies on knowledge of a graphing program such as GeoGebra, and simply leads students through an open investigation into the types of graphs possible from a cubic function. | |
Graphs | GCSE | Examples of the three main trigonometric functions as graphs (for students to label axes) along with some questions that can be answered using the symmetries of the graphs. Extension GCSE or A-level preparation. | |
Graphs | GCSE | An introduction to the exponential curve. Students fill in a table of values, then sketch a graph representing compound interest at 20%. The graph is then used to answer questions specifically related to the value of the loan. | |
Graphs | GCSE | A set of questions on finding the midpoint of two coordinates. Uses diagrams and scaffolding questions. Includes full solutions. | |
Graphs | GCSE | Sketch the graph of a parabolic trajectory from a given equation and table of values, then answer questions related to the application. | |
Graphs | GCSE | Examples and questions on solving simultaneous equations involving one linear and one quadratic function (including circles). Full solutions included. | |
Graphs | GCSE | Examples, questions and full solutions – sketching quadratics from nicely factorable expressions. | |
M1 | A-Level | This PowerPoint quiz encourages students to recognise and interpret the specialist vocabulary of the Maths Mechanics classroom. Common phrases and sayings are converted into Mechanics-speak and the students have to guess the phrase. | |
M1 | A-Level | Alternative to the above quiz – this is a worksheet that can be used to help students identify Mechanics lingo. Common phrases and sayings need to be matched up with their Mechanics-speak versions. | |
M1 | A-Level | Aimed at teachers, but can be used by students. This goes through the process of deriving the kinematics equations we know and love from the basic principles of the definition of average speed under constant acceleration and the definition of constant acceleration. | |
M1 | A-Level | The kinematic equations of motion for constant acceleration. Enter the known quantities for initial and final speed, distance, time and acceleration, and have this calculator work out the rest. | |
M1 | A-Level | Using the kinematic (SUVAT) equations, students calculate stopping distances for cars travelling at slightly different speeds, then investigate a scenario involving a motorway crash. Uses the deceleration rate used in calculations by the Highway Code and takes into account thinking and braking distances. | |
M1 | A-Level | A series of questions requiring use of kinematics SUVAT equations, number-crunching the Red Bull Stratos space jump by Felix Baumgartner. Includes extension question set on the moon (where parachutes do little good). Full solutions included. | |
M1 | A-Level | Based on the story of Touching the Void, this worksheet requires construction of accurate force diagrams, resolving of forces on a slope including friction and tension in a rope. | |
M1 | A-Level | An application of SUVAT equations, this task investigates how much you could slow down a falling object that was too heavy to hold, and how much extra time you could buy for yourself. Includes solutions. | |
M1 | A-Level | A pulleys question involving particles moving vertically. By resolving forces and using F=ma, followed by simultaneous equations, the resulting acceleration can be found for the various stages of motion, and SUVAT equations are used to find final velocity and time. | |
M1 | A-Level | One Land Rover pulling another over a peak. A problem involving pulleys and particles on inclined planes requiring resolving of forces and solving simultaneous equations to find out if a cable can take the strain. | |
M1 | A-Level | Applying knowledge of projectile motion using 2D kinematics formulae to heaving lines on board ship. Students are required to calculate horizontal range when starting and finishing height are different. | |
M1 | A-Level | A somewhat complex projectiles problem for Mechanics module M1, involving MJ falling from a balcony and Spiderman jumping after her from a nearby building. We suspect that being caught after such a fall would have an effect as devastating as a pavement, but that’s cartoons for you. | |
M1 | A-Level | Questions involving the Warwick Castle trebuchet. Find the range given the speed, the speed given the range and finally the angle given both the speed and the range (this last involves the sine double angle formula, but this is included in the question). Includes full solutions. | |
M1 | A-Level | A question involving the two ships of Lord Franklin’s famed attempt to chart the Northwest Passage. 2-D vectors, involves minimising a quadratic to find the closest distance between the ships. Includes solutions. | |
M1 | A-Level | An involved problem which incorporates elements of each of the chapters from the M1 textbook. The theme revolves around Zorbing. Includes solutions. | |
M1 | A-Level | Detailed explanation and clarification on the differences between weight and mass, addressing the common misconceptions held by many as a result of the two being used interchangeably outside the scientific community. | |
M1 | A-Level | The Paris Gun was one of the largest pieces of artillery ever, designed to fire a shell from Germany to Paris. This worksheet investigates its properties using projectile motion. | |
M1 | A-Level | A full worked solution for a notoriously tricky SUVAT question from the AQA M1 textbook involving the time it takes a train to pass between 3 telegraph poles. | |
M1 | A-Level | A 2-page summary of the key skills required by the Mechanics 1 module. Listed under chapter headings, with space for students to indicate their level of understanding. For use when revising and identifying areas of weakness. | |
M1 | A-Level | A test with no calculations or working out – these 20 questions (with attached solutions) are designed to make sure students have understood the key concepts, and to make them dig a little deeper into how well they understand the rules and formulae they apply. | |
M1 | A-Level | A helpful booklet detailing all the main facts, techniques and formulae that are required for the Mechanics 1 exam, but not provided in the formula book. Valuable for revision or as an additional resource during teaching of the module. | |
M1 | A-Level | Designed to fit on a single side of A4 (still readable when shrunk to A6 size as a pocket-sized revision card), this summarises all the key results, facts and formulae from the AQA Mechanics 1 Mathematics module. For more in-depth revision, see the M1 Not-Formula Book. | |
M2 | A-Level | When you’re carrying a sofa with someone, what do we mean by I’ve got the heavy end? The weight doesn’t change, and it’s not even a different distance from either end. This worksheet can be used to accompany a teaching point about moments and how we can use them to understand the forces being applied in this situation. | |
M2 | A-Level | Requires the student to annotate a diagram with forces based on a photograph of a real situation, and, using resolving of forces and taking moments, to calculate unknown forces as well as finding the coefficient of friction. Based on building a house out of railway sleepers. | |
M2 | A-Level | A useful calculator for compound centre of mass problems. Currently allows the user to calculate the combined centre of mass of a uniform lamina made of up to 10 triangles, or a convex polygon of up to 100 sides. | |
M2 | A-Level | This booklet covers all the key ideas about energy from Mechanics 2, from work done to kinetic, gravitational potential and elastic potential. Includes clear explanations of conservation of energy and real-world examples of energy quantities. Full of examples and pictures. | |
M2 | A-Level | An alternate version of the Space Jump worksheet, examining the Felix Baumgartner jump from 128000 feet using kinetic energy, gravitational potential and work done. | |
M2 | A-Level | A problem combining projectile motion and elastic potential energy, based around the popular foam-dart ‘Nerf’ guns. | |
M2 | A-Level | Input the natural length and modulus of elasticity for a bungee rope, and the mass of the jumper, and not only does this calculator tell you how far down you would go, but gives you the maximum speed and acceleration, as well as allowing you to analyse the energy transfer and velocity at any given point along the way. | |
M2 | A-Level | A worksheet based around the Verzasca dam bungee jump from GoldenEye. Requires the use of elastic potential energy. Includes fully worked solutions. | |
M2 | A-Level | Details of the amount and type of energy a bungee jumper has at different points in the jump. Energy is transferred from gravitational potential to kinetic initially, then to kinetic and elastic potential, then from gravitational and kinetic to elastic. Also includes details of speed and acceleration at key points. | |
M2 | A-Level | Requires use of the basic P=Fv formula for power, and makes use of real statistics on cyclist power output to calculate maximum speeds on flat ground. Includes a refinement taking air resistance to be proportional to the square of the speed. Includes full solutions. | |
M2 | A-Level | A tricky problem beginning with vertical circles and circular motion (a small sphere rolling off a larger one), and extending it to determine, through projectile motion (M1 material, but very algebraic) where the small sphere will eventually land. | |
M2 | A-Level | Introduction to circular motion using the idea of angular speed. The Earth travels around the Sun at a faster speed, but at a slower angular speed than the Moon goes around the Earth. | |
M2 | A-Level | Using some basic formulae from the start of horizontal circular motion, we calculate the required altitude for a geostationary orbit. Gravitational force formula provided, so the only requirements are calculating speed, angular speed, and using F=ma. | |
M2 | A-Level | Questions involving horizontal circular motion in the context of banked curves on roads and racetracks, and the part friction plays in maintaining motion in a circle. | |
M2 | A-Level | A challenging activity on the application of horizontal circles in M2. Based on the concept of the motorcycle daredevil display on a circular vertical wall. Why does the driver not fall down? What is the minimum speed necessary? How does friction affect it? | |
M2 | A-Level | Accompanying spreadsheet to Round The Bend and Up The Wall. To be used either in setting questions or in an interactive investigation. Allows the user to change conditions on banked curves (including wall of death scenarios) and observe the effects on horizontal circular motion. | |
M2 | A-Level | Building on the solution to a kinematics problem, this document goes through the mathematics behind circular motion, deriving it from first principles to find acceleration and velocity in relation to displacement. | |
M2 | A-Level | Details of the difference in approach between the three main types of vertical circular motion scenarios – inner circles (ball on string, car in loop-the-loop track), outer circles (car cresting hill, object rolling off a sphere) and fixed circles (bead on a wire, roller-coaster attached to track). | |
M2 | A-Level | A fill-the-blanks revision sheet for circular motion (constant and variable speed) including a copy with sections filled in. Contains a summary of all key information required for the course. | |
M2 | A-Level | Based on the Fifth Gear / Dunlop loop the loop stunt using a normal car and a 12m diamter loop of track. Asks questions involving minimum speeds and maximum normal reactions – the two main concerns of the stunt team setting up the stunt. | |
M2 | A-Level | A tricky set of questions involving the circular motion of the London Eye – a very large Ferris wheel. Made difficult because the circular motion is constant but – because it is vertical – the weight of each pod changes direction relative to the centre. Full solutions included. | |
M2 | A-Level | An explanation based on differentiation of the circular motion formulae. Not necessary for students to be able to derive, but reinforces understanding. | |
M2 | A-Level | Based on the Top Gear race between a VW Beetle and a Porsche 911, where the Beetle starts 1 mile above the finish line, this problem starts with straightforward kinematics and then energy considerations, then introduces differential equations to take into account air resistance. | |
M2 | A-Level | A 2-page summary of the key skills required by the Mechanics 2 module. Listed under chapter headings, with space for students to indicate their level of understanding. For use when revising and identifying areas of weakness. | |
M2 | A-Level | A test with no calculations or working out – these 16 questions (with attached solutions) are designed to make sure students have understood the key concepts, and to make them dig a little deeper into how well they understand the rules and formulae they apply. | |
M2 | A-Level | A helpful booklet detailing all the main facts, techniques and formulae that are required for the Mechanics 2 exam, but not provided in the formula book. Valuable for revision or as an additional resource during teaching of the module. | |
M2 | A-Level | Designed to fit on a single side of A4 (still readable when shrunk to A6 size as a pocket-sized revision card), this summarises all the key results, facts and formulae from the AQA Mechanics 2 Mathematics module. For more in-depth revision, see the M2 Not-Formula Book. | |
M5 | A-Level | A detailed introduction and derivation of the polar coordinates system (using the radial and transverse vectors frame of reference) required for AQA Mechanics 5. Explained as a generalisation of circular motion formulae from Mechanics 2. | |
Number | KS3 | A simple tool for understanding place value. Four random digits (from 0 to 9) are generated, and you have to rearrange them to make either the largest or smallest possible number. | |
Number | KS3 | Each block is the sum of the two blocks directly below it. The presentation includes some missing block problems. | |
Number | KS3 | To accompany the Number Pyramids presentation, this spreadsheet gives the opportunity to investigate rearranging the numbers on the bottom row for different totals at the top. | |
Number | KS3 | Two scenarios underlining the importance of performing calculations in the right order. | |
Number | Other | An all-singing all-dancing presentation of the mathematical convention of priority of brackets, orders, division, multiplication, addition and subtraction. | |
Number | KS3 | A PowerPoint version of the superb progression from outer galaxies to inner atoms taken from Magnet Lab at micro.magnet.fsu.edu | |
Number | KS3 | Based on the Practice/Recall/Extend/Think format, this homework activity involves research, literacy, memory, skills and stretch sections, enabling self differentiation. Involves multiplying and dividing by 10, 100, 0.1, 0.01, etc. Extension looks at numbers written as powers of 10. Includes solutions. | |
Number | KS3 | This is the numbers game from Countdown, the TV show. Shuffle the cards, choose between 0 and 4 of the large numbers, and make up to 6 in total from small numbers. Set the timer (customisable), generate your target number and off you go. | |
Number | KS3 | This is basically a random number generator with certain rules for participants to comply with. Fold your arms if it’s a multiple of 4, stand up if it’s a prime, etc. | |
Number | KS3 | The LCD display on a calculator shows numbers using combinations of 7 different sections. Which of these is used the most? Which the least? Includes clock. | |
Number | KS3 | If letters are assigned values according to where they are in the alphabet, and words are the sum of their letter values, can you find any words that score 50? | |
Number | KS3 | Gives a 5 by 5 table of multiplication questions which may be copied down and completed. Answers may be revealed by clicking the button. | |
Number | KS3 | Automatically generates times table questions based on the user’s input (specify either a range or specific numbers to focus on). Choose the number of questions, show or hide answers, and generate print-out or on-screen test pages. | |
Number | KS3 | A proportionality problem based on an odd ‘special offer’ at Sainsburys. | |
Number | KS3 | Calculates the product of two 2-digit or 3-digit numbers, giving the results of each step sequentially using the grid method. | |
Number | KS3 | Asks a variety of types of questions with negative numbers, gradually getting harder, keeping track of your score and throwing up more of the type of questions you struggle with. | |
Number | KS3 | Max and min January temperatures are shown for a variety of cities. Students must fill in the missing values for either max, min or range of temperatures (also illustrated as a chart). As an extension, students may guess which city is represented by which temperature. | |
Number | KS3 | Based on the Practice/Recall/Extend/Think format, this homework activity involves research, literacy, memory, skills and stretch sections, enabling self differentiation. Involves adding and subtracting negative numbers. Extension section begins to look at multiplying with negatives. Includes solutions. | |
Number | KS3 | Introduction to fractions by asking the question how can you share 3 pizzas between 4 people? Includes some examples of different ways of writing fractions. | |
Number | KS3 | A variety of images showing the wide scope of meaning attached to the concept of a fraction. | |
Number | KS3 | Examples, with working, for how to compare the size of two fractions, how to add fractions and how to convert between improper and mixed number forms. The values of the fractions may be altered, and steps can be advanced one by one using the spinner. | |
Number | KS3 | Uses elephants and giraffes to explain why fractions must have the same ‘name’ (denominator) in order to be added. | |
Number | KS3 | A thorough explanation ideal for consolidating early work on adding fractions. Emphasizes the key requirement (a common denominator) and gives examples. | |
Number | KS3 | Includes notes and examples for two different methods for adding fractions in mixed number form. Full solutions included. | |
Number | KS3 | Based on the Practice/Recall/Extend/Think format, this homework activity involves research, literacy, memory, skills and stretch sections, enabling self differentiation. Involves converting fractions to equivalent fractions with a given numerator or denominator, and some simplifying of fractions. Includes solutions. | |
Number | KS3 | Based on the Practice/Recall/Extend/Think format, this homework activity involves research, literacy, memory, skills and stretch sections, enabling self differentiation. Involves adding and subtracting fractions. Includes solutions. | |
Number | KS3 | Introducing the idea of finding a fraction of a given quantity. | |
Number | KS3 | This generates as many questions as desired, with the option to specify whole number answers, on fractions of amounts. | |
Number | KS3 | Based on the Practice/Recall/Extend/Think format, this homework activity involves research, literacy, memory, skills and stretch sections, enabling self differentiation. Involves finding simple percetages of amounts by converting to fractions, extending towards combining simple percentages. Includes solutions. | |
Number | KS3 | Rolling a pair of dice gives a numerator and denominator. Finding this fraction of 60 gives a number from the selection for a bingo-style game. | |
Number | KS3 | Based on the Practice/Recall/Extend/Think format, this homework activity involves research, literacy, memory, skills and stretch sections, enabling self differentiation. Involves multiplying fractions (non mixed numbers) including pre-simplifying. Includes solutions. | |
Number | KS3 | Starting with a ‘guess the topic’ combination of things with ‘cent’ in them, this introduces the idea of percentages as fractions of 100. | |
Number | KS3 | An introduction to the concept of % using picture clues, followed by questions converting between simple fractions and percentages. Includes chunking introduction, and different methods for calculating a percentage of an amount. Also includes 2 methods and a bunch of questions on percentage change (increase and decrease). | |
Number | GCSE | Designed to work as an independent investigation, students use a calculator to find the recurring decimal representation of different twelfths. The worksheet also requires students to simplify fractions to determine why some (such as 6/12) give a terminating decimal. | |
Number | KS3 | A6 sized cards containing 8 of the more common/useful percentages, their decimal and fraction equivalents and a description of the calculation they represent (eg divide by 10 then double). | |
Number | GCSE | Examples and method for calculating percentage change (increase, decrease, reverse increase or decrease). A simple explanation of the method followed by three examples. Designed for printing on A5. | |
Number | KS3 | Generates a random FDP equivalence test, random percentage of amounts questions, and random percentage increase and decrease questions, including solutions. Includes macros. | |
Number | GCSE | Developing the concept of percentage increase, decrease and reverse percentage increase or decrease through using a multiplier. Includes a table to fill in the blanks, and some interpreting of worded questions. | |
Number | GCSE | A computer-based homework. Students need to answer questions on percentages of amounts, percentage change (increase and decrease) and reverse percentage change. Also includes some compound interest questions. Work is automatically marked so students can retry questions they get wrong, and submit either by printing out or emailing to their teacher. | |
Number | GCSE | Using the concept of compound interest, this activity compares three different account options for a savvy millionaire saver. Would you rather a lower interest rate but an up-front bonus payment, or a higher interest rate but huge initial fees? Includes full solutions and graph. | |
Number | KS3 | A summary table showing some of the common methods for converting between fractions, decimals and percentages. | |
Number | KS3 | Interactive test – randomly generated at the click of a button. Includes print-out functionality. Tests conversion between fractions, decimals and percentages for the 8 common percentages: 100%, 75%, 50%, 25%, 20%, 10%, 5%, 1%. | |
Number | KS3 | The main elements of the study of fractions, decimals and percentages condensed into easy-to-read revision-style sheets. | |
Number | GCSE | An introduction to infinite series for pre-A-level students, perhaps for use as extension work when building up fraction skills. Gives the limits of a whole range of geometric series, including a neat interactive visual proof. | |
Number | GCSE | List of the first 20 unit fractions with their decimal equivalent (includes a blank copy for students to fill in themselves). Also cheat sheets for converting a fraction to a decimal and vice versa. Also gives a method for a recurring decimal with a non-recurring prefix. | |
Number | GCSE | A spreadsheet designed to give the exact decimal form of a fraction (recurring or terminating) or the fractional form of a decimal. Enter the whole number parts, the preceeding non-recurring part and the recurring section to find the fraction it represents. | |
Number | GCSE | Three questions involving upper and lower bounds. It is necessary to interpret the problem to ensure the appropriate combination of bounds for the right solution. Involves volume of a cylinder. Full solutions attached. | |
Number | GCSE | Calculating upper and lower bounds for the value of g (acceleration due to gravity) using approximate values for mass of the earth, etc. Finally using bounds to choose a suitable level of precision to use for the final answer. A good application of upper and lower bounds. Full solutions attached. | |
Number | KS3 | Using photographs to introduce the concept of ratio and proportion. | |
Number | KS3 | Four recipes with varying ingredients to be shared out in the same ratio for varying numbers of people. Includes additional questions. | |
Number | GCSE | Using ratio to investigate the gearing of Warwick Castle mill. For full functionality, also download the embedded video. | |
Number | GCSE | To go with gears presentation. | |
Number | GCSE | To go with gears presentation. | |
Number | GCSE | To go with gears presentaiton. | |
Number | KS3 | Definitions and helpful explanations of factors, multiples and prime numbers. Compares multiples to multipacks, and factors to factorys to aid memory. | |
Number | KS3 | A series of calculations (some to be done mentally, some with a calculator) that require the use of BODMAS (or BIDMAS) to get the correct order of operations. | |
Number | KS3 | Primarily for speeding up the process of factorising numbers, but useful in general for division. This sheet gives a brief summary of checking for divisibility by 10, 5, 2 and 3. | |
Number | KS3 | An introduction to fractions that begins with division. Some division questions have whole number answers. For those that don’t, we just cheat and leave the division sign in place. It hinges on using fraction notation for normal whole number division, then being happy leaving our answer as a fraction if it won’t give an integer. A nice way to understand equivalent fractions, too, before losing sight of whole numbers. 12 over 6 is equivalent to 18 over 9. | |
Number | KS3 | A few questions which all require division, but – crucially – require a firm grasp of context to give a sensible answer. For some, leave a remainder, for others, write as a rounded decimal or a fraction, or round your answer up, or down, or even more complicated. Solutions included. | |
Number | KS3 | A list of numbers in either fraction, decimal or percentage form to be placed in their correct position on the number line below. Full solutions included. | |
Number | KS3 | Fractional numbers written in a wide variety of ways, in a grid of match-up cards. Top-heavy, mixed numbers, divisons, number lines, sharing problems, additions, decimals, percentages. | |
Number | KS3 | Designed to help students who struggle with their tables to break it down into a more manageable task by considering the symmetry of the multiplication table and key results like the square numbers. | |
Number | KS3 | A few questions involving 2 or 3 digit multiplication, some involving decimals and a number of word problems with context. Solutions included. | |
Number | KS3 | Some beautiful colourful grids of the numbers from 1 to 100… in prime factor form. Colour-coded by total number of factors, primes stand out, and make the rest easy to identify by position, too. Excellent for HCF and LCM work as a cheat sheet for students. Also a nice way to check answers for 2 digit prime factorisation problems. | |
Number | KS3 | Beginning with the concept of factors and primes, then calculating the prime factorisation of the first 20 integers. | |
Number | KS3 | Interactively demonstrate Erastosthenes’ sieve for the first 10,000 numbers. | |
Number | GCSE | Finding reciprocals of a variety of numbers in different forms, plus a graph to sketch of the function y=1/x. | |
Number | KS3 | Adding, subtracting, multiplying with negative numbers. Includes full solutions as well as examples. | |
Number | GCSE | Calculations involving a large shipping container requiring not only use of bounds within calculations, but interpretation of results to solve related problems. Full solutions included. | |
Number | KS3 | Simple starter aimed at understanding why adding and subtracting fractions works the way it does (adding like objects analogy, leading on to why we change denominators if they are different). | |
Number | KS3 | Prime factorisation introduction. Explanation of factors and primes and demonstration of method. | |
Number | KS3 | A 1 to 100 grid where you can colour all the multiples of any given digit from 2 to 9 at the click of a button, revealing patterns and prime numbers. Includes a common factors facility, and a print-out for students to do a similar activity, filtering out the prime numbers. | |
Number | KS3 | A simple worksheet with an example and half a dozen numbers for students to break down into their prime factors. Includes reminders of divisibility rules and the first few prime numbers. | |
Number | KS3 | This elegant device calculates the prime factors of a number (up to the seemingly arbitrary limit of 15838) and displays the results of two different decompositions in Venn diagram form, in order to identify common factors and multiples. Also gives HCF and LCM. | |
Number | KS3 | A tool for finding the prime factor decomposition of a number (up to 100,000). It has facilities for HCF and LCM calculation, and a searchable database of the numbers within its range, for observing patterns within, for instance, numbers with an odd number of factors. | |
Number | GCSE | A thorough comparison of the two main methods for finding the highest common factor and lowest common multiple, indicating the value of the prime factor method for large numbers. | |
Number | GCSE | A few statements about primes for students to consider or research. Includes solutions: often ‘true-ish’, or ‘unknown’ but with additional background information such as the proof of infinite primes and possible formulas for the nth prime number. | |
Number | GCSE | Open-ended extension investigation into the link between the prime decomposition of a number and the total number of its factors. The link involves the powers of the prime factors, and this document includes tips for problem solving, specific starting point options and some extension questions. Solutions included. | |
Number | KS3 | An interesting concept, producing patterns of dots out of numbers. Alter the base number, and the invisible multiplication table will alter its shading pattern based on its factors. See distinctive patterns emerge for primes, squares, cubes, etc. | |
Number | KS3 | An accompanying hand-out for students to study for the numbers 1 to 32 for the above spreadsheet. | |
Number | KS3 | How many grains of wheat are there in a field? This activity (worksheet followed by instructions for teacher) requires problem solving skills, and the use of a series of facts to find the solution. | |
Number | GCSE | A step-by-step spreadsheet demonstration of a method for finding estimates for common exam-style calculations. | |
Number | KS3 | Can be used as an introduction to trial and improvement, photos of lots of bottles – you have to guess how many. Giving too high or too low each time usually narrows it down within half a dozen guesses. | |
Number | GCSE | Allows the user to specify square or cube roots, to pick a number and to fill in a trial & improvement table. Values (and ‘too high’ or ‘too low’) are automatically calculated, and a graph shows the progress towards the solution. | |
Number | GCSE | A short head-scratcher designed to highlight the concept of percentage decrease followed by percentage increase. | |
Number | KS3 | Three good ways to compare value: make the quantity the same, make the price the same or calculate the cost per item. A series of carefully created questions that lend themselves to these three methods follow (with full solutions) to develop a clearer sense of this fundamental multiplicative relationship. | |
Number | KS3 | A nice quick starter / introduction to sharing in a ratio. How should these two brothers share £600 if one worked 2 days and the other 3? Good for discussion. One person makes a suggestion, then we discuss which person might be happier with it. Can we find a fair solution, and what method would do this consistently in general? | |
Number | KS3 | A short test of a few key elements of early fractions work, beginning with finding half of a number and working through to equivalent fractions, decimals and percentages, then adding and subtracting where denominators need changing. Works well as a diagnostic tool. | |
Number | KS3 | Using the government regulations on ratios of adults to children in nurseries, a range of questions to answer, with full solutions included. | |
Number | KS3 | A neat idea where students need to multiply by 2 to work out the next number along, and by 5 to work out the next number up. This avoids the danger of multiplication tables where students are simply adding, but also gives a range of routes to fill in missing values. Going diagonally up? Just multiply by 10. Patterns can be picked out and discussed. | |
Number | KS3 | Finding equivalent fractions with a given denominator (integer multiple of given fraction), comparing fractions using common denominators, then adding or subtracting. Three short sections, each of which relies on the use of common denominators. | |
Number | GCSE | Can light get half-way around the world while sound is still getting its boots on? Similar to Wheat Grains, this is an activity which requires problem solving skills – all the required information is given on fact cards, and helpful problem solving hints are also given. | |
Number | GCSE | Accompanying presentation – gives illustration and solutions for the activity above. | |
Number | GCSE | A question that requires an understanding of factors and multiples, and the nature of square numbers. | |
Number | KS3 | The inventor of chess is said to have asked for one grain of rice for the first square, two for the second, four for the third and so on. This little fact sheet uses powers of 2 to investigate just how much rice this would represent (and how much it would be worth). | |
Number | Other | An introduction to continued fractions. Students follow an example with a method for turning any fraction into a continued fraction, including the common linear notation. A good prop for an open-ended investigation into this topic. | |
Other | A-Level | 60 questions taken from a graduate psychometric test designed to measure mechanical reasoning, including spatial awareness as well as understanding of some fundamental mechanical laws. These are often linked to the fundamental elements of various types of machinery. | |
Other | A-Level | Solutions to the Mechanical Reasoning test above – Answers to the multiple choice questions as well as explanations (intended to be thorough, but not overly technical). | |
Other | A-Level | Identical to the Mechanical Reasoning test above, but as a PowerPoint presentation. For Answers see Mechanical Reasoning Answers. | |
Other | KS3 | The Seven Bridges of Konigsberg problem is the beginnings of graph theory, but is a good spatial activity, and this version explores the possibility of destroying or building bridges to alter the situation. Use with accompanying worksheet. | |
Other | KS3 | Accompanying worksheet, explaining the Seven Bridges problem – can be used to accompany the PowerPoint or as a standalone activity. Remember, there is no solution (aside from a proof of impossibility) for the original problem, so it may take some time! | |
Other | KS3 | A complete activity pack including teacher notes, scope for extension and worksheets leading students through the invention of Braille. Investigates the number of combinations possible with 6 spaces and concludes with the Braille alphabet and writing in code. Involves looking for patterns, a systematic approach and powers of 2. | |
Other | GCSE | A combination of ‘Venn That Tune’ and Braille, use with the accompanying presentation which includes answers. A code-breaker with a twist. Some intelligent guesswork is required, and once you’ve cracked the code you’re still only halfway there. | |
Other | GCSE | To accompany Braille Venn worksheet. | |
Other | Other | Questions requiring some form of number answer, but not especially mathematical. Some customising will be necessary – one question requires estimates of sunrise and sunset that day (can be found by googling). | |
Other | Other | Questions ranging from the height of the Eiffel tower to the weight of the largest ship. Multiple choice, but even the wrong answers have pictures to go with them. | |
Other | Other | Designed to be nearly impossible to answer, but chock full of interesting facts, these 12 slides of christmas take anything from 30 to 60 minutes depending on how you play it. | |
Other | Other | A collection of problems that require calculation, careful deduction or out-of-the-box thinking skills. These are primarily lateral thinking questions. | |
Other | Other | A collection of problems that require calculation, careful deduction or out-of-the-box thinking skills. These are primarily logical questions. | |
Other | Other | A collection of problems that require calculation, careful deduction or out-of-the-box thinking skills. These are primarily mathematical questions. | |
Other | Other | A 4-minute video presenting the maths behind Santa’s Christmas eve exploits. | |
Other | Other | A list of challenges for students to attempt outside the classroom – extra-curricular investigations, using maths in other contexts, etc. | |
Other | Other | An introduction to modular arithmetic for bright students, designed to be used as a more or less independent investigation, discovering some of the properties of congruence with addition, multiplication and exponentiation. | |
Other | A-Level | Some examples of useful websites and YouTube channels that will enhance the enjoyment of a Mathematics A-level course. | |
Other | A-Level | Booklet of A-level topics – a taster for pre-A-level students to give them an idea of the material – covers circle geometry, kinematics and binomial theorem. | |
Other | KS3 | My version of the game – you buy lobster pots, place them in the bay or out at sea and reap the rewards, calm or storm. This includes a calculator as well as sheets to print off for a class, so you can play alongside without all the tedious adding up. | |
Other | KS3 | Nice end of term variation on battleships – the whole class fills in their 5 by 5 grid (with treasure, ‘rob someone’, ‘scuttle a ship’, etc) then as you hit squares in a random order, students carry out their actions, alternately ammassing wealth and destroying/perloining that of their friends. | |
Other | KS3 | A variant on the popular Mastermind peg game. You can vary the digits allowable in the four digit mystery code. The computer sets a code and you have to guess it in a limited number of attempts. Each guess yields some information (right number, wrong position or right number, right position). | |
Other | Other | How heavy is Niagara Falls? Exactly how much does the water currently going down the falls weigh? | |
Other | Other | A simplistic simulation of stock market currency trading. You begin with a certain amount of capital, and by observing the fluctuations of the market attempt to make money through buying and selling. | |
Other | Other | Designed as extension material beyond GCSE, students use a velocity-time graph to deduce the kinematics equations (or SUVAT equations), then answer questions using them. Designed as a standalone task, and includes full solutions. | |
Other | Other | Introduces the formula for gravitational force, derives the formula for acceleration due to gravity, and asks students to calculate acceleration due to gravity for a variety of bodies in the solar system. Concludes with three ‘paradoxes’ involving apparent weight. Full solutions included. | |
Other | GCSE | Making use of the AQA sheet of formulae to learn for the new GCSE, but adding extra details to enable students to make sense of the various formulae. They will be easier to memorise (and use) if they are understood more fully. Extra info on why they are true, and common errors also included. | |
Other | Other | A self-assessment diagnostic tool for students to use. Could be used part way through a topic or while working on an extended task. Students answer brief questions about how confident they feel, what they have learnt and what they still want to develop. | |
Other | KS3 | A deceptively tricky little puzzle, this is a capital T shape which has been cut into 4 pieces using straight cuts, and is surprisingly difficult to put back together due to certain unconscious assumptions we often make. | |
Other | GCSE | Can be used in planning or for pupil self-assessment. Gives details – and examples – for specific grades. | |
Other | GCSE | Covering just a handful of key topics for Higher GCSE, this gives a detailed step-by-step method along with examples, for how to pick up all the marks for Pythagoras, Right-angled Trig, Non-Right-angled Trig and Simultaneous Equations. | |
Other | Other | This spreadsheet is a template you can use to perform a detailed breakdown of a test or exam. Pupils names are entered at the top, the topic of each question, along with the number of marks, is entered down the side, then when results are inputted for each pupil not only are totals and grades (from customisable grade boundaries) automatically calculated, but poorly done questions are flagged up for teacher and students to take note of. | |
Other | Other | Summary of problem solving techniques. Encourages the user to ask: What do I know?, What do I want? and What will I need? along with information about what to do when you get stuck while solving a mathematical problem. For display or hand-out. | |
Other | KS3 | Nice starting point for introducing the subject – give students an idea of where our 70,000+ year old subject began, and how cultures all over the world developed the same concepts in order to solve the same problems. Also includes a summary of the broad areas of the modern subject (quantity, structure, space, change). | |
Other | Other | In answer to that oft-asked question, What’s the point of Maths? This booklet is a brief outline of a few reasons why Maths is important, broken down into: 1) Why maths is a big deal, 2) How maths might be useful to you and 3) The value of learning something even if you will never need it again, ever. PRINT VERSION: Columns | |
Other | Other | In answer to that oft-asked question, What’s the point of Maths? This booklet is a brief outline of a few reasons why Maths is important, broken down into: 1) Why maths is a big deal, 2) How maths might be useful to you and 3) The value of learning something even if you will never need it again, ever. WEB VERSION: A4 | |
Other | Other | Based on the Practice/Recall/Extend/Think format, this is actually designed for teachers, giving some advice on how a maths teacher can improve their mathematics and their teaching in the classroom. | |
S1 | A-Level | Taking advantage of the built-in binomial calculator of Microsoft Excel, this is a useful tool for checking solutions or quickly finding answers when dealing with the binomial distribution. Includes cumulative, avoiding the need for statistical tables. | |
S1 | A-Level | Makes use of Excel’s built-in statistical functions to calculate values from the normal and binomial distributions. Gives values as found in the statistical tables as well as more precise values so it can be used to check answers using tables. Includes inverse normal (percentage points) and cumulative binomial. | |
Statistics | KS3 | Interactive demonstration of the idea behind the mean average – four buckets contain varying numbers of bricks. By removing bricks from one and adding to another, we can even out the number in each until it is the same. This gives the average. | |
Statistics | KS3 | An introduction to the three averages, using limericks and investigating word length. | |
Statistics | GCSE | A presentation – best accompanied by print-outs of the slide with the limericks on – which helps to teach the basics of mean, median and mode from a frequency table. | |
Statistics | KS3 | Details of how to calculate the mean, median and mode for a list of numbers. | |
Statistics | KS3 | Based on the popular TV show, this works best if you have envelopes containing monopoly money (sheets available to print out in spreadsheet). Eight different values (changeable if need be) which can be removed, and an option to show the mean value. This version of the game lets players act as banker and make decisions based on expected values. | |
Statistics | GCSE | How to calculate the mean, median and mode from frequency tables (does not include grouped frequency). | |
Statistics | GCSE | Questions that require some careful thinking (algebra comes in handy but is not necessarily essential), involving averages. In particular, interpreting changes in the mean average when members are added or removed from the population. Full solutions included. | |
Statistics | GCSE | Based on the number of £5, £10, £20 and £50 notes in circulation in the UK, this uses mean, median and mode from a frequency table. Incorporates a sheet with hints, and another sheet with full solutions. | |
Statistics | GCSE | A frequency table detailing the heights of all 43 US presidents. Question involving estimating the mean from a frequency table. Full colour-coded solutions included. | |
Statistics | KS3 | Using a baby growth chart to answer questions involving percentiles. Includes some information on definitions of median, quartiles and percentiles. | |
Statistics | KS3 | A few short questions using data on income to interpret quartiles and percentiles. Includes some open ended questions and solutions. | |
Statistics | KS3 | A questionnaire with errors hidden in every question (some more important / obvious than others, some questions have more than one problem). Designed to draw attention to frequently encountered errors with questions. | |
Statistics | KS3 | Accompanying presentation giving descriptions of common problems with the survey worksheet and key points to remember. | |
Statistics | KS3 | Outlines the basics of data. Includes details of qualitative and quantitative, and continuous and discrete data. | |
Statistics | KS3 | To accompany Types of Data presentation. A fill-in-the-blanks sheet along with an additional task with a variety of examples of data collection. You are required to say what kind of data it represents. | |
Statistics | GCSE | A sheet for students to complete as part of a discussion of key terms required for the statistics element of a Maths GCSE. Includes types of data, types of data collection and forms of sampling. Includes full solutions. | |
Statistics | KS3 | This is a survey that can be completed in the classroom, on a laptop. Results are automatically collated and displayed both as results tables and as bar graphs on separate sheets. The questions currently are based on learning maths, but can be customised in the Instructions sheet to whatever you want. | |
Statistics | KS3 | Gives tips of what to watch out for when producing survey questions, then some introductory tasks (with timers) to build skills. | |
Statistics | KS3 | A summary of the data collection cycle, from predictions through questioning, collecting data, collating results, presenting data and drawing conclusions. | |
Statistics | KS3 | To accompany data collection cycle presentation. | |
Statistics | KS3 | Including a print-out version for students to use, this produces a pie chart based on values you can easily enter during a lesson. Categories easily customisable, numbers may be typed in or edited using a spinner. | |
Statistics | KS3 | An introduction to venn and carroll diagrams. | |
Statistics | KS3 | Using input data, a 2-set venn diagram is displayed, along with a selection of questions on the relative frequencies involved. 3-set venn diagram work in progress included. | |
Statistics | KS3 | Describes some of the most common types of graphs for representing data, along with some of their advantages and disadvantages. | |
Statistics | GCSE | Description of the basics of scattergraphs, including correlation and lines of best fit. | |
Statistics | GCSE | For drawing a scattergraph in Excel. Includes match-up cards for printing out to go with scattergraphs.ppt. | |
Statistics | KS3 | An all-in-one worksheet on scattergraphs including graph paper comparing the asking price and mileage of a fair selection of a specific car from AutoTrader. Includes questions on line of best fit, interpolation and extrapolation. | |
Statistics | KS3 | Examples from newspapers of artistic graphs which distort the true data by one means or another. | |
Statistics | KS3 | A list of creatures to memorise, with built-in timer. Designed to provide a fun talking tool and to use a graph to compare results and discuss reasons. Laws of primary and recency, etc. | |
Statistics | KS3 | Pictures to go along with the list in memory.xls. May be used before or after, for comparison. | |
Statistics | KS3 | Introducing the probability line, basic probability notation (fractions) and the basis for an experimental probability activity with sweets. | |
Statistics | KS3 | Using either one or two dice, the game involves making predictions about the outcome of the roll. Screen shows one or two dice, or a coin displaying H or T. Can be used with a class. Eg, have people guess if the roll will be a prime number, a multiple of 3, etc. | |
Statistics | KS3 | Kids can bet on the outcome of this pseudo-horserace. Each of the numbers from 1 to 12 are runners in this race, where a horse gets to move forward if its number is the sum of two D6s. In most cases, of course, number 7 will come in the top 3. Now includes 3-Dice version, How Many Heads coin version and relative frequency record log option. | |
Statistics | KS3 | A simple version of a fruit machine – click the button and see what colours show up. Useful for an interactive probability demonstration. Includes graphics of tree diagrams to show the range of options. | |
Statistics | KS3 | A number of counters must be distributed across the numbers 1 to 12, and a counter is removed when its number comes up as the sum of two dice. Experiment to find the optimal distribution of counters to minimise moves. | |
Statistics | KS3 | Demonstrates the nature of large samples for a probability distribution. Originally set up with the probabilities for the sum of two 6-sided dice, the outcomes and probabilities are completely customisable, and the number of trials can be altered. Pressing F9 runs the trial afresh, and the reliability of large samples is made clear. | |
Statistics | KS3 | A homework task requiring students to throw a pair of dice thirty times (or use random.org to do it for them). The investigation is intended to alert students to the fact that some totals are more common than others, and begin to get them thinking about why. Could be incorporated into whole class results subsequently. | |
Statistics | KS3 | A visual representation of randomness. A simple application of conditional formatting to show up in a grid (either a 10 by 10 or a 50 by 100 grid) the outcome of any simple binomial experiment. Set the probability (eg 1/6) and each square will change colour with that probability. Press F9 to refresh. | |
Statistics | GCSE | An introduction to the Lincoln Peterson index method for estimating populations. Fish are caught, tagged and released. A second sample is taken and the proportions used to infer the size of the total population. Relative frequency gives an estimate for probability which in turn predicts relative frequency. Can be used in conjunction with Counting Fish excel simulator. | |
Statistics | GCSE | Can be used in conjunction with Counting Fish worksheet. Allows the user to choose how many fish to tag and how large the sample taken subsequently should be, and awards payment based on the accuracy of predictions. Uses macros. | |
Statistics | GCSE | Questions on relative frequency, as an indicator of probability. Includes the idea of expected values. Automatically indicates when an answer is incorrect, so the homework can be checked and changed before being submitted. | |
Statistics | GCSE | Tree diagram for three consecutive biased coin tosses. Students can add the probabilities and use them to answer questions given. | |
Statistics | GCSE | Probability calculations using Scrabble tiles. With and without replacement questions, including ‘and’ and ‘or’ probabilities. | |
Statistics | KS3 | A simple card game based on probabilities – the player has to guess whether the next card will be higher or lower (5 cards altogether, from a 13 card suit). Optional computer calculation to give probabilities. | |
Statistics | KS3 | Roll a die as much as you like, to rack up a score of 100. Roll a 6 before you bank for your turn, however, and you forfeit that turn’s accumulated points. Available as a 1- or 2-player game. | |
Statistics | GCSE | This classic probability problem goes against intuitive thinking. The first step is to convince the audience that switching doors is a good idea (use the interactive spreadsheet to play the game). The second step is to explain why (use the accompanying presentation to illustrate the way probabilities change as new information is revealed). | |
Statistics | GCSE | To accompany Monty Hall presentation. | |
Statistics | GCSE | Ever tried to choose the biggest dessert at a restaurant, when they come out one by one? The theory of algorithms for choosing the best of a set of items when you only have the option to choose one at a time is an interesting one to investigate. Uses macros. | |
Statistics | GCSE | Using conditional probability and talking through all the steps, investigating false positive and false negative rates and what they really mean for medical tests. Uses tree diagrams and Carroll diagrams. | |
Statistics | KS3 | A Venn diagram version of the False Positive worksheet, using the diagram to interpret false positive results and determine the chance of being sick given a positive test result rather than the other way around. A notoriously confusing concept, made easier by considering frequencies rather than abstract probabilities. Full solutions included. | |
Statistics | KS3 | Toss a coin 20 times and record the results (HTT…), but first, cheat – write a series of Hs and Ts that seem random, and see if your teacher can guess which was the coin and which was you. Based on the fact that true randomness throws up more runs, and longer ones, more often than we naturally expect. | |
Statistics | KS3 | Introducing the concept of Venn diagrams for categorising various flags. Includes questions on probability which the diagrams help you to answer. Full solutions included. | |
Statistics | KS3 | An excellent introduction to some of the history and usefulness of a rigorous approach to chance and uncertainty. | |
Statistics | KS3 | For students to complete, investigating the distribution of scores when adding the total of two dice. While one individual’s results may not be too convincing, average a whole class’s results and it’ll be remarkably close to the theoretical distribution. | |
Statistics | KS3 | Like the dice version, this requires students to count the number of tails when 6 coins are tossed. Yields a binomial distribution. | |
Statistics | KS3 | Interactive demonstration of probability – set up your own distribution to generate random samples or use a basic binomial calculator to tell you how many of your results you would expect to lie between various numbers. | |
Statistics | KS3 | A few questions taking information from a table, involving conditional probability. | |
Statistics | KS3 | Mutually exclusive, and independent, events. Practice combining probabilities using scrabble tile frequencies. | |
Statistics | KS3 | Blanks for Venn diagram questions – two to a page, one sheet with 2-set Venn diagrams, one with 3-set diagrams. | |
Statistics | KS3 | Involved problems requiring Venn diagrams to solve, including hints pages and full solutions. | |
Statistics | KS3 | Introduction to the concept of categorizing using Venn diagrams with a few non-numerical examples, then one involving primes and factors. | |
Statistics | Other | A bit of fun based on the idea of random walks. Students generate a random direction (up/down/left/right) and race to see whose path leaves the square first. Designed for work in pairs, no dice needed. Can lead into investigations involving relative frequency and the laws of large numbers. | |
Statistics | GCSE | A few questions on the topic of musical and mathematical ability to explain conditional probability. Full solutions included. | |
Statistics | GCSE | A mathematical analysis of that popular XKCD cartoon on statistics. Uses conditional probability to determine whether or not the sun has gone nova. | |
Statistics | KS3 | Uses frequencies rather than probabilities to develop a good conceptual basis for tree diagrams. |