| Shape
and Space |
 |
Area
of
a Triangle
video: A
20-second clip demonstrating where the formula for the area of a
triangle comes from using cardboard. |
|
Area
of
a
Parallelogram video: A similar idea - cut a piece off one side and
stick it on the other to make a rectangle. |
|
Area
of
a Trapezium
video: A
more complicated formula, but can still be demonstrated with a bit of
cardboard and some cutting and moving. |
 |
Area and
Perimeter investigation: 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. |
 |
Circles
info sheet:
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. |
|
Accompanying
question sheet:
Can be used as a standalone worksheet, but relates to the previous info
sheet and has some more challenging questions based on area and
circumference. |
|
Area
of
common
shapes
interactive resource: New dimensions are given to the displayed shape
at the click of a button, and the answer (and working) displayed as
required. |
|
Area
and Perimeter Calculator interactive
resource:
Create your own shapes, and have Excel automatically calculate the area
and perimeter (toggle button to show/hide). |
|
Area
worksheet: A
series of
questions (with attached answer sheet) testing area calculations for a
variety of compound shapes. |
|
Area
Algebra
interactive
resource: 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. |
 |
Common
Volumes
quiz: A
handful of questions to test estimation skills and build an
appreication of cubic centimetres. Objects ranging from a
teaspoon to a bathtub. |
|
Counting
Squares
interactive
resource: This spreadsheet provides randomly generated rectangles or
irregular shapes made from squares, and displays the area and perimeter
on demand. |
|
Cuboid Surface Area: A
presentation illustrating the method for calculating, then an
interactive spreadsheet where random questions are generated and
solution working fully shown for each one. |
 |
Shack
worksheet:
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. |
|
UK
Area
worksheet:
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. |
|
Cube
Origami presentation: An accompaniment to an origami cube activity -
photographs of each stage, set on a loop. |
|
Volume
of Buildings
presentation: Various cuboid buildings with given dimensions to find
the volume, culminating in the Elephant Building as an extension.
|
|
Volume of a Hula Hoop
presentation: Uses volume of a cylinder knowledge to calculate the
volume of a hula hoop crisp.
|
|
Area of Pacman: A couple of
circle area problems introducing the idea of fractions of a circle in
the form of sectors. |
|
Morse Code interactive
resource: Type in a hidden message to have the morse code version
appear on the screen. Decoder by the side to help solve the
puzzle. |
|
The Impossible Triangle
presentation: 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.
|
|
Combined Circles area:
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. |
|
Circle Theorems
presentation: 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. |
 |
Circle Theorems
Investigation dynamic software: Important parts of the circle are
already constructed, with relevant lengths and angles marked. By
altering various points, the results of the circle theorems will become
apparent. |
|
Circle Theorem 1: The angle
at the centre is twice that at the circumference. Interactive
demonstration. |
|
Circle Theorem 2: The angle
in a semicircle is always a right angle. Interactive
demonstration. |
|
Circle Theorem 3: Angles in
the same segment are equal. Interactive demonstration. |
|
Circle Theorem 4: The sum
of opposite angles in a cyclic quadrilateral is 180 degrees.
Interactive demonstration. |
|
Circle Theorem 5: The angle
between a chord and a tangent is equal to the angle in the alternate
segment. Interactive demonstration. |
|
|
| Polygons |
|
Properties
of
Polygons
presentation: Illustrations of parallel and perpendicular lines
followed by line and angle properties of common quadrilaterals.
|
|
Guess
my
Quadrilateral
interactive resource: A series of questions which can be answered with
a yes or a no, progressively ruling out quadrilaterals that don't fit
the description (traffic light indicators) until it can tell you
exactly which four sided shape you are describing. |
|
Square
dynamic
geometry
resource: Designed by A. White, you can tug at the corners and move the
shame around, changing its size, but the fundamental constraints of the
square will still be preserved. |
|
Rectangle
dynamic
geometry resource: As above. |
|
Parallelogram
dynamic geometry resource: As above. |
|
Rhombus
dynamic
geometry resource: As above. |
|
Kite
dynamic
geometry resource: As above. |
|
Equilateral
Triangle dynamic geometry resource: As above. |
|
Isosceles
Triangle
dynamic geometry resource: As above. |
|
Tessellation
of
quadrilaterals dynamic geometry resource: With angles clearly marked
and labelled, this tesselation neatly demonstrates how any
quadrilateral can be tessellated. |
|
Tessellation
presentation: A few slides with examples of Escher tessellation.
|
|
|
| Angles
and Trigonometry |
|
Angle
Rules: The 5 most common angle rules, and an introduction to angles in
a polygon by splitting into triangles. |
|
Triangle
Angles
worksheet: A
collection of triangles where missing angles must be found using sum of
angles in a triangle and isosceles and equilateral properties.
|
|
Parallel
lines
dynamic geometry resource: |
|
Triangle
angles
dynamic geometry resource: |
|
Photo
Trigonometry:
Estimate the number of people in a large group photo by using
right-angle trigonometry to calculate the area of the (roughly)
triangular space. |
|
Ladder
Trigonometry: Investigation questions involving the 4:1 rule of ladder
safety. |
|
Square
Area: This rather
tricky problem requires only Pythagoras' Theorem and some basic algebra
to solve. All is explained in the presentation. |
 |
Sine Rule: 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. |
|
|
| Algebra |
|
Guess
the Rule
interactive
resource: 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. |
|
2-step
Function
Machines worksheet: Solving equations by means of function machine
notation and reversing operations. |
|
Equations
worksheet: A
customisable worksheet where you can input your own coefficients and
preferred solutions and both a question and answer sheet will be
generated automatically. |
|
Coins
and Cups
Algebra
presentation: Demonstrating the principles of removing the same thing
from both sides using a coins in cups analogy. |
|
Think
of
a Number
worksheet: A basic working-backwards function machines worksheet.
|
|
Matchbox
Maths
worksheet:
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. |
|
Simplifying
Expressions
bingo activity: A grid of expressions to be read out, with a class set
of bingo grids containing the same expressions in their simplest form.
|
|
Area
Algebra
interactive resource: 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. |
|
Linear
Equations Generator
interactive resource: Completely customisable random equation
generator. Click for a new equation, then click to go through
the
stages of solving, including explanations. |
|
Quadratic
Generator
customisable worksheet/classroom tool: Generates a completely
customisable series of double brackets and quadratics (toggle view
either one or both) for printing or on-screen use. |
|
Applied Quadratic example:
Worked example question with a given quadratic describing ballistic
motion. |
|
Formulae
presentation: To accompany the following resources as part of a
rearranging formulae activity. |
 |
Changing
the
Subject sheet 1: Examples of formulae to rearrange, making each term
the subject. |
|
Changing
the
Subject sheet 1 Answers |
|
Changing
the
Subject sheet 2 |
|
Changing
the
Subject sheet 2 Answers |
|
Changing
the
Subject sheet 3 |
|
Changing
the
Subject sheet 3 Answers |
|
Simpson's
Rule
formula
manipulation task: Proving that the volume of certain shapes can be
found exactly using Simpson's Rule. |
|
Sphere-Cone
formula
manipulation task: Combining volume formulae to find a formula for the
volume of a newly created 3D shape. |
|
Gunshot
formula
manipulation
task: Using constant acceleration SUVAT equations to prove results
about firing a gun into the air. |
|
Quadratic Graphs
presentation: Examples of use of the parabola, how to draw a quadratic
graph (including finding max or min from completing the square) and
investigating the focus of a parabola. |
|
Quadratic Sequence: A fully
worked method for finding the nth term of a quadratic sequence. |
|
|
| Fractions
and Number |
|
Fractions
of
Amounts presentation: Introducing the idea of finding a fraction of a
given quantity. |
|
Displaying
Fractions
presentation: A variety of images showing the wide scope of meaning
attached to the concept of a fraction. |
|
Adding Fractions
presentation: Uses elephants and giraffes to explain why fractions must
have the same 'name' (denominator) in order to be added. |
|
Introducing
Ratio
presentation: Using photographs to introduce the concept of ratio and
proportion. |
|
Ratio Recipes: Four recipes
with varying ingredients to be shared out in the same ratio for varying
numbers of people. Includes additional questions. |
|
Gears: Using ratio to
investigate the gearing of Warwick Castle mill. Includes
question sheet (pdf). For full functionality, dowload the embedded video. Also the answer sheet for the questions. |
|
Introducing Percentages
presentation: Starting with a 'guess the topic' combination of things
with 'cent' in them, this introduces the idea of percentages as
fractions of 100. |
|
Fractions
Consolidation
sheets: The main elements of the study of fractions, decimals and
percentages condensed into easy-to-read revision-style sheets.
|
|
Fractions
of Amounts Dice Bingo game:
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. |
|
Percentage introduction
and percentage change: An introduction to the concept of % and examples
of two methods for calculating a percentage change. |
|
Post-its: A short
head-scratcher designed to highlight the concept of percentage decrease
followed by percentage increase. |
|
Multiplication
Table
interactive resource: Not technically a multiplication table, this is 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. |
|
Grid Multiplication
interactive resource: Calculates the product of two 2-digit or 3-digit
numbers, giving the results of each step sequentially using the grid
method. |
|
BODMAS
Bank Robbery: Two scenarios underlining the importance of performing
calculations in the right order. |
|
Number Pyramids activity:
Each block is the sum of the two blocks directly below it. The
presentation includes some missing block problems, the spreadsheet
gives the opportunity to investigate rearranging the numbers on the
bottom row for different totals at the top. |
|
Negative Temperature
worksheet: Max and min January temperatures are shown for a variety of
cities. Cities must be linked first to their temperatures, then
missing values from min, max and range must be found. |
|
Negative Drill: 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. |
|
Times Table Drill: Gives a
5 by 5 table of multiplication questions which may be copied down and
completed. Answers may be revealed by clicking the button. |
|
Splitting the Number: Prime
factorisation introduction. Explanation of factors and primes and
demonstration of method. |
|
Prime
Venn Tool: This is a beautiful piece of work - it 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. |
|
Powers of 10: A PowerPoint
version of the superb progression from outer galaxies to inner atoms
taken from Magnet
Lab at FSU. |
|
|
| Graphs |
|
Grapher
interactive
resource: An easy-to-use interface allows the user to change the
equations of two displayed straight lines, gives the point of
intersection, can be set to constrain the second line to be parallel or
perpendicular to the first. An additional feature allows the
user
to input an arithmetic sequence and have it mapped to a line. |
|
Distance-Time
Graphs presentation: To accompany the following resources.
Introduces distance-time graphs. |
|
Distance-Time
Graphs worksheet: A description of a journey is to be converted to
graph form. |
|
The
Simpsons Logic
Puzzle:
In addition to the logic puzzle within this clip, it can be used with
the presentation above to link with distance-time graphs. |
|
Sweden activity: A
real-life distance-time graph of a journey into Sweden, travelling on
foot, by train, by ferry, by bus and hitch-hiking. |
|
|
| Transformations |
|
Rotation
booklet: A
dozen
or so pages covering the fundamentals of point and direction of
rotation for multiples of 90 degrees on co-ordinate grids. |
|
Translate
the
Square
interactive resource: Input the correct 2D trnaslation vector to move
the blue square to the position of the red square. |
|
Enlargement
dynamic
geometry resource: A customisable triangle with ray lines through each
vertex to a moveable point of enlargement, and its image, enlarged by a
customisable scale factor. |
|
Rotation dynamic geometry
resource: A customisable shape which may be rotated about a
variable point by a variable angle. |
|
|
| Construction
and Loci |
|
Circle
Construction
presentation: Introducing the fundamentals of compass construction -
drawing a circumscribed shape by following instructions.
Includes
examples of circle art. |
|
Bisectors
presentation: How to construct a perpendicular bisector and an angle
bisector. |
|
Perpendicular
bisector
dynamic geometry resource: Demonstrates how a pair of equal circles
produces an exact perpendicular bisector. |
|
Angle
bisector
dynamic geometry resource: Demonstrate how a pair of equal circles
exactly bisects an angle. |
|
Introducing
Loci
sheet: A revision-style sheet outlining the fundamental loci. |
|
Loci
Challenges
booklet: A
series of problems for learners to solve by obeying the constraints and
observing the resultant shapes. |
|
Loci
Construction
worksheet: A series of questions, with extension parts, requiring the
application of construction techniques and loci knowledge. |
|
Castle
Construction
task: Using loci knowledge to draw the described features. |
|
Restraining
Order
task: Making use of the XKCD
cartoon, requires the use of the
circle area formula.
|
|
Sniper
at the Gates
task:
A more open investigation on the best way of covering the perimeter of
a rectangle with circles. |
|
Loci
1
Presentation: Introducing the concepts of a given distance from a fixed
point and from a line. |
|
Loci
2
Presentation: Introducing the concepts of equidistance from two points
and from two lines. |
|
|
| Statistics
& Probability |
|
Common
Mistakes
Survey: 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. |
|
Types of
Data: A corresponding worksheet and presentation to outline the basics
of data. Includes details of qualitative and quantitative, and
continuous and discrete data. |
|
6 Steps of Data Collection:
A summary of the data collection cycle, from Predictions through
Questioning, Collecting Data, Collating Results, Presenting Data and
Drawing Conclusions. PowerPoint presentation and a corresponding
summary sheet to be printed out. |
|
Misleading
Graphs
presentation: Examples from newspapers of artistic graphs which distort
the true data by one means or another. |
|
Venn
and
Carroll
Diagrams presentation: An introduction to Venn and Carroll diagrams.
|
|
Venn
Diagrams
interactive
resource: 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. |
|
Probability
Worksheets:
Introducing the probability line, basic probability notation
(fractions) and the basis for an experimental probability activity with
sweets. |
|
Dice
Knock-out game: Using either one or two dice, the game involves making
predictions about the outcome of the roll. |
|
Piggy
Sixes game: 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.
|
|
Averages presentation: An
introduction to the three averages, using limericks and investigating
word length. |
|
Pie Chart interactive
resource: 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. |
|
Hi-Lo interactive game: 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. |
|
Monty Hall Problem: 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 PowerPoint presentation to
illustrate the way probabilities change as new information is
revealed). |
|
|
| A-level |
|
Jupiter's
Moons
activity:
Pupils have to produce a simplified astronomical model of the order of
Jupiter's moons and their equations of motion. |
|
Jupiter's
Moons
presentation: To accompany the above activity - gives the solution
equations. |
|
Log
Rules sheet:
Revision-style sheet covering the basics of logarithms and their
associated rules. |
|
Geometric
Series
Shapes
worksheets: Two examples of shapes created by an infinite iteration but
with finite area and perimeter, to be found by applying geometric
series formulae. |
|
SUVAT
Equations Calculator:
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.
|
|
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. |
|
Optimisation: A simple
optimisation problem based on a quadratic (so it can be solved by
sketching a curve or completing the square). |
|
Binomial Expansion
Calculator: For expansions of the form (a + b)c this will
give the expansion to the x10
term. Deals with negative and fractional powers, too. This
is made in Excel 2007, and contains macros. For the 97-03 version
(fewer features), click here.
|
|
|
| Starter
Activities |
|
BODMAS
video: An
all-singing all-dancing presentation of the mathematical convention of
priority of Brackets, Orders, Division, Multiplication, Addition and
Subtraction. |
|
The
Simpsons Logic
Puzzle:
A Homer Simpson twist on an old favourite - an engaging variant of the
Fox, Chicken, Bag of Corn problem. |
|
Battleships
game:
Place your ships, then input co-ordinates (1st quadrant) to select a
square. |
|
Number
Square game:
Each
pair of (hidden) numbers at the corners add up to the four numbers in
between. Find a set of four corner numbers that work.
The
difficulty level may be altered to allow bigger numbers. |
|
Triangle
Overlap
activity: Can you work out the area of the overlap between these two
identical equilateral triangles? 3 different variations.
|
|
Triangle
Trickery
activity: 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. |
|
T-puzzle
activity:
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. |
|
Very
Strange Game:
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. |
|
Nim:
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.
|
|
Summer Quiz: 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).
|
|
Big
Things Quiz: 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. |
|
Fenceposts
Problem: 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). |
|
Christmas Quiz: 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. |
|
The
Mathematics of Santa Claus video: A 4-minute video presenting the maths
behind Santa's Christmas Eve exploits. |
|
A
Pint
of Snow video: A
short experiment, carried out in non-laboratory conditions, to
determine how much snow you would need to melt for a pint of water.
|
|
Snow
Weight: 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.
|
|
Snow
Area: Somewhat more
complicated than the last one, but in a similar vein, this time you
have to use relative densities of new-fallen snow and snowball snow to
calculate the size of the field needed to make this snowball. |
|
Digit Problem: 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. |
|
Letterworth: 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? |
|
Problems lateral, logical
and mathematical: These are collections of problems that require
some calculation, some careful deduction or some out-of-the-box problem
solving skills. I've tried to split them up according to these
categories, but there will be some overlap. Also, difficulty-wise
there will be considerable variation. Where the answer is not
revealed as part of the slide I have written these into the notes
section. |
 |
Sphere, Cone, Cylinder Volume: Animated web page
demonstrating the link between the formulae for volume of these three
shapes. |
|
100
Lockers problem: A question that requires an understanding of factors
and multiples, and the nature of square numbers. |
|
Braille Venn: A combination
of Venn That Tune and Braille, the PDF worksheets are accompanied by a
PowerPoint with the 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. |
|
Chess Squares: The problem
is very simple - how many squares are there on a chessboard?
However, this includes 2 by 2 squares, 3 by 3, etc. |
|
How Many Bottles: Can be
used as an introduction to trial and improvement, but is basically some
photos of lots of water bottles where you have to guess how many.
Giving "too high" or "too low" for each guess means frequently
numbers can be spot on after only half a dozen guesses. |
|
Wheat Grains Activity:
This activity (worksheet followed by instructions for teacher) requires
problem solving skills, and the use of a series of facts to find the
solution. |
|
Light and Sound:
Interesting comparison of the speeds of light and sound. A radio
transmission to the moon would arrive sooner than a loudspeaker hail
across a field. With these figures you can prove it. |
|
Lobster Pot Game: 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. |
|
Pencil Raft: 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. |
|
Seven Bridges: 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. |
|
FlightPath:
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. |
|
|
|
Exam Question Analysis
Tool: 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. |
