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Please speak to Mrs Duthie for the updated challenges and competitions calendar.

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Please speak to Mrs Duthie for the updated challenges and competitions calendar.

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Diversity is celebrated within Maths through our Key Stage 3 Mathematical Literacy. This celebrates Mathematicians from a wide range of cultures throughout time and their contribution to mathematics as we know it today. From King Rituparna developing the idea of estimation to the early humans in Africa who began the early idea of "counting" to record the phases of the moon.

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Sparx Maths builds maths confidence through personalised homework for students aged 11-16 and is proven to significantly boost grades by the University of Cambridge

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This is for Year 10 and Year 11 students studying GCSE Further Maths

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This is for Year 10 and Year 11 students studying GCSE Further Maths

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This website requires you to make account. You can do this with your school email address. The teacher code is: k6s0t5 (zero not o)
A new challenge, called a Parallelogram, will be emailed to you at 3pm on a Thursday every week.

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A home for curious mathematical minds. For ages 10-16 anywhere in the world. 100% free. Live interactive Maths Circles and puzzle sheets every week.

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Buy What's the Point of Maths? by DK (ISBN: 9780241343524) from Amazon's Book Store. Everyday low prices and free delivery on eligible orders.

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There are lots of times tables games here which you can play if you need extra practice.

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Multiplication and Division - interactive maths games and free worksheets

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Short videos about lots of different aspects of Maths

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This is Numberphile. We mainly post videos about mathematics and just numbers in general.

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This is a brilliant website which also has explanation videos on all skills. You do not need an account to log in. They also have questions which you can practice.

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Angles: compass directions Video 27b Practice Questions

Area: quarter-circle Video 47a Practice Questions

Averages: combined mean Video 53a Practice Questions Textbook Exercise

Averages: mode (frequency table) Video 56a

Averages: range (frequency tables) Video 57a

Averages: Quartiles Video 57b Practice Questions

Circles: perimeter - quarter-circle Video 62a Practice Questions

Circle theorems proof: right angle in a semi-circle Video 65a Practice Questions

Circle theorems proof: angles at circumference\centre Video 65b Practice Questions

Circle theorems proof: angles in the same segment Video 65c Practice Questions

Circle theorems proof: cyclic quadrilaterals Video 65d Practice Questions

Circle theorems proof: alternate segment theorem Video 65e Practice Questions

Circle theorems proof: radius and tangent proof Video 65f Practice Questions

Circle theorems proof: Textbook Exercise

Constructions: loci part 3 Video 77 Practice Questions Textbook Exercise

Coordinates: 3D Video 86 Practice Questions

Data handling cycle Video 89 Practice Questions

Dimensional analysis Video 97 Practice Questions

Division: long division Video 98a

Enlargements: ray method Video 109 Practice Questions

Equations: involving fractions Video 111 Practice Questions Textbook Exercise

Equations: x squared Video 116a Practice Questions

Equations: Think of a number Video 116b Practice Questions

Factorisation: splitting the middle Video 119a Textbook Exercise

Factorisation: difference of 2 squares Video 120 Practice Questions Textbook Exercise

Fractions: finding the midpoint Video 141a Practice Questions

Graphs composite bar charts Video 148a

Graphs: dual bar charts Video 148b

Graphs: misleading graphs Video 160a

Graphs: real life linear graphs Video 171a

Linear graphs: real life Video 198a

Money - See Video 400 or click here for collection

Multiplication: grid method Video 199 Practice Questions Textbook 1 Textbook 2

Multiplication: column method Video 200 Practice Questions Textbook 1 Textbook 2

Multiplication: times tables Video 204a Textbook Exercise

Number: odd and even numbers Video 221a Practice Questions

Number: product of primes (squares/cubes) Video 223a Practice Questions Textbook

Percentages: simple interest Video 236a Practice Questions Textbook Exercise

Proportion: unitary method Video 255a Practice Questions Textbook Exercise

Proportion: Graphs Video 255b

Proportion: Time Video 255c

Pythagoras: area of a regular hexagon Video 262 Practice Questions

Quadratic graphs: sketching using key points Video 265 Textbook Exercise

Quadratic graphs: finding turning point Video 265a Practice Questions

Quadratic graphs: line of symmetry Video 265b

Quadratics: solving (factorising) Video 266 Practice Questions Textbook 1 Textbook 2

Quadratics: solving graphically Video 267c Practice Questions Textbook Exercise

Quadratics: solving graphically advanced Video 267d Practice Questions

Questionnaires Video 268 Practice Questions

Ratio: express as fractions or % Video 269a Practice Questions Textbook Exercise

Ratio: given two ratios Video 271a Textbook Exercise

Ratio: difference between Video 271b Textbook Exercise

Ratio: expressing as 1:n Video 271c Textbook Exercise

Ratio: equations/ratios Video 271d

Ratio: solving problems 1 Video 271e Textbook Exercise

Sampling: using samples Video 281a

Sampling: random Video 282 Practice Questions

Scales and maps Video 283 Practice Questions

Sequences: nth term for fractional sequences Video 289 Textbook Exercise

Similar shapes: definition Video 291 Practice Questions

Similar shapes: further Video 294 Practice Questions

Simultaneous equations (substitution, both linear) Video 296 Practice Questions

Simultaneous equations (graphical) Video 297 Textbook Exercise

Surface area: mixture Video 309 Practice Questions

Surface area: other prisms Video 312

Transformations: mixture Practice Questions

Transformations of graphs Video 323 Practice Questions

Transformations of trigonometric graphs Video 324 Practice Questions

Trigonometry: sine rule (ambiguous case) Video 334a Textbook Exercise

Trigonometry: area of a triangle Video 337 Proof Practice Questions Textbook Exercise

Types of data: primary & secondary Video 343a Practice Questions Textbook Exercise

Types of graph: cubics Video 344 Practice Questions

Types of graph: exponential Video 345 Practice Questions

Types of graph: reciprocal Video 346 Practice Questions

Types of graph: mixture

Units: types of metric and imperial unit Video 347 Practice Questions

Units: Converting imperial units for length Video 348a Practice Questions

Units: Converting imperial units for mass Video 348b Practice Questions

Units: Converting imperial units for capacity Video 348c Practice Questions

Units: metric to imperial (length) Video 349d Practice Questions

Units: metric to imperial (mass) Video 349e Practice Questions

Units: metric to imperial (capacity) Video 349f Practice Questions

Vectors Video 353 Practice Questions

Views: front/side elevation and plan view Video 354 Practice Questions

Volume: Frustum Video 360a Textbook Exercise

Additional Topics

Flow Charts Video 364 Practice Questions

Geometric Proof Video 366

Identities: Equating coefficients Video 367 Practice Questions

Identities, Formula, Equations etc Video 367a Practice Questions

Intersecting Chord Theorem Video 368a Practice Questions

Intersecting Secant Theorem Video 368b Practice Questions

Quadratic graph (completing the square) Video 371

Equation of a Tangent to a Circle Video 372 Practice Questions

Iteration Video 373 Practice Questions

Iterative Processes Video 373a

Change of Sign Video 373a Practice Questions

Arithmetic progressions Video 374

Geometric progressions Video 375

Set notation Video 379

Venn Diagrams Video 380 Practice Questions

Shortest distance from point to a line Video 381 Textbook Exercise

Time series Video 382

Population Density Video 384a Practice Questions

Invariant Points Video 392 Textbook Exercise

Simultaneous Equations (3 Unknowns) Video 393 Textbook Exercise

Measuring Lines Video 397 Practice Questions

Drawing Lines Video 397a Practice Questions

Money: Coins Video 400a Practice Questions

Money: Change Video 400b

Money: Buying Video 400c Practice Questions

Money: Regular Payments Video 400d Practice Questions

Money: Bills Video 400e

Money: Discounts Video 400f Practice Questions

Money: VAT Video 400g Practice Questions

Money: Wages Video 400h Practice Questions

Money: Bank Statements Video 400i Practice Questions

Money: Tax Video 400j Practice Questions

Money: Cost per kg Video 400k Practice Questions

Money: Cost per litre Video 400l Practice Questions

Money: Cost per metre Video 400m Practice Questions

Money: Reading meters Video 400n

Money: Profit Video 400p Practice Questions

Money: Greatest/Maximum Video 400q Practice Questions

Money: Estimation Video 400r Practice Questions

Money: Midpoint Video 400s Practice Questions

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Videos, Practice Questions and Textbook Exercises on every Secondary Maths topic

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Buy Humble Pi: A Comedy of Maths Errors by Parker, Matt (ISBN: 9780141989143) from Amazon's Book Store. Everyday low prices and free delivery on eligible orders.

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Press the green "PLAY" button to begin the game. This is also available for download on mobile devices.

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QR CODE

Scan this on mobiles and tablets to quickly open this web page.

Hit the Button is an interactive maths game with quick fire questions on number bonds, times tables, doubling and halving, multiples, division facts and square numbers. The games, which are against the clock, challenge and develop mental maths skills. An untimed, practise mode is available in our Hit the Button app along with lots more extra features.

The activities can be matched to appropriate mathematical ability. Regular use of Hit the Button can help students to sharpen their recall of vital number facts in a fun way and learning multiplication tables need not be boring.

AGE

6-11 Years

SUBJECTS

Maths Times Tables Division Number Bonds Doubles Halves Square Numbers

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Hit the Button - Quick fire maths practise for 6-11 year olds

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Quick fire questions on number bonds, doubles, halves, times tables, division facts and square numbers against the clock. Superb!

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largest negative integer

-0.083333333333333

0.5

real part of all non-trivial zeros of the Riemann zeta function - if the Riemann hypothesis is true!

0.577215664901532

Euler-Mascheroni constant γ

the limiting difference between the harmonic series and the natural logarithm

0.915965594177219

Catalan's constant G

unknown whether irrational or not

1.059463094359295

proportion between the frequencies of adjacent semitones in the 12 tone equal temperament scale

1.202056903159594

appears in quantum electrodynamics and random spanning trees

1.259921049894873

can't be constructed using ruler a compass, which was one of the three famous geometric problems of antiquity

1.414213562373095

first known irrational number, discovered by Pythagoras or one of his students

ratio of diagonal and the side length in a square

proportion between the sides of DIN paper sizes

1.618033988749894

Golden ratio φ

ratio of the side and one of the diagonals in a pentagon

1.732050807568877

the measure of the fish

length of the space diagonal of a cube with edge length 1

height of an equilateral triangle with side length 2

2.236067977499789

length of the diagonal of a 1 × 2 rectangle

2.502907875095892

second Feigenbaum constant α

ratio between the width of a tine and the width of one of its two subtines

2.718281828459045

Euler's number e

3.141592653589793

circumference of a circle with diameter 1

transcendental number, which means that the famous ancient problem of squaring a circle is impossible

closely approximated by or

4.669201609102990

first Feigenbaum constant δ

limiting ratio of consecutive bifurcation intervals in a one-parameter logistic map

6.283185307179586

circumference of a circle with radius 1

period of the sin, cos and tan functions

9

maximum number of cubes needed to sum to any positive integer

number of muses in Greek mythology

number of significant points in a triangle that lie on a circle: the Nine-Point circle

16

number of pawns in a chess set, and each player starts with 16 pieces

length of credit card numbers

23.140692632779269

24

largest number divisible by all integers less than its square root

number of hours in a day

26

number of sporadic groups

only positive number to be directly between a square and a cube

smallest non-palindromic number whose square is a palindrome:

27

sum of the digits of its cube:

in the Collaz Conjecture you need 112 steps to get from 27 to 1

32

ninth happy number

smallest nontrivial fifth power

sum of the totient functions of the first ten integers

freezing point of water at sea level in Fahrenheit

41

lucky number of Euler, and the largest such prime

number of Mozart's last symphony

45

triangular, hexagonal and 16-gonal number

47

largest number of cubes that cannot tile a cube

atomic number of silver

Carol number

49

multiplying the period of by integers coprime to 49 permutes the digits

type in your calculator and you will be very surprised...

50

represented by the letter L in Roman numerals

57

can be written as 111 in base 7

the 57-cell is a self-dual abstract regular four-dimensional polytope.

57.295779513082320

number of degrees in 1 radian

63

number of partially ordered sets of 5 elements

64

number of tiles on a chess board

maximum number of strokes in any Chinese character

smallest number with 7 divisors

index of Graham's number in the sequence 3, 27, 7625597484987, ...

65

smallest number that becomes a square when its reverse is either added to or subtracted from it

74

number of non-Hamiltonian polyhedra with a minimum number of vertices

78

smallest integer that can be written as the sum of four distinct squares in three ways

81

number of stable chemical elements

only non-trivial number which is the square of the sum of its digits

its inverse repeats all 10 decimal digits in order

89

11th Fibonacci number

91

smallest non-trivial cabtaxi number

sum of the squares of the first six integers.

95

smallest non-interesting number

96

untouchable number, since it cannot be expressed as the sum of some of the proper divisors of another integer

98

the decimal expansion of its reciprocal starts with the powers of two:

100

boiling point of water in Celsius

denoted by the letter C in Roman numerals

113

A113 was the Pixar animation classroom at the California Institute of the Arts

118

smallest number which can be written as the sum of three integers in four different ways, so that the product of every triple is the same: 118 = 14 + 50 + 54 = 15 + 40 + 63 = 18 + 30 + 70 = 21 + 25 + 72

128

smallest number that is the product of 7 prime factors ()

largest number that is not the sum of distinct squares

power of 2, all of whose digits are powers of 2 (unknown if there are any other numbers with this property)

132

sixth Catalan number

145

one of just four numbers to be the sum of the factorials of its digits: 145 = 1! + 4! + 5!

153

sum of the first 5 factorials and the first 17 natural numbers

212

the boiling point of water in Fahrenheit

255

largest number that can be represented using an 8-bit unsigned integer

261

number of hypercube unfoldings

341

smallest base 2 Fermat pseudoprime

365.2425

average number of days in a year, consisting of 365 days, 5 hours 48 minutes and 46.08 seconds

380

the A380 is the world's largest passenger aircraft.

500

denoted by the letter D in Roman numerals

676

smallest palindromic square whose square root 26 is not palindromic

747

the Boeing 747 aircraft is called the "Queen of the Skies"

786

sacred number in Muslim Abjad numerology

836

second weird number, after 70

1 000

1 001

is the product of three consecutive primes 7 × 11 × 13

1 089

1089 × 9 = 9801, the reverse of its digits

1 138

title of George Lucas' first film: THX 1138

1 540

one of just 5 numbers that is both triangular and tetrahedral

1 729

Hardy-Ramanujan number and second taxicab number

2 240

number of pounds in an (English) ton

2 310

2 592

3 003

smallest number to appear 8 times in Pascal's triangle (there is no other number less than 2^23 appearing 8 times)

3 600

number of seconds in one hour

3 999

largest number that can be written in Roman numerals, as MMMCMXCIX

4 900

the only square pyramidal number that is also a square:

5 040

mentioned by Plato as the ideal number of people living in a city, due to its high number of factors

5 913

sum of the first 7 factorials: 5913 = 1! + 2! + 3! + ... + 6! + 7!

6 174

Kaprekar's constant: take any four-digit number, rearrange its digits to make the largest and smallest possible number, subtract these numbers and repeat. Eventually you will arrive at 6174!

8 000

8 128

fourth perfect number

9 694

number of hypercube unfoldings in 5D

12 758

largest number that cannot be represented as the sum of distinct cubes

17 163

largest number that is not the sum of the squares of distinct primes

26 830

number of possible Tic-tac-toe games

40 585

sum of the factorials of its digits: 40,585 = 4! + 0! + 5! + 8! + 5!

40 755

first number, other than 1, that is simultaneously triangular, pentagonal and hexagonal

142 857

smallest base 10 cyclic number: multiplied by 2, 3, 4, 5 or 6, it simply rotates is decimal digits

recurring decimal expansion of

196 560

the number of spheres touching any other sphere in a 24-dimensional Leech lattice

502 110

number of hypercube unfoldings in 6D

666 666

area of the Pythagorean triangle with sides 693, 1924 and 2045

2 598 960

number of distinct, 5-card poker hands

4 729 494

a coefficient in Archimedes' cattle problem

31 557 600

number of seconds in a Julian astronomical year (365.25 days)

33 064 966

number of hypercube unfoldings in 7D

33 550 336

5th perfect number

275 305 224

the number of distinct magic squares of order 5 (excluding rotations and reflections)

299 792 458

speed of light in vacuum

739 391 133

the largest prime number (in base 10), that you can truncate to produce a sequence of smaller primes: 7, 73, 739, ...

2 642 657 228

number of hypercube unfoldings in 8D

3 816 547 290

the only 10-digit number such that, for every k between 1 and 10, its first k digits give a number that is a multiple of k

8 589 869 056

6th perfect number

9 814 072 356

largest perfect power that contains no repeated digits in base ten

137 438 691 328

7th perfect number

158 753 389 900

the probability of receiving a complete suit in the game of Bridge

248 639 631 948

number of hypercube unfoldings in 9D

262 537 412 640 768 743.999999999

a transcendental number which is an almost integer

2 305 843 008 139 952 128

8th perfect number, discovered by Euler in 1772

18 446 744 073 709 551 615

equals

the number of grains of rice required if you place one grain on the first square of a chess board, two on the second, 4 on the third, 8 on the fourth, and so on.

357 686 312 646 216 567 629 137

the largest prime number (in base 10), that you can truncate from its beginning to produce a sequence of smaller primes: 7, 37, 137, 9137, ...

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Almanac of Interesting Numbers - Mathigon

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Scroll along the number line, and explore hundreds of interesting curious properties and facts. Then zoom in and out to discover even more!

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It's a Numberful World: How Math Is Hiding Everywhere

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It's a Numberful World: How Math Is Hiding Everywhere

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It's a Numberful World: How Math Is Hiding Everywhere

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Buy It's a Numberful World: How Math Is Hiding Everywhere Illustrated by Woo, Eddie (ISBN: 9781615196128) from Amazon's Book Store. Everyday low prices and free delivery on eligible orders.

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A game using factors and basic numeracy with the goal of filling the screen with blocks

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Tutorial

Factris is a classic risk reward high score game. Just like in Tetris, you have to arrange falling blocks using the arrow keys, and when you fill an entire row, it disappears to make space for new blocks. However, there are two key differences:

The blocks are always rectangles of varying sizes. Rather than rotating them, you can "refactor" them. For example, a block might start out as 12×1 tiles, but by pressing the up key, you can successively change its size to 6×2, 4×3, 3×4, 2×6 and 1×12.

You can exponentially more points if you complete multiple rows at once. Every tile in the first row is worth 10 points, every tile in the second row is worth 20 points, then 40 points, 80 points, 160 points, and so on.

There is no undo, so you need to pay close attention to the size of the rectangles coming next. Improve your numeracy, packing and knowledge of factors with Factris!
Factris was invented by Richard Lissaman at MEI. This version was designed and developed by Philipp Legner.

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Factris is a fun game that teaches about simple arithmetic, divisibility and factorisation.

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Please enable JavaScript in your browser to access Mathigon.

Platonic Solids

Platonic Solids are the most regular polyhedra: all faces are the same regular polygon, and they look the same at every vertex. The Greek philosopher Plato discovered that there are only five solids with these properties. He believed that the they correspond to the four ancient Elements, Earth, Water, Air and Fire, as well as the Universe.

Archimedean Solids

Archimedean Solids, like the Platonic ones, consist of regular Polygons and look the same at every vertex. However the faces are multiple different regular polygons. There are 13 Archimedean Solids, two of which are reflections of each other. Explore 3D models on Polypad...

Further Reading

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Explore the beautiful world of Origami and mathematics. Be amazed by stunning photographs, try our folding instructions, or learn about the mathematical background.

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9-12 Reading age

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The Magic of Maths (Murderous Maths) : Poskitt, Kjartan, Davis, Rob: Amazon.co.uk: Books

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Times Tables Practice - Digital Flashcard

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Times Tables Practice - Digital Flashcard

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These beautiful flash cards use spaced repetition to teach multiplication facts. Achieve fluency with just five minutes of practice per day!

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There are countless different shapes that can be created using the seven Tangram tiles. What can you come up with?

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9-12 Reading age

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The Brain-Bending Basics (Murderous Maths)

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The Brain-Bending Basics (Murderous Maths) : Poskitt, Kjartan, Davis, Rob, Dunton, Trevor, Reeve, Philip: Amazon.co.uk: Books

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Times Tables Practice - Digital Flashcard, shuffle mode

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Times Tables Practice - Digital Flashcard, shuffle mode

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These beautiful flash cards use spaced repetition to teach multiplication facts. Achieve fluency with just five minutes of practice per day!

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Navigate using the Keyboard arrows or click anywhere on the slide to show the toolbars for more options.

As Alice falls down the rabbit hole, she sees many different numbers flying around. And they always appear in particular patterns - these are called sequences. Can you find the pattern in these five sequences?

In the first sequence the numbers are the multiples of three: and so the difference between two consecutive numbers is three.

In the next sequence the difference between two consecutive numbers is four. But since the first number, 3, is not divisible by 4, none of the others are.

In this sequence the difference between consecutive numbers are increasing integers: 1, 2, 3, and so on. These numbers are called the triangle numbers.

This is because if you were to build triangles out of, say, oranges, you would need precisely this sequence of numbers. Every new row has one more orange than the previous one, so we have to add the next bigger integer.

And here we have the square numbers: 1 squared is 1, 2 squared is 4, and so on.

There is a second way to calculate the square numbers: we start with 1 and keep adding the next odd number.

The final sequence is called the Fibonacci sequence. We start with two 1s and every new number is the sum of the two previous numbers.

Remember these five sequences, because we will see them again in this slideshow.

Alice hits the stone floor at the bottom of the rabbit hole. As she looks around she notices that the tiles are not simply black and white, they all have small numbers in them. And an inscription reads: Pascal's Triangle.

Alice notices that the triangle starts in one corner of the room but goes on forever in the other direction. And every new row is a bit bigger than the previous one. "This must be an awfully big room", she thinks.

The numbers also seem to get bigger, except along the edge where there are only ones. But Alice notices a pattern: every new number is the sum of the two numbers above it.

Can you find the next one or two rows of this triangle?

There are many mysterious patterns and secrets in this triangle. Before continuing, have a look at the numbers and try to find some of them.

Suddenly Alice sees a couple of bright buttons at the wall, and whenever she presses one of them, some tiles on the floor light up.

The first button lights up the outer diagonals which consist only of ones.

The second button lights up the second diagonals: and these are the integers 1, 2, 3, and so on.

The third button shows the third diagonals. This is one of the sequences we saw before and they are called the triangle numbers.

The fourth button also lights up the triangle numbers, but this time in pairs. And when you add up consecutive triangle numbers you get the sequence of square numbers.

Can you explain why that happens? Think about it geometrically!

And there are still more buttons left, more patterns to find in this mysterious triangle. The fifth button reveals a new diagonal in which every number is the sum of all cells in that row. In the third row, for example, 1 + 2 + 1 = 4. And in this new diagonal, every number is twice the previous one. 1 × 2 = 2; 2 × 2 = 4; 4 × 2 = 8 and so on. These of numbers are called the Powers of Two.

The next button highlights all rows in which the second number is a prime number. And Alice notices that all numbers in between are divisible by that prime. Does it work with any numbers which are not prime?

The final button suddenly shows many different cells in different colours. We are adding up the cells along certain "shallow" diagonals. And the results are 1, 1, 2, 3, 5 and so on - another sequence we already know: every number is the sum of the previous two. Remember these numbers because we will see them again...

You should think about each of these patterns and try to explain where it comes from.

Pascal's Triangle not only knows about countless patterns and sequences but appears in many different parts of mathematics. And there are many more secrets not shown so far, waiting to be explored by you.

Alice looks around the room and on a glass table she finds many glasses in different colours. And there is a sign saying "Put me on". She is curious and does put on the first pair of glasses...

As Alice looks through the first pair of glasses, suddenly many of the tiles on the floor disappear and she seems to float in mid-air. Only those remain which are divisible by 2. But these are not located randomly: they form many small and bigger triangles!

When Alice takes off the glasses, everything is back to normal. Each of the glasses corresponds to a particular number.

The red glasses, for example, show only those numbers divisible by 3. And again thy appear in triangles which get bigger and bigger.

Alice puts on the yellow pair of glasses and now she sees only those numbers divisible by four.

And finally, the green glasses show her only those numbers divisible by five.

Think about all these patterns and try to explain where they are coming from. You can also download a big copy of Pascal's triangle and colour it in yourself: for example those numbers divisible by six or seven.

When Alice leaves the curious room, she meets someone even more amazing than what she saw before: a fractal. A Fractal is a geometrical shape which copies itself again and again at smaller scales. You can zoom in forever and will always find new, smaller copies of the original shape.

Fractals have fractional dimensions, hence the name. You could imagine that in 2- or 3-dimensional space there simply isn't enough space for that many repetitions, so they need dimensions like 2.4, 3.6 or log ₂ 3.

This is of course very hard to believe but can be proved using mathematics. On the following slides we will see how to construct simple Fractals ourselves.

One of the simplest fractals is the Sierpinski triangle. We start with a plain triangle and cut out a smaller triangle in the centre.

We do the same with the four remaining triangles.

And again, and again, forever and ever.

Notice that the smaller triangles all look exactly the same as the entire big triangle. We therefore say that Fractals are self-similar.

If you remember the coloured patterns we saw in Pascal's triangle, you will notice that the Sierpinski triangle looks very similar.

Suddenly it starts snowing and Alice discovers that the snowflakes are also fractals. Again we start with a triangle and add smaller triangles to each side.

And again, and again, until we get a beautiful snowflake: the Koch snowflake. In this case, not the shape itself, but its border is self-similar.

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One of the most famous and most intriguing fractals is the Mandelbrot Set, named after the French mathematician Bernoît Mandelbrot (1924 - 2010). When rotated by 90° it looks a bit like a person, with head, body and two arms. And like before, we can zoom in forever, finding more and more beautiful patterns...

In real life, Fractals can't exist. If you zoom in further and further, you will eventually arrive at atoms and molecules - and there you have to stop. But there are many examples in nature of shapes that look almost like fractals: Vegetable, flowers and trees...

And here in Fractalland there even is a Mandelbrot Island!

After walking through a small forest, Alice comes to a big tea party of a rabbit family. And they tell her how the family evolved.

It all started with a pair of small rabbits being born in Wonderland.

After a year, they had grown up and after another year, they had children themselves: again a boy and a girl.

After another year, they had another pair of children, while their first pair had grown up.

And after another year, they had a third pair of children and their very first pair of children also gave birth to a new pair.

If we add up the number of rabbit pairs in every year we get an interesting sequence: 1, 1, 2, 3, 5, and so on.

We saw this sequence of numbers before: every new number is the sum of the previous two. The next number, for example, would be 3 + 5 = 8. They are called Fibonacci Numbers, named after the Italian Mathematician Leonardo Fibonacci.

Fibonacci Numbers appear everywhere in nature: such as pinecones or sunflowers.

If you count the number of spirals in Pinecones or Sunflowers, it will almost always be a Fibonacci number. We know that 8 is a Fibonacci number, and you can check that 34 is one as well.

If you count in the opposite direction, you get another number: but again a Fibonacci number.

Of course nature doesn't know about Fibonacci numbers: they just happen to come out of natural processes, such as growing plants or growing rabbit populations.

Now let us draw some squares with Fibonacci number side lengths.

If we connect the corner points we get a perfect spiral -

- another shape that appears everywhere in nature.

The proportions of our rectangles were the ratios of consecutive Fibonacci numbers. These form another sequence which gets closer and closer to a number we call Phi - or the Golden Ratio.

Some believe that the Golden Ratio is a particularly beautiful proportion, and that's why it is often used in architecture and art.

And while we found the golden ratio using a sequence of fractions, the golden ratio itself can't be expressed as a simple fraction. It is an infinite decimal number without any pattern or repetition.

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When Alice falls down the rabbit hole, she discovers curious and wonderful mathematics she could have never imagined.

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9-12 Reading age

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The Secrets of Sums (Murderous Maths) : Poskitt, Kjartan: Amazon.co.uk: Books

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Scroll down to where you see an option to "play game".

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Read the time on an analogue clock. Lots of choice over levels, including: reading time to the nearest hour, half hour, quarter hour, five minutes or minute. Options include using a 24 hour clock and seeing how many correct answers you can get in a given time.

This new version will work on any tablet or computer.
For more measuring and time resources click here.
Scan to open this game on a mobile device. Right-click to copy and paste it onto a homework sheet.

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Eureka is one of the oldest recreational mathematics magazines in the world, published since 1939 by The Archimedeans, the mathematical society of Cambridge University. It contains mathematical articles on a wide range of mathematical topics, as well as puzzles, games, artwork and book reviews.

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Eureka, published by the mathematical society of Cambridge University, is one of the oldest recreational mathematics magazines in the world.

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The Perfect Sausage and Other Fundamental Formulas

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The Perfect Sausage and Other Fundamental Formulas

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8-12 Reading age

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The Perfect Sausage and Other Fundamental Formulas (Murderous Maths)

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Buy The Perfect Sausage and Other Fundamental Formulas (Murderous Maths) 1 by Poskitt, Kjartan, Reeve, Philip (ISBN: 9781407107165) from Amazon's Book Store. Everyday low prices and free delivery on eligible orders.

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Multiplication practice

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Learn about the countless hidden uses and applications which mathematics has in everyday life: From weather prediction to medicine, video games and music…

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The Number Devil: A Mathematical Adventure

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The Number Devil: A Mathematical Adventure

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If you agree, we'll also use cookies to complement your shopping experience across the Amazon stores as described in our Cookie Notice. This includes using first- and third-party cookies, which store or access standard device information such as a unique identifier. Third parties use cookies for their purposes of displaying and measuring personalised ads, generating audience insights, and developing and improving products. Click 'Customise Cookies' to decline these cookies, make more detailed choices, or learn more. You can change your choices at any time by visiting Cookie Preferences, as described in the Cookie Notice. To learn more about how and for what purposes Amazon uses personal information (such as Amazon Store order history), please visit our Privacy Notice.

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The Number Devil: A Mathematical Adventure

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Buy The Number Devil: A Mathematical Adventure by Enzensberger, Hans Magnus, Heim, Michael Henry (ISBN: 8601404310003) from Amazon's Book Store. Everyday low prices and free delivery on eligible orders.

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Tommy's Trek - Times Tables

A fun platform game for children to practise their times tables. This game will work on any device.

Use the arrow keys to move Tommy. The ctrl key makes him jump and the up arrow selects a number.
Having problems controllingTommy on an iPad? Go to your browser's settings and make sure 'Request Desktop Mode' has not been selected. For more multiplication games click here. For more Tommy's Trek games click here.

Scan to open this game on a mobile device. Right-click to copy and paste it onto a homework sheet.

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You do the Maths: Launch a Rocket into Space

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You do the Maths: Launch a Rocket into Space

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7-11 Reading age

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Featuring maths problems from addition and decimals to line graphs and pie charts, these books have different challenges to be solved with a varying range of difficulty.

These four titles make maths accessible and exciting by relating it to the real world. Each title includes a glossary to explain any mathematical words or terms that the reader may struggle with, to aid the learning process.

The You Do The Maths series include:

Design a Skyscraper: - 978-1-78171-687-8

Launch a Rocket in Space: - 978-1-78171-686-1

Fly a Jetfighter: - 978-1-78171-688-5

Solve a Crime: - 978-1-78171-689-2

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You do the Maths: Launch a Rocket into Space

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Buy You do the Maths: Launch a Rocket into Space by Koll, Hilary, Mills, Steve, Aleksic, Vladimir (ISBN: 9781781716922) from Amazon's Book Store. Everyday low prices and free delivery on eligible orders.

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Fractions of Numbers - Mini Maths Golf KS2 Maths Game

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The Math Inspectors: Story One - The Case of the Claymore Diamond: Volume 1

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The Math Inspectors: Story One - The Case of the Claymore Diamond: Volume 1

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Reading age 9-12

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The Math Inspectors: Story One - The Case of the Claymore Diamond: Volume 1

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The Math Inspectors: Story One - The Case of the Claymore Diamond: Volume 1 : Kenney, Daniel, Boever, Emily: Amazon.co.uk: Books

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We celebrate the contributions of Alan Turing to mathematics and to the development of technology. Students will also visit Bletchley Park to learn more about him and his contributions.

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benedict cumberbatch artificial intelligence colorado computer science puzzle turing machine physics enigma machine bletchley park british mathematician

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In maths we celebrate all mathematicians who have made contributions throughout history and present day. These mathematicians are celebrated through a "Mathematician of the Week" in KS3. These can be seen in the column "Mathematicians Around the World".

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This is an overview of the challenges and competitions available across Year 7 to 11.

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This is an overview of the challenges and competitions available across Year 7 to 11.

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There are a range of challenges and competitions here to suit all students. From doing Maths, linking Maths to History and linking Maths to Art.

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GCSE Mathematics Specification for first teaching in 2015 (aqa.org.uk)