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Topics with Century Tech nugget list 2025 to 2026

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Topics with Century Tech nugget list 2025 to 2026

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2025-2026 GCSE Topics with mock and exam dates

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GCSE Maths Lesson Plan: Using BIDMAS

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GCSE Maths Lesson Plan: Number Patterns and Special Numbers

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GCSE Mathematics Lesson Plan: Understanding Prime Numbers

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Using a Venn diagram to find the HCF and LCM

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https://www.geogebra.org/

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GeoGebra - the world's favorite, free math tools used by over 100 million students and teachers

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Free digital tools for class activities, graphing, geometry, collaborative whiteboard and more

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Prime numbers, square and cube numbers and roots

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Foundation tier knowledge what students need to know

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Real life graphs

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Lesson 22 Parallel lines, angles and polygons

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Maad Mysterious Mathematical Magician's video from Count Suchodolski

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Maad Mysterious Mathematical Magician's video from Count Suchodolski

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Adding fractions with different denominators

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Australia
Canada
Egypt
France
Germany
Greece
India
Italy
Netherlands
Poland
Portugal
Romania
UAE
UK
USA

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Watch out for the Maad Mysterious Mathematical Magician's video clips

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Pick one 'Exam Question' to work through. Monday, Tuesday and Thursday from 4:30pm to 5pm.

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Pick one 'Exam Question' to work through. Monday, Tuesday and Thursday from 4:30pm to 5pm.

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End of lesson check Factorising expressions

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GCSE Maths Paper 1 Non-Calculator 05/11/2025

GCSE Maths Paper 2 Calculator 07/11/2025

GCSE Maths Paper 3 Calculator 10/11/2025

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Holiday Revision

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Parrallel lines and angles exam questions

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Substitution and like terms exam questions

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Lesson 8 Ratio & proportion exam questions

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Just for fun.

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Everyone needs some fun maths facts to brighten up a rainy day...

1. You can cut a cake into 8 pieces by using only 3 cuts.

You just need to make two cuts in a vertical plane and one in a horizontal plane. Save yourself some time next time you have a party!

If you can make cuts which aren't straight then you have some other options. Find out more

2. Dividing by zero once put a US Navy Warship out of action.

In 1997 an unwitting crew member onboard the USS Yorktown wrongly entered a zero into one of the ships computers. This caused the ship's software to divide by zero, meaning that it was stranded and unable to move for over two hours.

3. The number 0.999999..... is exactly equal to 1

Proof: Let x=0.9999...

Then 10x = 9.9999...

10x-x =(9.9999...)-(0.9999...)

9x=9

x=1

4. The word googol was made up by a 9-year old boy

In the 1930s an American Mathematician named Edward Kasner asked his nine-year old nephew Milton Sirotta to make up a word for him to use. Milton made up the world 'googol' which Edward Kasner later used to describe the number . The search engine Google was later named after the 'googol' meaning that Milton Sirotta had unwittingly helped name one of the world's most famous companies.

5. There are only 17 possible types of wallpaper pattern

If you look at the underlying symmetry in a wallpaper pattern then mathematicians have shown that there are only 17 possibilities. You can of course vary the colours and decoration, but you will still only be left with 17 different possible symmetries.

6. William Shanks calculated pi to 707 decimal places but made a mistake on the 528th digit.

Amateur mathematicia William Shanks (1812-1882) spent a good part of his life calculating mathematical constants by hand. Shanks never found out about his mistake as it wasn't revealed until after his death.

7. If you folded a piece of paper in half 103 times it would be the thickness of the observable universe

In practice, the world record for folding a piece of paper in half is only 12 times. If you go beyond that (in theory) you will quickly start to get some pretty huge thicknesses.

8. The only Shakespeare play to contain the word 'mathematics' is the Taming of the Shrew

The Taming of the Shrew does however contain the word 'mathematics' on three separate occasions.

9. The numbers on opposite sides of a dice always add up to seven

On a dice the numbers 1,2 and 3 all share a vertex. If these three numbers run clockwise round this vertex then the dice is called left-handed and if the three numbers run anti-clockwise round the vertex, then it is a right-handed dice. Chinese dice are normally left-handed and Western dice are normally right-handed.

10. Sergey Brin, co-founder of Google studied maths (and computer science) at university

Lots of tech entrepreneurs used maths to make their billions and Sergey Brin is no exception.

Article by Hazel Lewis

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10 fun maths facts to brighten up a rainy day - Maths Careers

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Everyone needs some fun maths facts to brighten up a rainy day... You just need to make two cuts in a vertical plane and one in a horizontal plane. Save yourself some time next time you have a party! If you can make cuts which aren't straight then you have some other options.

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Practice Questions

Training for a maths exam is a bit like training for a big running race - you can't just read about the theory, you need to do as much practice as possible. This is why practicing past papers is the number one tip for revising for a maths exam. Once you have done as many past exam questions as possible, then it is time to start doing text book questions, questions from online revision sites and questions from old homeworks.

You should never look at a question and say "I know how to do that, I won't bother trying". Firstly the question could have hidden features which you need to practice, and secondly, the more maths you do, the more agile your brain will be - ready for the day of the exam.

Check your answers

Once you have got into the habit of doing past maths exam papers, then it is really important to check your answers. If you make a mistake then you need to understand where you went wrong. You might be lucky and you may have just made an arithmetic mistake. On the other hand, your error might be due to a fundamental misunderstanding in your brain which you need to get sorted during your revision. If you can't understand the mark scheme (and they can be tricky) then you need to seek out some help from teachers or friends.

Don't forget the theory

Most maths exams require you to revise various theories, proofs and formulas - some of which you will need to learn off by heart. Therefore it is important to read back through your lecture notes, syllabus guides or revision books to check out what knowledge you need for the exam.

Hopefully most theory will come to light in past exam questions, but it is still worth checking that you haven't missed anything which you need. This is particularly important for undergraduate maths revision, where you might not have access to many past exam questions.

Committing the theory to memory

Everyone has different methods for revising, however for most people writing stuff down seems to help commit information to memory. Some people put post it notes around the house - this at least reminds you on a daily basis about what you need to know. Others choose to use flash cards - this is a good way to check that you can answer the maths questions which will be in your exam. Another useful approach is to try and cram all the knowledge you need for the course onto a one page summary sheet.

Don't ignore the things you can't do

Some people play a dangerous game where they ignore certain topics, with the hope that they won't come up in the exam. This is never a good idea, you need to make sure that you face up to your least favourite topics, seeking help for the areas which you are weakest at.

Avoid buying a whole set of new equipment ready for the exam

This is especially true of scientific calculators - if you aren't used to your calculator then you could easily make mistakes in the exam. Equally you don't want to find out that your pencil doesn't fit into your brand new pair of compasses or that you don't know how to use your fancy new protractor. Make sure that you revise with the equipment which you will use on the day of the exam. (Although you might want to buy some new batteries for your calculator!)

Don't fall into the natural brilliance trap

Some people don't revise enough because they think they are naturally brilliant at maths. This type of person will usually hit a point where they underachieve. Don't lull yourself into a false sense of security - even gifted mathematicians still need to revise.

Another type of person writes themselves off, even before they have started their revision. They think that they aren't naturally brilliant enough to do well in a maths exam, and therefore only revise half-heartedly. What they forget is that a lot of maths revision is about the sweat and toil rather than the natural ability of a candidate. If you put in the hours understanding past paper questions, you will be able to do better than you could have ever imagined.

Maths is a social subject

What most people don't realise is that most professional mathematicians spend a lot of time working with each other discussing mathematics, rather than hiding away in isolation.

When you are planning your maths exam revision, make sure to plan in a mixture of group study sessions with friends alongside time alone for revising. Discussing and explaining mathematics can help us understand the subject much more deeply.

Don't forget your general revision tips

Make sure you follow all the general revision advice which can help you to revise for any subject.

Make a revision plan and stick to it

Sleep well, eat well and drink plenty of water

Take breaks in revision

Stay calm and keep your exam in perspective

Attend any extra revision sessions which are put on for you

Talk to your friends and family about how you are doing

Keep your eye on the prize

Revising for maths exams can be hard work - it can mean making sacrifices where you choose to prioritise revision over seeing your friends or relaxing in front of the TV. Therefore it is always important to keep your eye on the prize. Think about what your maths qualification will mean for your future life and career. Hopefully this will keep you motivated when times are tough during revision.

Article by Hazel Lewis

Image credits

Protractors by Dean Hochman@Flickr

Math Formulas by João Trindade @Flickr

Scientific Calculator by Liesl@Flickr

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What is the best way to revise for a maths exam? - Maths Careers

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Training for a maths exam is a bit like training for a big running race - you can't just read about the theory, you need to do as much practice as possible. Practicing past papers is the number one tip for revising for a maths exam.

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Crime is a problem everywhere, and especially in big cities, but why are some areas more at risk than others? The police call these danger zones "crime hotspots", and try to focus their resources in these locations. They're usually successful in reducing the number of crimes committed in a hotspot, but it can sometimes end up increasing crime elsewhere. Mathematicians have analysed how crime hotspots come together and move about, revealing some hotspots are harder to cool than others.

Neighbourhood watch

Just as bees will seek out the gardens with the most flowers, criminals are attracted to certain areas more than others. Broken windows and walls covered in graffiti are an invitation to would-be criminals, advertising that this neighbourhood is being neglected and makes an easy target. On the other hand, streets bristling with CCTV cameras that are constantly patrolled by the police are unlikely to get hit.

Looking at a map of a city, you can imagine that each point has a certain risk of crime that varies according to the nature of the area and the time of day. This risk is also related to the number of criminals in the area at any given moment and the way they behave. Surprisingly, most perpetrators look for opportunities fairly close to their home or workplace, rather than somewhere further away. They also like to revisit the location of a successful crime to have another go, leading to an increased risk in neighbouring areas.

Putting all these factors together, mathematicians at the University of California, Los Angeles, used reaction-diffusion equations to create a model showing how crime risk spreads. These equations describe the way different substances can interact or disperse, and have previously been used to explain how animals such as leopards get their spots. In this case the "substances" are the levels of criminals and crime risk in a particular area.

The model suggests that crimes are surrounded by an "area of influence" in which more crimes may be committed. If individual crimes are spread out so that these area don't overlap, the overall level of crime in a city will be roughly the same wherever you are. A similar thing happens if each crime has a large area of influence - there's so much overlap that the level of crime is constant. It's only when just a few crimes overlap that hotspots begin to emerge.

Supervillians and subvillians

These hotspots fall into two distinct types. The first are called supercritical, and tend to occur when the background level of crime is low, and sudden crime spikes in a particular area stand out to form a hotspot. These hotspots typically represent a rise in crimes such as burglary or car theft. The other kind of hotspots are subcritical, formed when increasing crime creates overlapping areas of influence, such as when individuals dealing drugs on street corners turns into a full-blown drugs market.

The two types of hotspot respond to policing in different ways. Sending officers into a supercritical hotspot suppresses crime in that area, but the criminals just spread to the surrounding neighbourhoods, forming a "hot ring" of crime. When the police leave, the criminals move back in and crime levels shoot back up. The opposite is true of subcritical hotspots though, as police presence will cut down the crime level permanently and criminals won't simply try their luck elsewhere.

Police departments are used to plotting crimes on a map in order to hunt for patterns, but only this kind of mathematical analysis can reveal the difference between hotspots. Further research could eventually help the police apply specific crime-fighting strategies to different hotspots, and find the best way to keep the streets safe.

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Crime is a problem everywhere, and especially in big cities, but why are some areas more at risk than others? The police call these danger zones "crime hotspots", and try to focus their resources in these locations. They're usually successful in reducing the number of crimes committed in a hotspot, but it can sometimes end up increasing crime elsewhere.

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Have you ever wondered about how many gifts the singer received in the famous Twelve Days of Christmas song? The answer reveals a surprising mathematical pattern!

(If you need reminding about the lyrics they can be found at the bottom of this page.)

Let us look at how many gifts were received on each day.

Total Gifts

The first nice fact is that the singer receives 364 gifts in total - one for every day of the year apart from Christmas day!

There are also some other nice hidden mathematical patterns.

Gifts received each day

Let us look at what happens on day n. On this day the singer receives 1+2+3+...+n gifts. This is also the definition of the nth triangular number. On day 7 for example the singer receives 28 gifts which is the 7 th triangular number.

There is also a well known formula for adding up the first n natural numbers which is:

1 + 2 + 3 + ... +

If we imagine that the singer had continued singing for 20 days they would have received:

= 210 gifts on the 20th day!

Running total of gifts

Let us now look at the running total of gifts at the end of day

The running total will be equal to where stands for the th triangular number. We are basically adding up the first triangular numbers. . If you add up the first triangular numbers you end up with what is called the th tetrahedral number.

Luckily we have a formula for the nth tetrahedral number which is

Let's check it works for our running total on day 12:

Now imagine if the singer had continued receiving gifts from their true love for 20 days. The singer will have: gifts! No wonder the true love stopped after 12 days!

Lyrics of the Twelve Days of Christmas

On the first day of Christmas,
my true love sent to me
A partridge in a pear tree.

On the second day of Christmas,
my true love sent to me
Two turtle doves,
And a partridge in a pear tree.

On the third day of Christmas,
my true love sent to me
Three French hens,
Two turtle doves,
And a partridge in a pear tree.

On the fourth day of Christmas,
my true love sent to me
Four calling birds,
Three French hens,
Two turtle doves,
And a partridge in a pear tree.

On the fifth day of Christmas,
my true love sent to me
Five golden rings,
Four calling birds,
Three French hens,
Two turtle doves,
And a partridge in a pear tree.

On the sixth day of Christmas,
my true love sent to me
Six geese a-laying,
Five golden rings,
Four calling birds,
Three French hens,
Two turtle doves,
And a partridge in a pear tree.

On the seventh day of Christmas,
my true love sent to me
Seven swans a-swimming,
Six geese a-laying,
Five golden rings,
Four calling birds,
Three French hens,
Two turtle doves,
And a partridge in a pear tree.

On the eighth day of Christmas,
my true love sent to me
Eight maids a-milking,
Seven swans a-swimming,
Six geese a-laying,
Five golden rings,
Four calling birds,
Three French hens,
Two turtle doves,
And a partridge in a pear tree.

On the ninth day of Christmas,
my true love sent to me
Nine ladies dancing,
Eight maids a-milking,
Seven swans a-swimming,
Six geese a-laying,
Five golden rings,
Four calling birds,
Three French hens,
Two turtle doves,
And a partridge in a pear tree.

On the tenth day of Christmas,
my true love sent to me
Ten lords a-leaping,
Nine ladies dancing,
Eight maids a-milking,
Seven swans a-swimming,
Six geese a-laying,
Five golden rings,
Four calling birds,
Three French hens,
Two turtle doves,
And a partridge in a pear tree.

On the eleventh day of Christmas,
my true love sent to me
Eleven pipers piping,
Ten lords a-leaping,
Nine ladies dancing,
Eight maids a-milking,
Seven swans a-swimming,
Six geese a-laying,
Five golden rings,
Four calling birds,
Three French hens,
Two turtle doves,
And a partridge in a pear tree.

On the twelfth day of Christmas,
my true love sent to me
Twelve drummers drumming,
Eleven pipers piping,
Ten lords a-leaping,
Nine ladies dancing,
Eight maids a-milking,
Seven swans a-swimming,
Six geese a-laying,
Five golden rings,
Four calling birds,
Three French hens,
Two turtle doves,
And a partridge in a pear tree!

Article by Hazel Lewis

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The Maths Inside the Twelve Days of Christmas - Maths Careers

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Have you ever wondered about how many gifts the singer received in the famous Twelve Days of Christmas song? The answer reveals a surprising mathematical pattern! (If you need reminding about the lyrics they can be found at the bottom of this page.) Let us look at how many gifts were received on each day.