# Activities

## Maths on the DART

If all knows are truths and some unknowns are known, which of these statements must be true?
Travelling by Dart avoids the traffic. But what if you were driving and you calculate that you must achieve and average of 60 km/hr to make your destination on time? The traffic is heavier than anticipated but clears when you reach the half-way point where you realise you have only managed an average speed of 30 km/hr. What average speed would you have to drive for the remaining half of the journey to arrive on time?
What is the next entry in this sequence?
What is the next entry in this sequence?
What is the next entry in this sequence?
What is the next entry in this sequence?
24 x 8 + 48 = ?
What is one million plus ten thousand plus one thousand plus one hundred and 10 plus eleven?
Which is greater a third of half of sixty minutes or six times two -and-a-half times one minute?
Three customers are charged €30 between them for their pizzas. They give the waiter €10 each and when he gets to the till he is told that the bill should be €25 and he is give 5 €1 coins change. Unable to divide €5 by 3 he gives the customers €1 each and slips €2 into his pocket. So the customers page €9 each that's €27 and the waiter has €2 - that's €29 where is the missing euro?
Why are most manhole covers circular?
An array of squares that will fold into a cube is called a net of a cube. Which of the following nets will not fold to make a cube?
Thanks to DART and Irish Rail we have a series of great posters on the DART and in Dublin commuter stations.
Dart Posters 2011
DART Poster Magenta

## Attacking the Castle

A square medieval castle sits on a square island surrounded by a square moat and was under siege. All around the island, there is a 5 metre wide water moat. There's ground on the other side to rest the bridge on (if you can get it to stretch that far).

The attacking king sent his men back to build two wooden foot bridges. Unfortunately these clever men came back with two bridges exactly 5 metres long. (that meant that they couldn’t be supported on the ground at both sides of the moat). They have no nails or rope is there any way they can get across?

### Solution

See the solution here »

## Expanding Car Park

A client wants to double the size of his car park (shown below). He insists on retaining a square shape and as many of the trees as possible. What is the best solution?

### Solution

See the solution here »

## Expanding Car Park Diagram

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## Making Up Time: Solution

It is impossible to arrive on time. Doing the calculations will yield an answer of infinity. By driving at half the required speed the allotted time will be used up at the halfway point. For example, suppose that the time allowed for the journey is one hour then the distance would be 60 km and the half way point will be 30 km. Travelling at 30km/hr will take one hour to reach the half way point - therefore no time left.

## Picture of Castle Layout

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## puzzle-attacking-the-castle-1.jpg

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## Maths Heroes

Here are suggestions and resources for discovering the wonderful stories in mathematics

Maths Heroes – links to the past

An appreciation of the history of mathematics can motivate some students as it gives an insight into how great mathematicians of the past have experimented with the subject.

Using the websites and books listed below students can make posters and booklets of their mathematical heroes. Along the way collecting interesting stories such as:

Carl Friedrich Gauss was not always the old man shown in this portrait. This famous mathematician showed early promise when at the age of 3 he corrected a bookkeeping error of his father’s and as a youth astounded a teacher by finding a quick way to add up all the numbers from 1 to 100.

The story of the 350-year quest to solve Fermat's Last Theorem which was finally achieved by Andrew J. Wiles in 1994, after eight years of intensive and creative work.

The mathematician Abraham de Moivre developed a great amount of new mathematics and is also famous for predicting the day of his own death. He found that he was sleeping 15 minutes longer each night and this added up to the fact that he would die on the day that he slept for 24 hours. Unfortunately he was right!

Some possible resources to help children create their posters:

## Websites on Mathematical Heroes

MacTutor History of Mathematics: Indexes of Biographies

www.gap-system.org/~history/
This is a comprehensive collection of biographies and  a great reference for maths teachers or students in middle school and above. It also contains posters and mathematical stamps which can be used for wall displays and posters.

As well as having a section on “Famous Mathematician of the Day” and “Quotation for today”

Mathematicians' Anniversaries throughout the Year

www-history.mcs.st-andrews.ac.uk/Day_files/Year.html
This page indexes the same collection of biographies by significant dates (births, deaths, key discoveries). Looking up what mathematical anniversaries are being celebrated on any given day of the school year can be fun.

History of Mathematics for young mathematicians.

Website gives a student friendly gallery of some famous mathematicians

www.mathsisgoodforyou.com/people/famousmathematicians.htm

Biographies of Women Mathematicians

Contains interesting stories on women in mathematics over the years.

www.agnesscott.edu/lriddle/women/women.htm

Math Marvels
A secondary school maths class in America created this Website of 32 mock interviews with famous mathematicians in 2001-02. Your students will find the interviews fun. There is also a set of resources at the end of each interview.

www.3villagecsd.k12.ny.us/wmhs/Departments/Math/OBrien/mathmarvels.html

Math Quiz
On this site students can take a preferences quiz and find mathematicians with similar interests to them.

http://nces.ed.gov/nceskids/grabbag/MathQuiz/

The Greatest Mathematicians of All Time

Website gives you their top 100 mathematicians of all time.

http://fabpedigree.com/james/mathmen.htm

Online Math Applications!: History
This site includes some biographies of mathematicians.

http://library.thinkquest.org/4116/History/history.htm

The Story of Maths

Marcus du Sautoy presents this BBC series on the history of mathematics.

## Books on Mathematical Heroes

Mathematicians Are People, Too: Stories from the Lives of Great Mathematicians, by Luetta and Wilbert Reimer. Dale Seymour Publications, 1990 (Vol. 1), 1995 (Vol. 2)

www.amazon.co.uk/Mathematicians-are-People-Too-Stories/dp/0866515097/ref=sr_1_1?s=books&ie=UTF8&qid=1315838723&sr=1-1

These two volumes, featuring 15 compelling stories in each are written for ages 8-12. They are great for reading aloud to a class, or for independent reading for students aged 10 and above.

Math & Mathematicians: The History of Math Discoveries Around the World, Vol. A-H and I-Z, by Leonard C. Bruno. UXL, 1999.

www.amazon.co.uk/Math-Mathematicians-History-Discoveries-Around/dp/0787638137/ref=sr_1_1?s=books&ie=UTF8&qid=1315838769&sr=1-1

This two-volume set is organized alphabetically, like a selective math encyclopaedia, with 50 short biographies (including fourteen 20th century mathematicians). It includes a detailed mathematical timeline, glossary, and alternate table of contents organized by math field and ethnicity. The writing style is reasonably accessible for upper-primary read-aloud (with some paraphrasing) or for independent reading at secondary-school level.

The Experimenter's A-Z of Mathematics: Maths Activities with Computer Support by Steve Humble. David Fulton Publishers, 2002

www.amazon.co.uk/Experimenters--Z-Mathematics-Activities-Computer/dp/1853468177/ref=sr_1_1?s=books&ie=UTF8&qid=1315838885&sr=1-1

Mathematics at all levels is about the joy in the discovery; it's about finding things out. This fascinating book is a guide to that discovery process, presenting ideas for practical classroom-based experiments and extension activities. Each experiment is based on the work of a key mathematician who has shaped the way that the subject looks today, and there are historical notes to help teachers bring this work to life.

Of Men and Numbers: The Story of the Great Mathematicians, by Jane Muir. Dover Publications, 1996,

www.amazon.co.uk/Men-Numbers-Story-Great-Mathematicians/dp/0486289737/ref=sr_1_1?s=books&ie=UTF8&qid=1315839464&sr=1-1
These stories are lively and embellished with fictionalized details.

Math Through the Ages: A Gentle History for Teachers and Others, Expanded Edition, by William P. Berlinghoff and Fernando Q. Gouvea. Mathematical Association of America, 2003.

www.amazon.co.uk/Math-through-Ages-Mathematical-Association/dp/0883857367/ref=sr_1_1?s=books&ie=UTF8&qid=1315839184&sr=1-1
This engaging book, organized by mathematics topic and is recommended for students 10 years and older. The expanded edition includes classroom resource material.

Please note that CALMAST / Maths Week Ireland has no control over the content of these sites. Teachers and parents must satisfy themselves as to the suitability of any of these sites.

## Maths Puzzle Day

Here is advice from expert Steve Humble on running a maths puzzle day in your school

Maths Puzzle Day

There are a number of formats you can use for a Maths puzzle day, such as:

• Student teams move around a room (classroom/Hall) tackling the puzzles. For each puzzle challenge they are given a set amount of time. Each team gets a score depending on how many puzzles their team solves.
• Teams are given puzzle challenges. Once the team has solved the puzzle correctly they are given the next.
• A set of puzzle challenges is given out at the beginning of the week to all students in the school.
• Quick-fire short puzzles can be given out daily.

Create your own Puzzle Day by using the resources below:

Puzzle.com is a fantastic website full of great puzzles. All puzzles come with clear solutions.

www.puzzles.com/

Venture into the world of Puzzleland created by Sam Loyd

There is an enchanted place where every sign is a puzzle, every question a riddle….

www.samloyd.com/puzzleland/index.html

Find out more about one of the great puzzlers of all time www.samuelloyd.com/

Another puzzler is Henry Dudeney and you can find links to his puzzles at http://en.wikipedia.org/wiki/Henry_Dudeney

Nrich website has a range of good puzzles and mathematical challenges for students of all ages  http://nrich.maths.org/public/search.php?search=puzzles

Primary Mathematics Challenge papers from 2008 to 2011 with answers are free to download. These questions make a good source of puzzle challenge questions for team games.

www.m-a.org.uk/jsp/index.jsp?lnk=251

The FunMaths Roadshow is a collection of 350 mathematical activities suitable for use with school pupils between the ages of 5 and 20. It is an excellent instant resource when creating at Maths Puzzle Day. Costs 40 Euros including P&P

www.maths.liv.ac.uk/lms/funmaths/

Centre for Innovation in Mathematics Teaching has over 100 competitions puzzle challenges with answers ready to be cut out and used

www.cimt.plymouth.ac.uk/resources/puzzles/default.htm

## Maths Mazes

A maze is great fun and it can be a maths learning experience too!

Maths Mazes

Mazes offer open ended problem solving for all ages in an imaginative and creative environment. They develop mathematical logic skills and also require students to memorise quite lengthy sequences of moves in a particular order.

There are a great range of mathematical mazes. The maze designer Adrian Fisher has created a set of interesting logic mazes called “6 minute mazes” For more information visit

On the streets during Maths Week Ireland we have used these 6 minute mazes

The Jumping Maze

How to play
Start at the black square with the "1" on it in the centre of the bottom row, and jump forward, sideways, or backwards, but never diagonally, the number of squares indicated by the number on the square. The objective is to find your way to the central square.

It is not as easy as it looks.

Archery Maze
How to play
Starting at the arrow in the black square, find your way to the central target. Move any distance in the direction indicated. Whenever you stop, change direction as indicated by the arrow on whichyou land.

Note this is a very difficult maze as there are 20 moves in the correct path!

No Left Turn Maze

These mazes only allow right turns. (You are not allowed to turn around fully or go backwards). Here is one example and solution (below).

Of course you can also make no right turn mazes.

These mazes may be made in chalk in the playground or by many other ways. It could for instance be made with square bales of straw.

A Maths Maze Day in your school offers the opportunity for students to develop creative maths problem solving skills.

How to design a logic maze

Choose an entry point to the maze which must be on the edge of the maze. Then choose a final destination square and draw a main path, or solution route, from this square to the entry point in the  maze. For example, when creating your own Jumping Maze you would need to work backwards from the centre square like this:

The solution route created is 1, 1, 3, 3, 2, 2, X

To complete this maze simply put other numbers into the blank squares on the grid. The level of complexity of the final maze depends on the position of the numbers on the grid.

Most of the mazes that your students create will have a number of different solution routes to the final destination square. To create a unique solution path (only one way to the final destination square), none of the other numbers placed on the grid should allow you to “jump” onto the solution route. This offers a difficult yet very motivational challenge to students.

Make sure when creating a maze that the path is not too short or your maze will be solved very quickly. Alternatively don't make the path too long, as you won't be able to have many choices or dead-ends, and then the maze becomes less of a challenge. Think carefully about the design and the way the maze looks; this will be important when it comes to getting others interested in playing your maze.

Here are some logic mazes you can show students before they start to design their own mazes. To motivate students it is a good idea to chalk mazes on the playground or to mark them out with tape in the school hall.

No Left Turn Mazes

www.logicmazes.com/easy/maze1.html

Eyeball Shape Mazes

www.logicmazes.com/eyeball.html

Alice and Arrow Mazes

www.logicmazes.com/alice.html

Number Mazes

www.logicmazes.com/n1mz.html

Rolling Block Mazes

www.logicmazes.com/rb/column.html

More ideas on designing a maze

http://gwydir.demon.co.uk/jo/maze/design/index.htm

Books on Mazes

The Amazing Book of Mazes by Adrian Fisher

Adrian Fisher is without question the worlds leading maze designer, and here presents a comprehensive, fascinating and fun account of the history of the maze that has an equally strong interactive element. This stunning volume will delight mass audiences everywhere.

Mathematics Galore! by Christopher Budd and Christopher Sangwin, Published by Oxford University Press

www.amazon.co.uk/Mathematics-Galore-Masterclasses-Workshops-Applications/dp/0198507704/ref=sr_1_1?ie=UTF8&qid=1315947277&sr=8-1

The book has a chapter on Mazes. Other chapters are on the maths of folk dancing, sundials, magic, castles, codes, number systems, and slide rules.

Problem Solving through Recreational Mathematics by Averbach and Chei. Published by Dover

www.amazon.co.uk/Problem-Solving-through-Recreational-Mathematics/dp/0486409171/ref=sr_1_1?s=books&ie=UTF8&qid=1315947823&sr=1-1

Understanding the maths involved in mazes - Networks and Graph Theory – can get complex. If you wish to teach students some of this maths this book has accessible examples and exercises for 10 to 16 year olds. Its also has some really nice puzzles and problems.

## Steve Humble

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## Arrow Maze

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## Maths Trail Example Durham

A maths trail example

Durhamtrail.pdf — PDF document, 811 kB (831332 bytes)

## Maths Art

Maths Art – explore the Maths in Art

There are many geometrical links between mathematics and art. During your Maths Art Day you can choose to explore a certain artist or style of painting with the students creating their own art or posters.

Escher Tessellated Fish

www.tessellations.org/eschergallery10.htm

Random Art – use a dice to determine colours used

www.maths2art.co.uk/

Galileo wrote that, “The Universe is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures”

The Golden Ratio was thought by the Greeks to have certain aesthetic properties which link to nature. It has been used by artists and architects for generations.

Finding the Golden Ratio

See Dr Maths (aka Steve Humble) uncovering the golden ratio in the architecture of a Cathedral.

www.teachersmedia.co.uk/series/secondary-lesson-starts

Fibonacci Number and Nature

Maths links to nature with Rabbits, Honeybees, Sea Shells, Flower Petals and leaves

http://www.teachersmedia.co.uk/series/secondary-lesson-starts

The teacher package on Maths and Art from Plus Magazine brings together all Plus content on maths and art in the following categories and is a good place to start and get ideas for your Maths Art Day; Maths and the Visual Arts, Maths and Design, Maths and Music, Maths and Film, Maths and Theatre, Maths and Writing.

http://plus.maths.org/content/teacher-package-maths-and-art

Maths2art

A website suggesting ways to use art to teach maths.

www.maths2art.co.uk/

## Escher Fish

Click to view full-size image…
Size: 41.9 kB

First+School+Easter+Trail.pdf — PDF document, 522 kB (535235 bytes)

Maths on the Quayside.pdf — PDF document, 237 kB (243144 bytes)

Irish Maths Week Walk.pdf — PDF document, 330 kB (338493 bytes)

Maths-Walk-activities.doc — Microsoft Word Document, 87 kB (89088 bytes)

## Code Breaking for Young Secret Agents

The world of secret codes holds a fascinating air of mystery with secret agents trying to discover the enemy’s plans before the enemy uncovers theirs. The Spartans are credited with creating the first system of military secret codes, or secret ciphers, as they are sometimes called. This is why the study of secret codes and methods of breaking these codes is called Cryptology, from the Greek kryptos meaning hidden or secret.

One example of a secret code method is called a Keyword Cipher

With this secret code keyword is placed at the beginning and this shifts the remaining letters of the alphabet, not used in the keyword, to the right. The letters that are not used in the keyword are placed in line in alphabetical order.

For example if the keyword was JAMESBOND the code would read as follows:

To code the message:  SEND HELP QUICKLY

The code for this is:    RSIE NSGL PUDMFGY

Here is a challenge for you to try, use the JAMESBOND Keyword Cipher to break the code and find the answer to this question.

In the James Bond film The Man With The Golden Gun, how many shots does Scaramanga have with his Golden Gun?

Below is the coded answer to this question.

GDHDTSE TK CURT KIS AUGGST

Organising the Code Breaking Day

There are many different types of secret codes and you can organise different types of challenges for students to take part in.

• Student teams move around a room (classroom/hall) decoding to find the hidden message(s). For each challenge they are given a set amount of time. Each team gets a score depending on how many codes their team solves.
• Teams are given code breaking challenges. Once the team has decoded the message correctly they are given the next.
• A set of coded messages are given out at the beginning of the week to all students in the school.
• Quick-fire short secret codes can be given out daily.
• You can work out the relative frequency of letters in the written word by looking at newspaper articles and books. This is useful to spies since if you know E is the most frequent letter and you are decoding a paragraph with lots of Hs, you would guess that E has been replaced by H in the code.

Create your own Code Breaking Day by using the resources below.

Websites on Code Breaking

Codes and Ciphers Teaching Resources Website

Great resource for your code breaking day on Substitution Ciphers, Braille, Bar Codes, ISBN Numbers, Genetic Fingerprinting, Postcodes, Semaphore, Morse Code, and many others. Each comes with lesson plans, pupil information and exercises, and teacher notes.

www.cimt.plymouth.ac.uk/resources/codes/default.htm

Secret Code Breaker

Learn all about secret codes including Caesar Ciphers, Auto Key Ciphers, and Monoalphabetic Substitution Ciphers. Online and downloadable solvers are provided for many of the common ciphers. The website also contains some interesting history stories on code breaking

Kids Spy Equipment

Fun website on how to make spy equipment – How to build a periscope, Keyhole spy tool, Spy ID card, Make Invisible Ink and  Fingerprint powder.

Codes, Ciphers & Codebreaking

Comprehensive guide to codes

www.vectorsite.net/ttcode.html

The Secret World of Codes and Code Breaking

Stories to use for background history on code breaking

http://nrich.maths.org/2197

Books on Code Breaking

The Secret Life of Codes (Murderous Maths) by Kjartan Poskitt

Readers will learn how to encode and decode their own messages in as many ways as possible with Poskitt hilarious characters.

www.amazon.co.uk/Secret-Life-Codes-Murderous-Maths/dp/1407107151/ref=sr_1_1?s=books&ie=UTF8&qid=1316003120&sr=1-1

### The Code Book: The Secret History of Codes and Code-breaking by Simon Singh

Contains many fascinating accounts of code-breaking in action, from its use in unmasking the Man in the Iron Mask and the defeat of the Nazis to the breaking of a modern cipher system by a world-wide army of amateurs in 1994.

Secret Code Breaking for the young secret agent

Watch out for Dr Maths (aka Steve Humble) book on code breaking coming out in January 2012

www.greenboardgames.com/Home1.htm

## Dub1in by Numb3rs

Dublin by Numbers Maths Podcast.

Dub1in by Numb3rs is a Mathematical Walking Tour of Dublin developed by Ingenious Ireland and launched for Maths Week Ireland 2011.

While on your tour, you can also take photographs of mathematically related scenes or objects and upload them to this website. See below for instructions.

See Photo Gallery Here:

## Win an Apple iPOD Touch

### Take photos on the trail and share them!

Dublin by Numbers and Maths Week Ireland
Photo Competition - Take a Photo of numbers, shapes or patterns along the route and submit them to Maths Week Website
Two Categories:
- Primary
- Post-Primary

Terms and Conditions can be found below

While on your tour, you can also take photographs of mathematically related scenes or objects.

You can then load up the photos here on this website

Or, if you are using a mobile phone, you can easily send

them by MMS to 087 113 2062 (normal charge from your mobile provider applies)

And they'll be loaded onto the Dub1in by Numb3rs Gallery.

Terms and Conditions

a. Closing date for receipt of entries is 5pm on Friday, November 18th 2011.

b. Winners will be drawn out of a hat and announced on Sunday November 20th 2011

c. There will be 2 categories open for entry – primary students, and post-primary. There will be one

winner per category.

d. Image entries can be uploaded to the dedicated Maths Week Ireland competition site:

http://www.mathsweek.ie/2011/gallery/submit-your-dublin-maths-walk-photo

OR sent from your phone by MMS to 087 113 2062. NOTE: your Network provider may charge you to

send an MMS. Hard copies cannot be accepted.

e. Only one entry is allowed per person.

f. Photographs must be the entrant’s original work.

g. The decision of the judging panel is final. No discussion will be entered into pre or post judging

Supported by:

## The Magic of Maths – become a Maths Magician

You may be surprised to learn that there is a lot of mathematics behind magic, and by giving your students maths magic tricks to investigate, you and your class can learn new applications of mathematics and become maths magicians. You will find that these activities can be engaging for even the most reluctant maths student.

The following simple illusion is just one example that intrigues young and old alike. Cut along the dotted line and slide the lower half along by one face and magically one of the faces vanishes! Challenge your students to draw their own illusion. Start with something simple like a picture of pencils, blocks or hats.

The website Geometrical Vanishes is a good place to start when looking at visual magic

http://library.thinkquest.org/28049/geometrical_vanishes.htm

Some more Visual Maths Magic can be investigated with the area of these shapes.

This set of four pieces is called Hooper’s Paradox. The top rectangle has an of area of 30 (10x3) and can be rearranged into the bottom shape, which is made up of two rectangles. Strangely these two rectangles have a combined area of 32 (2x6 + 4x5 ). When the magician performs this trick he exclaims how he has gained 2 more pieces for free.

To see Hooper’s Paradox being performed by a professional magician play this video to your students, then ask them to make cardboard versions of Hooper’s Paradox and investigate how it works.

Websites on Mathematical Magic

Google – Maths Magic on YouTube and you will discover hundreds of videos.

One of my favourites is “Math magic card trick!!” as it shows two teenagers demonstrating a card trick in the park. At the end of the video one of the teenagers says “How does it do it, I don’t know!”

What a great place to start the lesson with your class….. www.youtube.com/watch?v=NLJYZJ_ZuGA

Tricks and Games on Murderous Maths website

Prime number trick, Predictor cards, Five card trick, Calendar trick and many more

www.murderousmaths.co.uk/games/gamesint.htm

Stunning Friends with Math Magic

A collection of 22 card tricks, number guessing games, paper and glue magic, and other maths magic tricks. Each trick is explained

www.cut-the-knot.org/arithmetic/rapid/magic.shtml

Maths & Magic

Website gives a range of interesting maths magic tricks

Website gives 15 interesting mathematical tricks of varying difficulty

Books on Mathematical Magic

Mathematics, Magic and Mystery by Martin Gardner

Magic tricks that may be played with cards, common objects, special equipment, drawings, and pure numbers. This is one of the great maths magic books.

www.amazon.co.uk/Mathematics-Magic-Mystery-Dover-books/dp/0486203352

Creative Magic by Steve Humble and Martin Duffy

Children and adults will improve their mathematical skills in a friendly and fun way. This book shows you how to perform magic and how to create your own versions of classic magic tricks. The creativity comes from the chapters ideas on how to develop the tricks to make them your own.

www.amazon.co.uk/Creative-Magic-Steve-Humble/dp/1446116174

Or from iTunes at £1.99 -

http://itunes.apple.com/us/book/become-maths-wizard-creative/id467188942?mt=11

Magic for Kids by Andrew Jeffrey

It includes a huge range of mathematical tricks which both teach and entertain.

www.andrewjeffrey.co.uk/products.asp

Murderous Maths books by Kjartan Poskitt

All the books in this series contain some maths magic tricks

www.amazon.co.uk/Murderous-Maths-Everything-Kjartan-Poskitt/dp/1407131435/ref=pd_sim_b4

## Why not run an event yourself

Steve Humble (aka Dr Maths) gives advice on running in-school maths enrichment activities.

Steve Humble (aka Dr Maths) believes that the fundamentals of mathematics can be taught via practical experiments. Having worked as a maths subject leader in various educational establishments for over 20 years, he has spent the last five years as a Senior Regional Coordinator for the National Centre for Excellence in the Teaching of Mathematics (NCETM). Now working as a Freelance Mathematics Consultant, he supports schools in raising their student achievement through creating a positive attitude to maths. Steve also works with the Further Mathematics Support Programme and teaches mathematics on the Primary PGCE Course at Newcastle UniversityIn his role as a maths publicist he writes a fortnightly column for the Evening Chronicle newspaper to help create greater public understanding of mathematics. Carol Vorderman’s recent UK government report on mathematics education described Steve as “an inspiring individual, providing opportunities for children to do mathematics that they find exciting and interesting”. He holds the Guinness World Record for the most children learning maths outside the classroom.

For more on DrMaths see www.drmaths.co.uk or email drmaths@hotmail.co.uk

How to Create a Fun Maths Day

Does the prospect of coordinating a Maths Day event during Maths Week Ireland seem a little daunting? This guide of resources and ideas aims to alleviate those fears, giving you helpful advice on how to successfully run your very own maths event.

You may decide to have a particular theme for your Maths Day or to use a variety of ideas. Click on the following links to help you plan and organise your schools Maths Day:

Maths Heroes – links to the past

Maths Puzzle Day

Maths Trails - Walk on the wild side with maths

Maths Mazes

The Magic of Maths – become a Maths Magician

Code Breaking for the Young Secret Agent

Maths Games and Challenges

Maths Art – explore the Maths in Art

Use Maths to design your very own Kite

Maths Computer Activities

Cross Curricular Maths

How will Maths Day work.

• Work together with other members of staff in your school – it’s always good to bounce ideas off each other and everyone has their own strengths you can draw on. Having decided upon an idea or theme for your Maths Day involve the students in a brainstorming and decision-making session for ideas on what they would like to do. Set up a smaller team of students to help you plan and create the resources required. Your students will have lots of creative ideas to help.

• Work with your team on the details of each activity. Guide the student team to keep the activities easy to understand.

• You may want to have small prizes or rewards when challenges have been successful completed.

• As part of the Maths Week Ireland you could plan to have a family fun afternoon/evening to celebrate the successes of the week. Give out prizes and/or fun certificates for game winners.

• Have a team of students capture the day on video or in photographs and use this to share the positive experiences of the day.

• If it’s your first time organising a maths day it’s a good idea to keep it simple, and then build on the activities you have found to be most successful year on year.

Tell us about successful events you have run, or if you have any good web resources, suggestions or ideas for Maths please email us at mathsweek@wit.ie and let us know.

## Maths Trails

Walk on the wild side with Maths

"Do you know what my worst lesson is? It’s maths…but I really like doing maths when it’s outdoors!"

"My favourite bit this week was the maths trail because it’s outside and you get to do more things."

The above sentiments were expressed by children, who had just completed a maths trail as part of their school’s mathematics week.

There are numerous mathematically rich examples, living and non-living, that can be found in the school playground, the local shopping centre, the neighbourhood park, the local sports ground, and the city museum/art gallery, to name a few.

Take a walk on the wild side and create a math trail. The trail consists of a sequence of designated sites along a planned route where students stop to explore mathematics in the environment.

We recommend introducing children to math trails by having them explore, in small groups, 4-5 areas of interest within their own classroom. Writing a maths question for the area they are in. Following several of these classroom explorations and follow-up class discussions, children could venture outside to create maths questions at 4-5 named locations. These questions can then be discussed and developed into your very own maths trail.

It is good to have a range of question starting points, such as:

• Look at that. Look around you. What can you see?
• How many?
• How far or near?
• How long, short, tall, high, deep, heavy?
• How much do you see? How much more is hidden?
• Estimate the size, height, length, weight of …….?
• What is the name of ……..?
• Can you continue this pattern?
• What is the chance of that?
• What kind of shape? What shapes do you see? Draw them.
• Why do you think the path does not follow a straight line?
• What if we change this?
• What if we add a line? What if we add a shape?
• What difference does it make? Is it still symmetrical?
• Could you make a pattern with …….?
• Show that this works. Is it always true?

Maths trails can also be designed to link strands and strand units of the mathematics curriculum. The mathematics curriculum can also be linked and integrated with other subject areas such as PE, geography, history and science, using a topic-based trail.

Both students and teachers can create math trails that target a range of mathematical understandings. Specifically, math trails can be:

Student-generated, designed for their grade-level peers or younger peers to undertake;

Teacher-generated, which are trialled and modified by children to produce a new, improved math trail;

Teacher-generated, designed for children and their families to explore in their school surroundings, their home, or their local environment;

Teacher-generated, designed for their teaching peers to trial, improve, and implement.

Examples of Maths Trails:

A student-generated math trail, The Easter Trail. It was created by a class of 7-year-old children, with some teacher support, for a parent/child activity day.

A Teacher-generated maths trail, Maths on the Quayside. It was created trialled and modified by 10-year-old children, with teacher support for a large cross school event. During the two day event 2,600 children walked this maths trail.

A Teacher-generated maths trail, The Hidden Beauty within Durham City. It designed for 14-year-old children and their families to explore their local environment. The local Tourist Information Centre provide this trail to families who are interested in searching out the hidden maths in their city.

Maths Week Ireland  maths trail takes a walk down South King Street in Dublin. This trail is designed to show young people and families that maths is related to the real world around them and that while challenging, maths can be enjoyable.

USEFUL SITES

See here for template for designing maths walks

The following websites give background and ideas on how to organise a maths trail:

A pdf file which outlines the steps to making a maths trail, and gives some examples which are relevant to the Irish primary school maths curriculum.

www.primarymaths.ie/files/mathstrail1st2nd.pdf

A Maths trail of the Botanic Gardens, Dublin designed by Marino College of Education.

UK Maths Trails

www.foresteducation.org/resources/woodland_m_1122560070.pdf

An example of a woodland maths trail, developed with a view to reinforcing school maths and making a link with a woodland environment.

nrich.maths.org/public/viewer.php?obj_id=2579

From the NRICH group in University of Cambridge. Gives ideas on how to develop a maths trail, and gives locations in the UK of cultural sites which contain maths trails for children.

www.brandlingprimary.org/2007/06/maths_on_the_quayside.html

An example of a maths trail around the city of Newcastle.

an example of a maths trail in the UK with downloadable material.

## General Activities

Additional maths related material and activities suitable for primary school students will be continuously added. Please tell us about resources you have used and activities you have run in your school so we can share them.

The following sites have fun interesting maths for kids and ideas for teachers.  Please note that CALMAST has no control over the content of these sites. Teachers and parents must satisfy themselves as to the suitability of any of these sites. If you have any other good web resources for Maths please email us at MathsWeek@wit.ie and let us know.

There are loads of great sites on the web with maths puzzles and challenges for all interests.

### Manga High (http://www.mangahigh.com)

Mangahigh's math games are designed with math at the core!

### Maths is fun (http://www.mathsisfun.com/)

A U.K. based website which covers basic maths skills with some simple and more complex stuff.

### Oracle ThinkQuest (http://www.thinkquest.org/)

Many maths resources for all ages. Select an age group from the left hand side of this screen.

### PRISM (http://www.maths.nuigalway.ie/PRISM)

Problem Solving for Irish Second Level Mathematicians - interesting problems posted each week.

## Activities for Primary Schools

Additional maths related material and activities suitable for primary school students will be continuously added. Please tell us about resources you have used and activities you have run in your school so we can share them.

The following sites have fun interesting maths for kids and ideas for teachers.  Please note that CALMAST has no control over the content of these sites. Teachers must satisfy themselves as to the suitability of any of these sites. If you have any other good web resources for Maths please email us at MathsWeek@wit.ie and let us know.

#### These websites have various maths resources for primary school ages

MathShere Maths Puzzles http://www.mathsphere.co.uk/resources/MathSphereMathsPuzzles.htm
This British website features a great set of maths puzzles for upper primary children, which are ideal for printing out in colour and laminating, making a long lasting resource.

Maths resources for kids
http://www.coolmath4kids.com/
A U.S. website designed for primary school children, which is full of puzzles and lessons which make maths fun.

Maths games and resources
This Australian website has a lot of maths games and maths lessons designed for primary school children.

Woodland maths zone
http://www.woodlands-junior.kent.sch.uk/maths/index.html
This is a U.S. website with interactive maths activities aimed at 7-11 year olds.

Project Happy Child
http://www.happychild.org.uk/wks/math/
This website provides many different free maths worksheets and educational resources for all school levels.

BBC school resources
http://www.bbc.co.uk/schools/websites/4_11/site/numeracy.shtml
A BBC website dedicated to numeracy and maths skills, with activities for different age groups and abilities.

http://www.bbc.co.uk/schools/numbertime/ For kids 4- 11 years old has songs and games etc. including printable worksheets to download.

Mathwire games
http://www.mathwire.com/games/games.html
This website features games from the many different strands of maths.

SuperKids math worksheet creator
http://www.superkids.com/aweb/tools/math/index.shtml
This website allows teachers and parents to make maths worksheets for a wide range of mathematical problems.

## Activites for Secondary Schools

Maths related material and activities suitable for secondary school students can be found on the web. Please tell us about resources you have used and activities you have run in your school so we can share them.

The following sites have fun interesting maths for kids and ideas for teachers.  Please note that CALMAST has no control over the content of these sites. Teachers must satisfy themselves as to the suitability of any of these sites. If you have any other good web resources for Maths please email us at MathsWeek@wit.ie and let us know.

http://www.maths.nuigalway.ie/PRISM - Problem Solving for Irish Second Level Mathematicians - interesting problems posted each week.

http://library.thinkquest.org/4116 - categories include investing, history of maths, maths and music, maths and science.

Plus+ magazine

http://plus.maths.org

Plus+ is a complementary online magazine, which to tell students about the diverse applications of mathematics to solve problems in physics, chemistry, biology, engineering, and economics. It provides stories about new developments in mathematics and mathematical sciences, interviews with mathematicians, information about degree courses, history of mathematics and science, mathematical biographies, and links to other mathematics websites and resources.

Skoool.ie

http://www.skoool.ie/junior.asp?id=1171

This Irish website has resources for junior cycle secondary school.

http://www.scienceu.com/geometry/classroom/buildicosa/index.html - Lots of shapes for kids to make including a team project to build a massive icosahedron.

http://www.coolmath-games.com - maths games, maths lessons, maths puzzles and maths fun for kids of all ages :-)

http://www.mathsisfun.com - MathsIsFun.com is developed and maintained by Rod Pierce, who loves mathematics and fun. The idea behind the site is to offer mathematics as well as some fun bits, and to combine the two wherever possible.

http://library.thinkquest.org/4116 - categories include investing, history of maths, maths and music, maths and science.

## Activities and Puzzles

### Dub1in by Numb3rs

Free Podcast Walking Tour of Dublin

### Maths Heroes

Here are suggestions and resources for discovering the wonderful stories in mathematics

### Maths Puzzle Day

Here is advice from expert Steve Humble on running a maths puzzle day in your school

### Maths Mazes

A maze is great fun and it can be a maths learning experience too!

### Maths Art

Explore the Maths in Art

### Code Breaking for Young Secret Agents

The world of secret codes holds a fascinating air of mystery with secret agents trying to discover the enemy’s plans before the enemy uncovers theirs.

### The Magic of Maths

You may be surprised to learn that there is a lot of mathematics behind magic, and by giving your students maths magic tricks to investigate

### General Activities

Resources and materials suitable for children of all ages.

### Primary Schools

Resources, materials and activities suitable for Primary Schools

### Secondary Schools

Resources, materials and activities suitable for Secondary Schools

## Puzzles

### Attacking the Castle

A square medieval castle sits on a square island surrounded by a square moat was under siege. All around the island, there is a 5 metre wide water moat. There's ground on the other side to rest the bridge on (if you can get it to stretch that far).