Noughts and Crosses

Starter of The Day Transum Mathematics Topics

Topics: Starter | Combinations | Puzzles

Transum,
Another game which is isomorphic (same strategies) to noughts and crosses is the game of Fifteen. The numbers 1 to 9 are written on cards. Players take it in turns to take a card. The first person who can make a total of 15 with the cards they have is the winner.
If you arrange the nine numbered cards to form a magic square you will see the similarities with noughts and crosses.
We have invented a game called Trilett. Play it a few times and see if you can work out why it is isomorphic to noughts and crosses.

Here are links to the related interactive activities:

Noughts and Crosses | Fifteen | Trilett
Miss Mears, Stockport
A nice starter - we then extended the idea to the general case of an nxn grid and used some algebra as well.
Mark, New Zealand
Surely there are only three ways that the first cross can be placed: centre, side or corner. In any meaningful analysis of the game the sides are all identical and should not be distinguished.
Mrs. S. Farragonda, Fernan Elementary, CDA, ID
This game is very mental, and fun for both teachers and students! We now do the "secret student" thing with our class laptops. If the secret student is playing and X wins, the class wins. So everybody is motivated to do well.

[Transum: There's no better way to select a 'secret student' than to use the Random Student Generator.]
Transum,
Tired of the usual noughts and crosses? Why not mix things up with an interesting twist? In this variation, the basic rules remain the same, but with one key difference: each player can choose whether to place an X or an O on their turn. That’s right - you can switch between X and O as you wish. One turn you might play X, and the next you might choose O, or you can stick with the same symbol if you prefer. The goal remains the same: be the first to line up three of the same symbols in a row to win.

I heard about this variation called "naughty naughts and crosses" in a book by John Driscoll called A Hen and a Half, Intriguing Conundrums, Confusing Paradoxes, Baffling Conjectures and Challenging Puzzles.
Team Fortress 2 Soldier, Valve Studio (not The Real Valve Of Course)
Me and my friends loved this game, it's quite fun and relaxing, it would be amazing if you could play this on a long car trip but there is no internet on the road sadly.
overall great game.

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.
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Answers

Extension

In how many different ways can the first three moves be placed on the grid? First four moves etc.?

How many different games are there?

How many different arrangements of noughts and crosses are possible on a full grid?

People Maths

Instead of using paper and pencil, play noughts and crosses with people! You can find instructions on the People Maths page.

Christmas Present Ideas

It is often very difficult choosing Christmas presents for family and friends but so here are some seasonal, mathematics-related gifts chosen and recommended by Transum Mathematics.

Go Genius Maths

Transform maths practice into an exciting adventure with Go Genius Maths! This award-winning board game is designed to make learning maths enjoyable and engaging for children aged 7 and above. Perfect for family game nights or classroom activities, Go Genius Maths helps players develop essential arithmetic skills while having heaps of fun.

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How Not To Be Wrong

The maths we learn in school can seem like an abstract set of rules, laid down by the ancients and not to be questioned. In fact, Jordan Ellenberg shows us, maths touches on everything we do, and a little mathematical knowledge reveals the hidden structures that lie beneath the world's messy and chaotic surface. In How Not to be Wrong, Ellenberg explores the mathematician's method of analyzing life, from the everyday to the cosmic, showing us which numbers to defend, which ones to ignore, and when to change the equation entirely. Along the way, he explains calculus in a single page, describes Gödel's theorem using only one-syllable words, and reveals how early you actually need to get to the airport.

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Graphic Display Calculator

This handheld device and companion software are designed to generate opportunities for classroom exploration and to promote greater understanding of core concepts in the mathematics and science classroom. TI-Nspire technology has been developed through sound classroom research which shows that "linked multiple representation are crucial in development of conceptual understanding and it is feasible only through use of a technology such as TI-Nspire, which provides simultaneous, dynamically linked representations of graphs, equations, data, and verbal explanations, such that a change in one representation is immediately reflected in the others.

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Apple iPad Pro

The analytics show that more and more people are accessing Transum Mathematics via an iPad as it is so portable and responsive. The iPad has so many other uses in addition to solving Transum's puzzles and challenges and it would make an excellent gift for anyone.

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Before giving an iPad as a Christmas gift you could add a link to iPad Maths to the home screen.

Craig Barton's Tips for Teachers

Teaching is complex. But there are simple ideas we can enact to help our teaching be more effective. This book contains over 400 such ideas." more... #ad

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The Story Of Maths [DVD]

The films in this ambitious series offer clear, accessible explanations of important mathematical ideas but are also packed with engaging anecdotes, fascinating biographical details, and pivotal episodes in the lives of the great mathematicians. Engaging, enlightening and entertaining, the series gives viewers new and often surprising insights into the central importance of mathematics, establishing this discipline to be one of humanity s greatest cultural achievements. This DVD contains all four programmes from the BBC series.

Marcus du Sautoy's wonderful programmes make a perfect Christmas gift more... #ad

Christmas Maths

This book provides a wealth of fun activities with a Christmas theme. Each photocopiable worksheet is matched to the Numeracy Strategy and compatible with the Scottish 5-14 Guidelines. This series is designed for busy teachers in the late Autumn term who are desperate for materials that are relevant and interesting and that can be completed with minimun supervision.

All the activities are suitable for use by class teachers, supply teachers, SEN teachers and classroom assistants and cover topics such as 'How many partridges did the true love give all together?' and 'Filling a sleigh with presents by rolling a dice!'. Children will have lots of fun working through the Christmas Maths themes but also gain valuable skills along the way.

A great source of ideas and another reasonably priced stocking filler. more... #ad

A Compendium Of Mathematical Methods

How many different methods do you know to solve simultaneous equations? To multiply decimals? To find the nth term of a sequence?

A Compendium of Mathematical Methods brings together over one hundred different approaches from classrooms all over the world, giving curious mathematicians the opportunity to explore fascinating methods that they've never before encountered.

If you teach mathematics to any age group in any country, you are guaranteed to learn lots of new things from this delightful book. It will deepen your subject knowledge and enhance your teaching, whatever your existing level of expertise. It will inspire you to explore new approaches with your pupils and provide valuable guidance on explanations and misconceptions. more... #ad

Math with Bad Drawings

I had been tutoring the wonderful Betsy for five years. When the day came for our last ever session together before the end of her Year 13, I received this beautiful book as a gift of appreciation.

This a very readable book by Ben Orlin. I'm really enjoying the humour in the writing and the drawings are great.

Ben Orlin answers maths' three big questions: Why do I need to learn this? When am I ever going to use it? Why is it so hard? The answers come in various forms-cartoons, drawings, jokes, and the stories and insights of an empathetic teacher who believes that mathematics should belong to everyone. more... #ad

Click the images above to see all the details of these gift ideas and to buy them online.

Maths T-Shirts

Maths T-Shirts on Amazon

Your access to the majority of the Transum resources continues to be free but you can help support the continued growth of the website by doing your Amazon shopping using the links on this page. Below is an Amazon link. As an Amazon Associate I earn a small amount from qualifying purchases which helps pay for the upkeep of this website.

Educational Technology on Amazon

Teacher, do your students have access to computers such as tablets, iPads or Laptops? This page was really designed for projection on a whiteboard but if you really want the students to have access to it here is a concise URL for a version of this page without the comments:

Transum.org/go/?Start=November7

However it would be better to assign one of the student interactive activities below.

Laptops In Lessons

Here is the URL which will take them to a similar activity.

Transum.org/go/?to=Badges

Ultimate Noughts and Crosses is the new game that I get really excited about playing. It's magnificent, have a look!

Transum.org/go/?to=Ultimate

The javascript for this game above was kindly made public by Stephen Ostermiller (GNU General Public License as published by the Free Software Foundation).

A Mathematics Lesson Starter Of The Day