When they danced as couples there was one person left over.
When they danced in threes one person was left over.
When they danced in fours one person was left over.
When they danced in fives one person was left over.
Topics: Starter | Factors | LCM | Number
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What if the problem above was changed?
What if the group sizes were 3,5,7 and 8?
This Starter is a simple problem which can be solved by using the Chinese remainder theorem first published in the 3rd to 5th centuries by the Chinese mathematician Sun Tzu. In its basic form, the Chinese remainder theorem will determine a number n that, when divided by some given divisors, leaves given remainders.
What is the lowest number that
when divided by 3 leaves a remainder of 2,
when divided by 5 leaves a remainder of 3,
and when divided by 7 leaves a remainder of 2?
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 MathsTransform 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. Whether you’re looking for a gift to inspire young minds or a tool to supplement maths education, Go Genius Maths is the ultimate choice. Spark curiosity, nurture mathematical talent, and turn learning into an unforgettable journey! |
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How Not To Be WrongThe 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. What more could the inquisitive adult want for Christmas? This book makes a cosy, interesting read in front of the fire on those cold winter evenings. more... #ad |
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Graphic Display CalculatorThis 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. For the young people in your life this is a great investment. Bought as a Christmas present but useful for many years to come as the young person turns into an A-level candidate then works their way through university. more... #ad |
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Apple iPad ProThe 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. The redesigned Retina display is as stunning to look at as it is to touch. It all comes with iOS, the world's most advanced mobile operating system. iPad Pro. Everything you want modern computing to be. more... #ad Before giving an iPad as a Christmas gift you could add a link to iPad Maths to the home screen. |
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Craig Barton's Tips for TeachersTeaching 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 "The ideas come from two sources. First, from the wonderful guests on his Tips for Teachers podcast - education heavyweights such as Dylan Wiliam, Daisy Christodoulou and Tom Sherrington, as well as talented teachers who are not household names but have so much wisdom to share. Then there's what he has learned from working with amazing teachers and students in hundreds of schools around the world. |
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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 |
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Christmas MathsThis 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 |
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A Compendium Of Mathematical MethodsHow 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 |
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Math with Bad DrawingsI 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 |
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Click the images above to see all the details of these gift ideas and to buy them online.
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The following was one of Alex Bellos' Monday Puzzles published in The Guardian online newspaper. it features the Indian mathematician Brahmagupta during the 7th century AD posed the following problem:
When eggs in a basket are taken out 2, 3, 4, 5 and 6 at a time, there remain 1, 2, 3, 4 and 5 eggs respectively. When they are taken out 7 at a time, none are leftover.
Find the smallest number of eggs that could be in the basket.
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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=January28 However it would be better to assign one of the student interactive activities below. |
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Here is the URL which will take them to a student number patterns activity.
Transum.org/go/?to=satisfaction
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An interactive calculator designed to solve this type of problem is available to teachers, parents and turors when signed in. The solutions to this and other Transum puzzles, exercises and activities are available when you are signed in to your Transum subscription account. If you do not yet have an account and you are a teacher or parent you can apply for one here. A Transum subscription also gives you access to the 'Class Admin' student management system and opens up ad-free access to the Transum website for you and your pupils. |
