A Maths Starter Of The Day

How many people were at the dance?

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.



A Mathematics Lesson Starter Of The Day

Topics: Starter | Factors | LCM | Number

  • Mr Heeley's Y7 Krew, Rawthorpe High in da Hud
  • We thought that this was a totally cushtie starter and Lydia figured out that it must be the (LCM 0f 2,3 4 and 5) +1. Keep them coming Transum. As Depeche Mode said in 1983 - "We just can't get enough"!
  • Mr. Davies, British International School, New York
  • Fergus in Year 7 also suggested 61x61 = 3721 people would work too!
    That's alot of people dancing if you're the only one left without a partner!
  • Year 9, Coln House School
  • This gave the class lots of discussion but we were disappointed with the answer because it was unclear whether you could dance in combinations or not.
    If combinations were not allowed we thought 11 might be a possible answer.
    If combinations were allowed then 8 x 5 plus 7 x 3 = 61 works.
  • Mrs R,
  • I didnt think it was unclear at all. The students knew that phrases 'danced in 3's' meant that everyone was in groups of three except 1.
    Perhaps saying 'When they all danced in threes' would help remove any doubt.
    I like this type of starter it makes some kids feel very smart when they get it and it isnt always the ones with the high grades as it takes a different type of skill to use your brain in this way. Well done transum.
  • Mr Walkers Year 4 Mathematical Genii, Forest Gate London
  • It was a good activity to help with times tables and if we didn't know the 8 times table we did a pattern to work it out.
    "It made our brains exercise.".
  • Mr Spurling And His Homies,
  • This was a totally sic starter. We took a while to get it but it was off the hook.
  • Miss Wilson's Awesome Year 7SC Class!, Ascot International School Of Awesomeness, 3rd Floor, End Of Corridor, Bangkok, Thailand
  • We come from thailand,bangkok,ascot international school We danced to the music first to get our brain's going and it worked! Wong Zi Xiang Gu Rock!!!
  • Miss Berry, St Wilfrids Northenden
  • This is so good! My Year 6 except Abel,Josh and Srijan can not do this one!
  • 6H Maths Group, Nevill Road Junior, Stockport
  • Poppy and Tianna reckon that as long as the unit is 1 and all the other digits are 6, it will work! e.g 61, 661, 6661 etc. We have not yet tried them all, are they correct?
  • Mr Clifford, Heath Park 8LD
  • We say 61!
  • Class 11, Ermine Primary Academy
  • Kameron in Class 11 also got the answer 61.
  • Transum,
  • Thanks so much for all the comments. What a wide range of age groups and locations! I will take this opportunity, just in case you didn't know, to say that as well as all of the Starters on this website there are also a growing list of mathematical puzzles. The puzzle are interactive and would also make a worthwhile starter to a Maths lesson if pupils have access to computers. You could also go to the Factors page to see a list of Starters and interactive activities on a closely related topic.
  • Mrs Carnegie, Highfield Middle School
  • Stefan in Year 7 realised straight away that it would have to be an odd number and Kieran quickly decided it must end in 1 because it would be a multiple of 5 +1. We worked out it could be 61 + multiples of 60. Rhys said this is because 60 is the LCM of 2,3,4 and 5.
  • Jonathan, Califonia
  • 60x+1.

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.
Click here to enter your comments.

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Extension 1

What if the problem above was changed?
What if the group sizes were 3,5,7 and 8?

Chinese Remainder Theorem

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.

Extension 2

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.

Equate board game

Here's a great board game that will give any family with school-aged kids hours of worthwhile fun. Christmas is a time for board games but this one will still be useful at any time of year. Games can be adapted to suit many levels of Mathematical ability.

For Maths tutors working with just one or small groups of pupils this game has proved to be an excellent activity for a tutorial. Deciding on the best moves can spark pertinent discussions about mathematical concepts.

Equate looks a bit like Scrabble--for aspiring mathematicians, that is. Designed by a real mathematician, it works like this: You put down tiles on a board and make points by correctly completing simple equations. Your nine tiles include both numbers and mathematical symbols; you can add on to previous plays both vertically and horizontally. more... #ad

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.

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

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.

For the young people in your life it 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

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.

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.

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

"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.

Another Craig Barton Book

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

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
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


Eggs in a Basket

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:

Extension 3

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.

Online Maths Shop

Laptops In Lessons

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:


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 student number patterns activity.


Student Activity


Chinese Remainder Solver

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.


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