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 | LCM | Number

• Mr Heeley's Y7 Krew, Rawthorpe High in da Hud
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• 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
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• 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
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• 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,
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• 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
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• 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.
• Mr Spurling And His Homies,
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• 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
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• 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
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• This is so good! My Year 6 except Abel,Josh and Srijan can not do this one!
• 6H Maths Group, Nevill Road Junior, Stockport
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• 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
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• We say 61!
• Class 11, Ermine Primary Academy
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• Kameron in Class 11 also got the answer 61.
• Transum,
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• 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.

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.

If you don't have the time to provide feedback we'd really appreciate it if you could give this page a score! We are constantly improving and adding to these starters so it would be really helpful to know which ones are most useful. Simply click on a button below:

Excellent, I would like to see more like this
Good, achieved the results I required
Satisfactory
Didn't really capture the interest of the students
Not for me! I wouldn't use this type of activity.

This starter has scored a mean of 3.6 out of 5 based on 167 votes.

Previous Day | This starter is for 28 January | Next Day

Students could use a spreadsheet to create a list of possible numbers of people at the dance. Columns could be set up to show the remainder after dividing by 2 or 3 etc. The MOD function could be used for this:

Eg =MOD(A7,4) shows the remainder when the number in cell A7 is divided by 4.

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...

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...

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...

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 Christmas gift for anyone.

You have to hold iPad Air to believe it. It’s just 7.5 millimeters thin and weighs just one pound. The stunning Retina display sits inside thinner bezels, so all you see is your content. And an incredible amount of power lies inside the sleek enclosure. So you can do so much more. With so much less. more...

Aristotle's Number Puzzle

It’s a bit of a tradition to give puzzles as Christmas Gifts to nieces and nephews. This puzzle is ideal for the keen puzzle solver who would like a challenge that will continue over the festive period (at least!).

This number puzzle involves nineteen numbers arranged into a hexagon. The goal of the puzzle is to rearrange the numbers so each of the fifteen rows add up to 38. It comes in a wooden style with an antique, aged look.

Keep the Maths in Christmaths with this reasonably priced stocking filler. more...

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...

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

 Teacher, do your students have access to computers?Do they have iPads or Laptops in Lessons? Whether your students each have a TabletPC, a Surface or a Mac, this activity lends itself to eLearning (Engaged Learning).

Transum.org/go/?Start=January28

Here is the URL which will take them to a student number patterns activity.

Transum.org/go/?to=satisfaction