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

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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.
• Mrs Carnegie, Highfield Middle School
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• 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.

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This starter has scored a mean of 3.2 out of 5 based on 379 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?

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 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