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.
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Topics: Starter  LCM  Number
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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.
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?
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Teacher, do your students have
access to computers? 

Here a concise URL for a version of this page without the comments.
Transum.org/go/?Start=January28
Here is the URL which will take them to a student number patterns activity.
Transum.org/go/?to=satisfaction
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 adfree access to the Transum website for you and your pupils. 