Days and Dates
Why do this problem?
This problem gives an insight into modular arithmetic without worrying too much about notation, by looking at the concept of remainders. It gives students the opportunity to share ideas, listen to each other justify their assertions, and come up with convincing arguments and proofs using simple algebra.
Possible approach
This printable worksheet may be useful: Days and Dates.
Start by making sure everyone is convinced that 702 days after a Monday will be a Wednesday, by thinking about whole numbers of weeks and days left over. Students can then work out what day it will be in 15 days, 26 days, 234 days. Make sure everyone understands that for the purposes of this problem we are always counting from Monday!
Key questions
What will numbers have in common if they take us to a particular day of the week?
If the first day of this month was ... what can we say about the first day of next month, and why?
Possible support
Students who are struggling with finding the remainder when dividing by 7 could investigate division by 5 instead; this could be a model for the working week ignoring Saturday and Sunday.
Possible extension
Investigate patterns when dividing by numbers other than 7. Does the same thing always happen? Students could be introduced to the language and notation of modular arithmetic; if the remainder is 2 when we divide 23 by 7, we write:
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