How many days in your week? (or, modulo arithmetic..)


Here is a fun way to introduce kids to the concept of modulus (without ever saying the word): ask, why does a week have 7 days? Suppose you could change it - how many days would you put in the week? Then ask some questions about 'in X days, what day would it be?'

It helps to ask the child to consider the days as being named by number at first, to look at the patterns, starting with Zero-day and continuing as One-day, Two-day (which conveniently becomes Tuesday if Sunday is Zero-day), etc.

Start with simple questions like "So if your week has 5 days, and today is Three-day, what day will it be in 6 days?"

Make sure to ask several with the modulus "If your week has 4 days, and today is Zero-day, what day will it be in 4 days? 8 days? 16 days?"

Once they realize that it always goes back to the same day every time the number is a multiple of the days in the week, kids can have fun answering what sound like 'hard' questions: "So your week has 9 days, today is Seven-day, what day will it be in 80 days?" (answer - Six-day, one before the same day since 80 is one before an even multiple of 9)

Other interesting questions might be 'can we have a half-week?' Or for more advanced students, suppose you have weeks and grods, weeks are 8 days and grods are 4 days. Is it always the same weekday on the same grod-day? What if weeks are 7 days?