In this session we looked at division problems with remainders. First, Zoe’s three children—Alice, Bob, and Charlotte—tried to divide some cookies evenly, but there were two cookies left over. Thinking quickly, Zoe realized that she and the children could share the cookies so that everyone got the same number. We figured out that there could have been 8 cookies. Other possible numbers were 20, 32, 44…

We looked at similar questions with pirates trying to divide up coins: when 11 pirates try to divide up the coins, there is 1 left over. When 10 pirates try to divide them up, there are 3 left over. And when 9 pirates try to divide up the coins, there are 6 left over. From this information, we can figure out a possible number of coins.

We tried a variety of strategies, ranging from listing out possible numbers and using trial and elimination, to the Chinese Remainder Theorem. We saw some other applications of the Chinese Remainder Theorem, including secret sharing and breaking big calculations into smaller pieces.

Here we found the last digits of some big numbers.

If you’re interested, please take a look below at the slides that we used for the activity.

Handout from the session

(Header image Pot of Gold courtesy of Jeremy Schultz.)