Preparation: Write each number from 1 to 18 on a note card.

This activity works well if you have a class of 18 students or less.
As the students enter the classroom, give each student a card with a number from 1 to 18 on it.   Do not tell them what it is for.

After all the cards have been given out, tell the students that they must pair up with another student, so that the sum of their cards is a perfect square.
The catch is that all pairs of students must have a perfect square sum.
Then give the students time to mingle and find a partner.



The key is that some numbers may have multiple partners (1 could be used with 3, 8, or 15) whereas other numbers have only one possibility (18 can only be paired with 7).
So, the person with 18 has to find and then convince the person with 7 to be her partner.   The person with 7 could have been matched with 2 or 9.




Here are the matching pairs:
    1 - 15
    2 - 14
    3 - 13
    4 - 12
    5 - 11
    6 - 10
    7 - 18
    8 - 17
    9 - 16