I used this trick whenever I was teaching addition of positive and negative numbers.
After discussing the rules for adding signed numbers, I display a table of 16 numbers
(or any square array of numbers).
First, I tell the students that I am going to have them pick any four numbers from
the following array.
I tell my students that my favorite number is 7, and how nice it would be if they would
pick four numbers that would add up to my favorite number.
The only restriction about picking numbers is that once they have picked a number
from a particular row and column, they cannot pick another number from either
that row or that column.
How does it work?
The restriction above forces the student to choose exactly one number from each row and column.
So, the sum of the four numbers is really the sum of the 8 numbers of the addition table (the blue numbers in the row and column headings below).
The sum of -3 + 0 + 4 + (-1) + 5 + (-2) + 8 + (-4) = 7.