Ask students if they are able to see whether any of their previous work can help us to figure out the pattern? You may have to give a few more examples or lead them to see that six is a sumdifference number. Then lead them into a discussion about why four is so special. Allow for a whole class discussion. Then give students an opportunity to work in their groups to see if they can figure out any more numbers that fit the pattern. Students will record their work on a large white piece of construction paper.
After 10 -15 minutes, students will then choose one person to come up front with their groups’ construction paper and explain their thinking aloud to the class.
Conclusion This simple mathematical game leads to very deep mathematical concepts. Anyone can consider the problem finding sum-difference numbers, which is evident in the classroom activity for fourth graders. Yet the problem quickly lends itself to deeper mathematics that would be appropriate for high school or college level students to study as the major theorem of the paper demonstrates.
Reference (1) Y. Shi, Sum-Difference Numbers, the College Mathematics Journal, Volume 41, Number 5 (2010), pp. 404 - 405.