Maximize the Sum Puzzle

Today I want to share the Maximize the Sum Puzzle with you.

My Algebra 1 classes managed to get a bit off schedule of one another this past week. So, I declared Monday to be a “Catch-Up Day.” My classes that were behind were given our latest assignment and the class period to work on it. My classes that were caught up worked on finishing the assignment they had already started and working on any other missing assignments.

My classes that were ahead of my other classes were given the chance to “Maximize the Sum.” This is yet another puzzle that I found in Puzzle Box, Volume 3. Yes, I know I seem a bit obsessed with this series of puzzle books. I promise it is for good reason!

Students are given a grid of 25 numbers. Their task is to circle five numbers from the grid that will maximize the sum. There is a twist: no two numbers can be circled if they are in the same row or column. So, you will end up with one number in each row and one number in each column.

My students had a hard time understanding these rules despite reading them (at least I think they read them!) and my going over the rules at least twice.

I printed off the maximize the sum puzzles and slid them each into a dry erase pocket so that students could easily change their circled numbers after finding the sum.

If you don’t have a classroom set of dry erase pockets, you could also use heavy duty sheet protectors. But, I highly recommend investing in a classroom set of the pockets since they are so much more durable.

I had students yell out their sums as they found them, so that students would know what the “sum to beat” was. My students ended up coming up with a higher sum than the answer key at the back of the book said, so I’m pretty confident we maximized the sum.

When I solved the maximize the sum puzzle, I found it very interesting that my first and second approaches to the puzzle which I thought would maximize the sum actually didn’t! This puzzle didn’t take my students very long at all. We were completely done with the puzzle in less than five minutes. So, this one is great if you are short on time!