While looking around on the web for a problem that is accessible for students and interesting for me, I came upon the Build It Up problem. The directions are very easy, it’s the execution that provides a challenge.
Directions from the site:
At first, I must not have paid too close of attention to the example solution because I had it in my mind that I needed to use all different numbers, it didn’t take long to figure out that it is impossible to get to 15 with all different numbers.
I then started playing around with different combinations, and after MANY failed attempts I started to get the hang of it and found a little bit of success. When I was working through my failed attempts I was reminded of the SMP.1 standard, “Make sense of problems and persevere in solving them,” as it would have been very easy to say this is difficult and I’m not doing it right so I give up, so to get to the place where you can find multiple correct answers takes perseverance.
One big thing that I noticed was how important the placement of the numbers is, I became very intentional with their order. Using the same four numbers, they would both result in 15, or not 15, it all depended on how I ordered them.
Another big noticing was, with all the combinations that added up to 15, the original 4 numbers added up to an odd number. Yes, some combinations that added up to an odd number didn’t result in 15. I didn’t come across any 4 original numbers that added up to an even number that also resulted in 15; this makes sense to me as: an even number+ an even number= an even number, and 15 is odd.
After having some success (it was tedious though) with building up, I decided it would be easier and would involve less guess and check and more meaningful actions if I try to build it down. I started with writing out the factors of 15 that would withstand being decomposed twice, (12,3) won’t work because 3 can only be decomposed once before it won’t work with our set-up. After I made the list of factors finding solutions was a lot easier and faster.
Saying that this way was easier and faster worries me though, I don’t want my students to always try to find the easiest and/or fastest way to do something. I am appreciative that I went through the struggle of figuring out how to build up to 15. If I didn’t go through the struggle I would not have made the observations I did and wouldn’t have come away from the problem with as much regard for factors.
I think this problem is accessible for students, they will go through the same process as I did of struggling and then making noticings and then testing their wonders to find solutions. I am interested in a few things about this problem. First, I am interested in how the students go about solving it, what they notice and wonder, what solutions they come up with, and what their “take away” is. I am also interested in all the possible solutions. While reading the comments about the puzzle, I noticed some people came up with equations for it. I would like to test myself and see what I can come up with.