What's All the Buzz About Math Write-up 11/5
1. Problem Statement
For this problem you are given a shape that appears to be in the shape of a honeycomb (as shown in the image above), so the title of the problem, “What’s All the Buzz About Math?”, is properly suited to the problem. Given that there are three in the first column, four in the second, five in the third, four in the fourth, and three in the fifth, you know there are nineteen spaces. Each of those spaces need to be filled with a number from 1-19, with none repeating. These numbers need to be ordered in a way that from all directions(as shown below), the line would add up to 38.
2. Process Description
When my group was first given this problem, the first thing we all tried was just guess and check. We all came up with different strategies that we thought might work. It was agreed that we should try to find the outer ring out first and then work from there. We tried things like putting the biggest numbers on the corners, putting biggest across from smallest, biggest across from the number minus ten, and so on. Once we realized none of those ended up working we tried random numbers with no specific ordering, hoping to get lucky. Eventually, one of our group members found a pattern of numbers that worked as an outer ring and at that point we thought we had it and all we had to find was the middle. After working with that outer ring it was decided that it was incorrect and we had to start with a blank slate. By this time we were on our second friday of attempting to solve the problem and our teacher so kindly agreed to give us three hints. As a group we conversed and decided on which numbers or spots we wanted to use for our hints. We ended up asking what the middle spot was, where the 19 was placed, and the very bottom spot. Now that we had our hints we could slowly add up the outer ring to get them all to equal thirty-eight. From there on we all worked individually to find the outer ring until one of us figured it out. We all checked each others work and continued on to find the middle ring numbers. Again after trial and error, one group member claimed he figured it out. The other three of us checked his work and reassured him that he had solved the problem. We never really found a pattern or an equation that helped us to solve this problem.
3. Solution
Our solution is the order of numbers above. We know this solution is correct because we had all group members check over it, with calculators, and our teacher also told us it was correct.
4. Self-‐Assessment and Reflection
This problem taught me more life skills than it did about math. This problem got frustrating at a lot of points and having to sit there for long periods of time while I got answers that weren’t correct was aggravating. The life lesson taught by this problem was perseverance. My group was also very encouraging, to get you to keep going. I would give myself a ten out of ten as a grade just because I see these problems as an effort based assignment. Even though I wasn’t the one who solved the problem, I did my best to keep trying and giving input towards group work. As for the poster I believe I contributed a lot in completing and decorating it. For the Mathematical Practice and Expectation I believe “making sense of a problem and persevere in solving” was most used with this specific problem. I say that because perseverance was a big part in finally coming up with an answer instead of giving up on the first day. As for making sense of the problem, we never found an explanation as to why the numbers were placed where they were but our final answer does make sense to us.
5. Compare and Contrast
When meeting up with the other group and talking about how we solved the problem we found that we went about solving it similarly in the beginning, but tried very different things towards the end. Something they tried that we didn’t even think of was putting it into an algebraic function to try to figure out the outer ring. They said it wasn’t very useful but I saw it as a creative way of going about solving the equation. We both solved the problem by figuring out the outer and then inner rings. The other group also asked for different clues. Instead of asking for specific numbers, they asked for certain spaces on the outer ring. I think the hints they got were more helpful than the ones we asked for because knowing the middle number didn’t help us narrow down anything.