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Problem Statement
What I believe the problem was asking is “Where will the next white triangle be placed in the black triangle when n=4”, in other words, based on the preceding pattern of triangle placements in the whole black triangle, find how many triangles should be added, and where they should be. Process Description As we worked through the problem, we first set out to identify what the pattern. We already new that Fibonacci was something about spiraling lines, so we incorporated that into our search. We saw that the triangles seemed to be moving along that spiral line, making smaller triangles as it went around and touched each edge of the triangle. The second task was a bit harder since we had to find the area of the triangles each time a new one was made. We all did the work pretty equally, and we all shared our thoughts and ideas to come up with the final answer. Solution The solution we reached for the area problem is that the area is 1/8 of the previous triangles area. We aren't completely sure if this is right since we don't know exactly how to calculate areas like these. The answer to the triangle problem can be found to the left. Self Assessment and Reflection Doing this problem, I learned how to better solve patterns and relate those patterns to other questions for it. I was able to use what I found about the triangles and make an educated guess as to how the area was divided up for each triangle addition. Overall I think I earned a 9/10 for my work. I was the first one to find out how the triangles divided, and did the majority of the work on developing and explaining that, especially on the poster. I did get stuck on the area part and kinda ended up leaving the others to find it, but was able to make the connection afterwards. The most relevant mathematical practice would be 'make use of structure.' We used the structure of the of the given parts of the triangle to make a guess as to where the next one would be placed. I believe that without this structure example, we probably would have not been able to come up with any solution to the problem. |