Introduction
Throughout the week of inspirational math we engaged in two activities to peek our interest in math. Firstly we watched series of inspirational videos about how there is no such thing as a math person and how mistakes let your brain grow. We also did a series of open ended problems that encouraged group work among us.
The problems that we did all in one form or another had rules that you could discover and use to make the questions easier. While finding the rules wasn’t always necessary I found it interesting to try and find easier ways of getting answers than my peers around me. The Videos That we watched in summery told us that any person as long as they try can learn to not only become a better mathematician but also enjoy math. Along with that a constant point made was that when you make mistakes in math your brain learns and grows, and being slow in math can mean that you think about problems in a deeper way.
The Videos
Out of the five videos we watch one in particular made me think a little deeper than I normal do. The video itself was about how using your fingers to count isn’t a bad habit. The video explained that using your fingers can drastically improve your mathematical abilities. This really stuck with me as even though I don’t use my fingers often if at all it made me think about my process in math. How my way of solving a problem might be drastically different than my peers and how that could lead us to having two completely ways of solving problems. Those to methods if communicated between us could really improve both of our conceptions of the problems and math as a whole.
Painted Cubes
The problem I am choosing to do my write up on is the sugar cube problem. In this problem we were tasked with trying to fill in a table. You can see my table in the image below. The table asked that if we had a 3 by 3 by 3 cube made of smaller 1 by 1 by 1 cubes and we dunked it in 3x3x3 cube in a bucket of paint, then took the 3x3x3 cube apart. How many cubes will have 0,1,2,and 3 sides painted? What if the cube had 4x4x4 sides, or x by x by x sides. The reason I picked this very simple problem to extend upon for the 4x4x4 cubes and the x by x by x cubes, was because I wanted to find a rule. I find it easiest in math to find a pattern and work off of that. And because in class we finish this problem quite quickly, I felt there was more that could be done with it, so I decided to search for rules. Find out these rules was fairly straightforward process. First I completed a table for a 4x4x4 cube then I compared that to the 3x3x3 table and found the patterns for the different painted sides. As seen below in both my 4x4x4 table and my x by x by x table.
The Challenge
The biggest challenge I had was the 4x4x4 square. In class we made a 3x3x3 cube of sugar cubes and colored them to get our first table, But I didn't have that for my 4x4x4 square So I had to slowly and logicality imagine a 4x4x4 cube accompanied by a crude drawing in the image above to help me fill in that table. The most obvious Habit I used was looking for patterns as that was the point of what I did I was looking for the pattern or rule. How ever a habit of visualization would be more fit in this case as to do the crucial step in the problem I had to visualize and draw out the cube to fill in the table.
Final Statement
Finally I hope through out this year I can continue doing two things I did during this week. I hope to continue to find patterns and methods for making problems easier to solve, and secondly I felt that throughout this week I was really open to what other people did to solve these problems. This is what I really want to continue doing this year, so I could possibly learn more straightforward solutions to problems.