Week of Inspirational Math
Overview
The first week of school was spent doing problems that can be interpreted as "inspirational math". During the week, we worked on problems that involve critical thinking. Some of the problems were fitting the fewest amount of squares in a rectangle, finding patterns, and creating solutions. The purpose of the problems I believe was to get our minds thinking, be introduced to the group work, and to begin problem solving.
YouCubed Videos
We also watched multiple videos created by YouCubed at Stanford, and the topics were typically promoting to believe in yourself, use your resources, and ask questions. The purpose of watching the videos was for us to learn what the classroom environment will be like and to be confident in class this year. One of the videos we watched really clicked with me - it was about how nobody is a math person but you can become one. This video completely changed my mindset! Before I had always believed I wasn't the type of person to fully comprehend math on my own. Ever since, I have felt like if I take the time to think about the problem or project, I will figure out a way to solve it. Another video that informed and surprised me, was about how it is okay to make mistakes. I normally think that when I make a mistake I will be put down and not be taught the correct way or answer. But, the video described that your brain grows 2x when you make a mistake - learning the topic and learning that you made the mistake. Overall, the videos informed me about subjects and ways of learning I didn't know were okay, and I cannot complain about setting aside time to watch them.
Reflection
Reflecting back on my work this week, I have discovered that throughout the rest of the year I will be thinking deeply about each problem and trying new ways to find the answer. I have learned that it isn't always about the answer, but mainly about the process.
Painted Cubes
For example, one of the problems that we focused on, was called Painted Cubes. For this problem, I was told to create a 3x3x3 cube with sugar cubes. We then were asked to count which sides were painted if it was dunked in paint. Along with which sides were painted, how many sides were painted on each cube. For my findings, I discovered that there was one cube that was not painted, six cubes that were painted on one side, twelve cubes that were painted on two sides, and eight cubes that were painted on three sides.
Extension
I then had extra time and decided to try 4x4x4 and 5x5x5 cubes. I discovered this: The cubes with three painted sides will always stay at eight because a cube's corners do not multiply. Also, that if you multiply what you got from the 3x3x3 square by four, you get the answers for the one sides painted once and twice. Here is a visual: