Week of Inspirational Math
Painted Cube Problem
What was The Week of Inspirational Math, what was the purpose?
The week of Inspirational Math was a series of videos and problems that opened up different forms of Math. It showed us that it's ok to do math in different ways and that math is not something to fear. In class we watched videos showcasing different ways to approach math and then afterward did problems to showcase the approaches. Approaching problems with techniques that are usually frowned upon was really really enjoyable. We were allowed to visualize a problem physically which usually is not allowed.
The week of Inspirational Math was a series of videos and problems that opened up different forms of Math. It showed us that it's ok to do math in different ways and that math is not something to fear. In class we watched videos showcasing different ways to approach math and then afterward did problems to showcase the approaches. Approaching problems with techniques that are usually frowned upon was really really enjoyable. We were allowed to visualize a problem physically which usually is not allowed.
Overview of Videos and Problems
Day 1:
The first video we watched was about the way people visualize mathematics. The video capitalized on the fact that no one is born a "Math person," because anyone can be a math person. Math is about your brain growing and changing, which it constantly does. Everyones brain has a potential to grow and be good at math. Synapses occur when you learn, ultimately causing brain growth. The problem we focused on was the Fewest Squares problem. We had to find the least amount of squares that could fit in an 11 x 13 rectangle. For the challenge option we had to find how many squares would fit in a 12 x 15 rectangle.
Day 2:
The second video we watched was about the way mathematical mistakes are extremely beneficial. It showed us that its 100% ok to make mistakes in math, as I said its extremely beneficial. By making mistakes in math you are allowing your brain to expand. Mistakes in your brain help you learn. The third video (same day) was about how a good mindset can make math easier. Math is about mindset, and a positive mindset helps your brain grow. The problem we focused on was the Squares to Stairs problem. We had to find a pattern with an increasing staircase. Each staircase increased in size and height. It was very visual and was honestly a job to solve.
Day 3:
The fourth video we watched was about the way speed in equation can be very counter productive. The video talked about how fast calculation can lead to errors and has no connection to skill. Understanding math is much much more important. Time restrictions can cause stress which leads to worse mathematics and answers. Math is NOT about speed, its about thinking slowly and truly understanding the problem. The problem we focused on was the Hailstorm Sequences. This problem was very difficult because there wasn't a solid answer, only a pattern rule. Implementing the rule was a big challenge and you really had to take your time to find a usable equation.
Day 4:
The fifth and final video we watched was about how visualization can help with mathematics. The video justified the use of visualization such as counting with fingers and drawing out your problem. It told us that using your fingers and drawing your problem is 100% rational and actually very effective. The problem we focused on was the Painted Cube problem. We had to figure out how many 1 x 1 x 1 squares in a 3 x 3 x 3 cube would be 3 sided, 2 sided, 1 sided, or no sided when dipped in paint.
Day 1:
The first video we watched was about the way people visualize mathematics. The video capitalized on the fact that no one is born a "Math person," because anyone can be a math person. Math is about your brain growing and changing, which it constantly does. Everyones brain has a potential to grow and be good at math. Synapses occur when you learn, ultimately causing brain growth. The problem we focused on was the Fewest Squares problem. We had to find the least amount of squares that could fit in an 11 x 13 rectangle. For the challenge option we had to find how many squares would fit in a 12 x 15 rectangle.
Day 2:
The second video we watched was about the way mathematical mistakes are extremely beneficial. It showed us that its 100% ok to make mistakes in math, as I said its extremely beneficial. By making mistakes in math you are allowing your brain to expand. Mistakes in your brain help you learn. The third video (same day) was about how a good mindset can make math easier. Math is about mindset, and a positive mindset helps your brain grow. The problem we focused on was the Squares to Stairs problem. We had to find a pattern with an increasing staircase. Each staircase increased in size and height. It was very visual and was honestly a job to solve.
Day 3:
The fourth video we watched was about the way speed in equation can be very counter productive. The video talked about how fast calculation can lead to errors and has no connection to skill. Understanding math is much much more important. Time restrictions can cause stress which leads to worse mathematics and answers. Math is NOT about speed, its about thinking slowly and truly understanding the problem. The problem we focused on was the Hailstorm Sequences. This problem was very difficult because there wasn't a solid answer, only a pattern rule. Implementing the rule was a big challenge and you really had to take your time to find a usable equation.
Day 4:
The fifth and final video we watched was about how visualization can help with mathematics. The video justified the use of visualization such as counting with fingers and drawing out your problem. It told us that using your fingers and drawing your problem is 100% rational and actually very effective. The problem we focused on was the Painted Cube problem. We had to figure out how many 1 x 1 x 1 squares in a 3 x 3 x 3 cube would be 3 sided, 2 sided, 1 sided, or no sided when dipped in paint.
Most Impactful
The most impactful math video was definitely the Speed video. I'm very type A personality and really want to complete my work as efficiently and fast as possible. Theres a bit of irony with this because I test very very slowly. I've always rushed math assignments mainly because of time restrictions but I end up not learning much. I really hope that changes this year. I've always been aware that rushing math is generally a pretty bad idea but I haven't really listened. I'm motivated more to complete my work than understanding it which brings me to my next point.
The second most impactful video was the Motivation video. I've always been motivated in math but for the wrong reason, to get finished with it. This year I hope to turn that around and care about turning in genuine, well thought out work. Good uncompleted work is more important than sloppy completed work in my opinion. One of my biggest goals this year is to turn in quality work that I actually grow with. I want to learn math, not just study it.
The most impactful math video was definitely the Speed video. I'm very type A personality and really want to complete my work as efficiently and fast as possible. Theres a bit of irony with this because I test very very slowly. I've always rushed math assignments mainly because of time restrictions but I end up not learning much. I really hope that changes this year. I've always been aware that rushing math is generally a pretty bad idea but I haven't really listened. I'm motivated more to complete my work than understanding it which brings me to my next point.
The second most impactful video was the Motivation video. I've always been motivated in math but for the wrong reason, to get finished with it. This year I hope to turn that around and care about turning in genuine, well thought out work. Good uncompleted work is more important than sloppy completed work in my opinion. One of my biggest goals this year is to turn in quality work that I actually grow with. I want to learn math, not just study it.
Painted Squares
The objective of the problem was to figure out how many 1 x 1 x 1 cubes in a 3 x 3 x 3 cube would have 3 sides painted, 2 sides painted, 1 side painted, or no sides painted. We were given the opportunity to visualize it with sugar cubes although I will say they were unnecessary. There is a very easy way to solve this problem no matter how large the cube is.
I chose this problem because I found it the most fun and honestly the most intriguing. Not only did I think it was extremely cool but I had an extremely good idea on how to explain it.
The objective of the problem was to figure out how many 1 x 1 x 1 cubes in a 3 x 3 x 3 cube would have 3 sides painted, 2 sides painted, 1 side painted, or no sides painted. We were given the opportunity to visualize it with sugar cubes although I will say they were unnecessary. There is a very easy way to solve this problem no matter how large the cube is.
I chose this problem because I found it the most fun and honestly the most intriguing. Not only did I think it was extremely cool but I had an extremely good idea on how to explain it.
I think this explains it all very nicely. This process can be used for any sized cube as long as things stay organized.
A huge problem I faced while doing this problem was figuring out the best way to display it. I wanted to keep things step by step but still wanted it to make sense. I overcame this by doing everything digitally as opposed to writing it out.
The main habit I used was staying completely organized. I wanted things to be legible and easy to understand. I went through and described everything on paper but then transferred it onto the computer. By doing the lesson digitally I've made it much easier to understand. I kept all of my information together and made sure to use every piece.
A huge problem I faced while doing this problem was figuring out the best way to display it. I wanted to keep things step by step but still wanted it to make sense. I overcame this by doing everything digitally as opposed to writing it out.
The main habit I used was staying completely organized. I wanted things to be legible and easy to understand. I went through and described everything on paper but then transferred it onto the computer. By doing the lesson digitally I've made it much easier to understand. I kept all of my information together and made sure to use every piece.
Reflection
The Week of Inspiration Math has really opened my eyes to the changes I need to make with the way I look at math. Math needs to be about learning and growth but I've made it a thorn in my side. Dr Drew and the videos we watched in class really govern the fact that math should be fun and full of incite. Mathematics should NOT be rushed, pushed aside, or labeled as irrelevant. Math is important. Math promotes growth in the thing that keeps our bodies together, the brain. The videos and problems have really given me a sense that mathematics aren't evil. I will strive to push myself much further in math this year.
The Week of Inspiration Math has really opened my eyes to the changes I need to make with the way I look at math. Math needs to be about learning and growth but I've made it a thorn in my side. Dr Drew and the videos we watched in class really govern the fact that math should be fun and full of incite. Mathematics should NOT be rushed, pushed aside, or labeled as irrelevant. Math is important. Math promotes growth in the thing that keeps our bodies together, the brain. The videos and problems have really given me a sense that mathematics aren't evil. I will strive to push myself much further in math this year.