Week One: Hailstone Sequences
This week of class left us with a message I doubt any of us will forget. My teacher showed us videos made by stanford about the significance of failing and the effects it has on your brain. He had us watch these and discuss our opinions on the subject. The purpose of these videos was to teach us that failing isn’t the end of your success in school. The videos taught us that failing makes your brain grow. My teacher is putting lots of significance on the fact that failing isn’t bad and will improve our brains as we progress in our academic virtues.
After learning about all of the videos we did, we had a series of several activities to complete. All of which corresponded to the initial message. We completed “Tiling a Rectangle” and attempting to figure out the smallest amount of squares we could get from a 11 x 13 rectangle. The second activity we did was completing the “Squares to Stairs” problem. In this problem, we were asked to give our opinions on how we saw the stairs grow. From there, we attempted to figure out how many squares were in a certain figure as it grew. The third activity was “Hailstone Sequences”. In this problem we were shown an example of a sequence and were asked to find a pattern. From there, we made our own sequences to show the class. The fourth activity we completed was “Painted Cube”. We were given a prompt to try and test as a group. The prompt was asking how many sides would be painted if a cube was completely submerged in paint. We used sugar cubes and sharpies to act as supplies and attempted to figure it out. This week was full of important problems that got us into the routine of school.
The videos we viewed in class were significant in relation to the brain. We learned lots of new material about brain growth. One significant message being that every time you make a mistake your brain grows. The brain sees a mistake and learns from it. We had a lesson about how you shouldn’t fear mistakes, you should embrace them. One other lesson I learned was that speed has no contributing factor to your intelligence. Answering a question faster has no relation to whether it’s right or not. These lessons will stick with me for the rest of the year. They made me realize that I am comfortable in math and it is a judge free environment.
One significant activity we did this week was the hailstone sequence problem. In this problem we were shown a set of numbers and asked to find a pattern. The pattern was (20,10,5,16,8,4,2,1) We eventually found the pattern and proceeded to write up an example. I decided to write about this problem because at first look, I found this problem very overwhelming. After receiving an explanation, I realized it wasn’t scary at all. This problem turned out to be very fun and left me feeling excited and ready for what this class has in store. When attempting to solve this problem, I first thought it was just dividing by two, but at second look, I realized that wouldn’t work. I then proceeded to try other kinds of patterns. I thought that dividing might be the right way to go, but when you reach a certain point, you change your form of solving it. After lots of brainstorming my teacher explained to us hailstone sequences. These are a pattern that involves rules with odds and evens. The rules for even numbers are dividing, as I originally thought. When you reach the point of dividing into an odd number (as you can’t get a whole number from it), you must change it to multiplication. With an odd number you multiply it by 3 and add 1. The sequences that I chose to try were both even and odd. I found this problem challenging in the beginning due to my thoughts at first look. This is often my problem in math, as I am afraid to attempt a problem instead of trying it without worrying if you are wrong. We reflect on problems we have completed by using habits of mathematicians. These are ways that mathematicians solve their problems. One habit I used during this problem was conjecture and test. I thought of many different numbers I could start with and tested each of them. This is a valuable skill that all mathematicians use.
Coming into math class this week, I wasn’t sure what to expect. I had easily adjusted to 9th grade math and I was worried it wouldn’t be the same this year. I realized that my worry was in my head and I shouldn’t be afraid of new math problems and strategies. I really enjoyed the work we did in class this week and felt that I could easily understand it and collaborate with my classmates. I am looking forward to math class this year and I am excited for what is to come.
After learning about all of the videos we did, we had a series of several activities to complete. All of which corresponded to the initial message. We completed “Tiling a Rectangle” and attempting to figure out the smallest amount of squares we could get from a 11 x 13 rectangle. The second activity we did was completing the “Squares to Stairs” problem. In this problem, we were asked to give our opinions on how we saw the stairs grow. From there, we attempted to figure out how many squares were in a certain figure as it grew. The third activity was “Hailstone Sequences”. In this problem we were shown an example of a sequence and were asked to find a pattern. From there, we made our own sequences to show the class. The fourth activity we completed was “Painted Cube”. We were given a prompt to try and test as a group. The prompt was asking how many sides would be painted if a cube was completely submerged in paint. We used sugar cubes and sharpies to act as supplies and attempted to figure it out. This week was full of important problems that got us into the routine of school.
The videos we viewed in class were significant in relation to the brain. We learned lots of new material about brain growth. One significant message being that every time you make a mistake your brain grows. The brain sees a mistake and learns from it. We had a lesson about how you shouldn’t fear mistakes, you should embrace them. One other lesson I learned was that speed has no contributing factor to your intelligence. Answering a question faster has no relation to whether it’s right or not. These lessons will stick with me for the rest of the year. They made me realize that I am comfortable in math and it is a judge free environment.
One significant activity we did this week was the hailstone sequence problem. In this problem we were shown a set of numbers and asked to find a pattern. The pattern was (20,10,5,16,8,4,2,1) We eventually found the pattern and proceeded to write up an example. I decided to write about this problem because at first look, I found this problem very overwhelming. After receiving an explanation, I realized it wasn’t scary at all. This problem turned out to be very fun and left me feeling excited and ready for what this class has in store. When attempting to solve this problem, I first thought it was just dividing by two, but at second look, I realized that wouldn’t work. I then proceeded to try other kinds of patterns. I thought that dividing might be the right way to go, but when you reach a certain point, you change your form of solving it. After lots of brainstorming my teacher explained to us hailstone sequences. These are a pattern that involves rules with odds and evens. The rules for even numbers are dividing, as I originally thought. When you reach the point of dividing into an odd number (as you can’t get a whole number from it), you must change it to multiplication. With an odd number you multiply it by 3 and add 1. The sequences that I chose to try were both even and odd. I found this problem challenging in the beginning due to my thoughts at first look. This is often my problem in math, as I am afraid to attempt a problem instead of trying it without worrying if you are wrong. We reflect on problems we have completed by using habits of mathematicians. These are ways that mathematicians solve their problems. One habit I used during this problem was conjecture and test. I thought of many different numbers I could start with and tested each of them. This is a valuable skill that all mathematicians use.
Coming into math class this week, I wasn’t sure what to expect. I had easily adjusted to 9th grade math and I was worried it wouldn’t be the same this year. I realized that my worry was in my head and I shouldn’t be afraid of new math problems and strategies. I really enjoyed the work we did in class this week and felt that I could easily understand it and collaborate with my classmates. I am looking forward to math class this year and I am excited for what is to come.