Activities
This was the first week of school and we did four different activities and watched 5 different videos. The purpose of it was for us to see that our brains could grow through failure and no on was born with a math brain. It was also to get introduced to the Habits of a Mathematician. For this week we did four different mathematical activities: Building Shapes, in which we had to make one of 6 different shapes using rope and our hands. This was done in a group of four. The teachers were skeptics and we had to justify why the shape we created was accurate. The second was Number Visual Pennies, in which we had 100 pennies and had to stack them in piles of 3, 5, 6, 7, and 9. We had to make sure each pile individually had the same pennies using all 100 of them. The third was One-Cut Geometry. In this activity we had a square piece of paper and had to draw a scalene triangle in the middle. None of the sides or corners of the triangle could touch the sides of the paper. Then we had to cut out the triangle using only one cut. It was challenging because I tried folding it and it always came out a little differently than how I drew it. The fourth and final activity was Square Mania. In this activity there were two examples of figures with 17 squares created using 10 line segments, and 20 squares using 9 line segments. Then it said what is the least amount of line segments you could use to make exactly 100 squares.
Videos
The first video we watched was about different strategies for mathematics. There were 5 mentioned in the video which were: 1. Draw It Out, 2. Teamwork, 3. Experiment, 4. Look for Different Resources, 5. Start with a smaller case. The second video was about how speed wasn't important in math. It talked about how a lot of top mathematicians were really slow, because they were thinking very deeply about the work and how they felt stupid while they were in school because they weren't as fast as other kids. The third video was about how our brains can grow and change. There is a myth about how some people are just naturally "math people," but that isn't true. Anyone can be good at math and there is science that backs it up. When we learn something new, pathways are formed in our brains. The more we practice it, the stronger the pathways become. Everyone's brain does this so everyone can be equally good at math. The fourth video was about how you should believe in yourself and have confidence. People who believe in themselves, their brain will grow more than the people who don't believe in themselves. People who believe in themselves and know their brain can grow is called a growth mindset. The people who don't believe their brain can change is called a fixed mindset, and they don't improve as much as the people with a growth mindset. The final video was about how mistakes are powerful. When you're making a mistake, that is when your brain is struggling and being challenged. That is actually the best time for brain growth and you can learn a lot. It isn't about getting the solution to the problem, it's about how much you learn while you're solving it.
One-Cut Geometry
The problem I found most intriguing was One-Cut Geometry. I chose this problem partly because I struggled a lot with it but I felt like I was growing throughout the process. I connected to the last video we watched and how our brains grow when you make mistakes. I could feel my brain growing and changing for the better. I got right into it and tried multiple strategies but I couldn't seem to find a solution. At that point I was getting pretty frustrated with myself that I hadn't solved it yet. I told myself to take a deep breath and calmed down to get me on track again. It wasn't until I talked with some of my peers that I actually found a solution. The solution wasn't what really mattered, though, it was about the process I took and the steps I took to solve the problem. To make sure the solution worked, I drew a scalene triangle with different lengths. I cut out the triangle and it worked! I then decided to take the problem further and see if my strategy worked with other figures. I drew a four sided polygon and tried using the same strategy I had on the triangle. It also worked. To be 100 percent sure, I drew another four sided polygon, but this time with different measurements. It had the same outcome as the other attempts. Overall, I really enjoyed this problem since it was so challenging for me and I learned a lot from it. In this problem, I used two Habits of a Mathematician. The first one I used was Be Confident, Patient and Persistent. There were many times when I felt like giving up during the problem. I couldn't figure it out and I was getting frustrated. I told myself, though, to keep trying and have confidence in my abilities. I ended up getting a solution and I was really proud of myself. The other Habit of a Mathematician I used was Collaborate and Listen. When I was stuck, I went to my peers for inspiration and that really helped to get me thinking. We shared ideas and that was what led to me finding a solution. Without them, I wouldn't have solved it. That's why I think it is really important to work together because 4 heads are better than one. The biggest thing I will take away from this week is to persevere. Multiple activities this week were challenging, but I didn't let that stop me. I always have to give my all, even if it hard, to produce high quality work. That way my brain will grow and, ultimately, I will learn something new.
This was the first week of school and we did four different activities and watched 5 different videos. The purpose of it was for us to see that our brains could grow through failure and no on was born with a math brain. It was also to get introduced to the Habits of a Mathematician. For this week we did four different mathematical activities: Building Shapes, in which we had to make one of 6 different shapes using rope and our hands. This was done in a group of four. The teachers were skeptics and we had to justify why the shape we created was accurate. The second was Number Visual Pennies, in which we had 100 pennies and had to stack them in piles of 3, 5, 6, 7, and 9. We had to make sure each pile individually had the same pennies using all 100 of them. The third was One-Cut Geometry. In this activity we had a square piece of paper and had to draw a scalene triangle in the middle. None of the sides or corners of the triangle could touch the sides of the paper. Then we had to cut out the triangle using only one cut. It was challenging because I tried folding it and it always came out a little differently than how I drew it. The fourth and final activity was Square Mania. In this activity there were two examples of figures with 17 squares created using 10 line segments, and 20 squares using 9 line segments. Then it said what is the least amount of line segments you could use to make exactly 100 squares.
Videos
The first video we watched was about different strategies for mathematics. There were 5 mentioned in the video which were: 1. Draw It Out, 2. Teamwork, 3. Experiment, 4. Look for Different Resources, 5. Start with a smaller case. The second video was about how speed wasn't important in math. It talked about how a lot of top mathematicians were really slow, because they were thinking very deeply about the work and how they felt stupid while they were in school because they weren't as fast as other kids. The third video was about how our brains can grow and change. There is a myth about how some people are just naturally "math people," but that isn't true. Anyone can be good at math and there is science that backs it up. When we learn something new, pathways are formed in our brains. The more we practice it, the stronger the pathways become. Everyone's brain does this so everyone can be equally good at math. The fourth video was about how you should believe in yourself and have confidence. People who believe in themselves, their brain will grow more than the people who don't believe in themselves. People who believe in themselves and know their brain can grow is called a growth mindset. The people who don't believe their brain can change is called a fixed mindset, and they don't improve as much as the people with a growth mindset. The final video was about how mistakes are powerful. When you're making a mistake, that is when your brain is struggling and being challenged. That is actually the best time for brain growth and you can learn a lot. It isn't about getting the solution to the problem, it's about how much you learn while you're solving it.
One-Cut Geometry
The problem I found most intriguing was One-Cut Geometry. I chose this problem partly because I struggled a lot with it but I felt like I was growing throughout the process. I connected to the last video we watched and how our brains grow when you make mistakes. I could feel my brain growing and changing for the better. I got right into it and tried multiple strategies but I couldn't seem to find a solution. At that point I was getting pretty frustrated with myself that I hadn't solved it yet. I told myself to take a deep breath and calmed down to get me on track again. It wasn't until I talked with some of my peers that I actually found a solution. The solution wasn't what really mattered, though, it was about the process I took and the steps I took to solve the problem. To make sure the solution worked, I drew a scalene triangle with different lengths. I cut out the triangle and it worked! I then decided to take the problem further and see if my strategy worked with other figures. I drew a four sided polygon and tried using the same strategy I had on the triangle. It also worked. To be 100 percent sure, I drew another four sided polygon, but this time with different measurements. It had the same outcome as the other attempts. Overall, I really enjoyed this problem since it was so challenging for me and I learned a lot from it. In this problem, I used two Habits of a Mathematician. The first one I used was Be Confident, Patient and Persistent. There were many times when I felt like giving up during the problem. I couldn't figure it out and I was getting frustrated. I told myself, though, to keep trying and have confidence in my abilities. I ended up getting a solution and I was really proud of myself. The other Habit of a Mathematician I used was Collaborate and Listen. When I was stuck, I went to my peers for inspiration and that really helped to get me thinking. We shared ideas and that was what led to me finding a solution. Without them, I wouldn't have solved it. That's why I think it is really important to work together because 4 heads are better than one. The biggest thing I will take away from this week is to persevere. Multiple activities this week were challenging, but I didn't let that stop me. I always have to give my all, even if it hard, to produce high quality work. That way my brain will grow and, ultimately, I will learn something new.