Overview of the week
During the first week of school during Dr. Drew’s class we watched videos that taught us the simple traits of a mathematician and we were also given 4 different worksheets throughout the course of the 5 days we attended school. We were told to find ways to solve the problem creatively and “experiment”. I believe the reason we did these little assignments was so that we could break the ice between each other but also so we could warm-up our brain in the morning and get it awake. Also so we can develop a closer sense of community and being comfortable while sharing ideas along with working as a team.
Activities:
On the first day I worked together with my table mates to create shapes from a square to a tetrahedron. Once we made the assigned shape we were to call over a teacher who posed as a skeptic who tried to find flaws in our geometrical designs for each shape. At first I thought the activity would be simple since the first shape my group tackled was a square. Once we called over a skeptic he approved of our square making skills. We then went onto a star and our shape making streak came to a halt. We for some odd reason could not make a perfect star. We tried tracing a star after we drew it on a white board, but that didn’t work. Then as we were just messing around with the rope we made a pentagram. We called over a skeptic and the skeptic did not approve so our group tried to make other shapes, but they ended similar to the star.
The second day, we were given multiple patterns and we were to explore those patterns and find some similarities. Then on the back side of the paper we were given a task to figure out how to fit 100 pennies into a figure of 3, 5, 6, 7, and 9. But on the sheet there was a layout for the stacks of pennies we would have to make. For example, the 3 stacks made a triangle and we would have to make the pennies stack according to the shape each figure posed as.
On the third day, our class was given the challenge of cutting a scalene triangle out using only one cut. I found this activity to be quite challenging, after multiple trial and errors, I wasn’t able to find a way to cut out the scalene triangle using only one cut. The hope for this activity was so that we could learn from our mistakes and hopefully learn from them. But some of my classmates figured it out and went on to solve the more challenging ones such as cutting out shapes like parallelograms and octagons. It was interesting to watch them do it, I observed them and their strategy they used to solve the triangle problem didn’t work so they were back to trial and error.
Then on Friday which is the last day, we were assigned a worksheet where we were supposed to find squares within a rectangle. At first this task seemed simple and very basic, but as I observed, I found many little squares that would make up a bigger square. And I found this activity to be quite challenging. But more confusing than anything. With all my pencil marks, and numbers over the diagram marking the square it made it hard to tell if there was a square.
Videos:
The videos we watched all had a common theme and that was that anyone can do math as long as you have a growth mindset and if you believe you can learn the subject. The cast in the videos went into the science behind why anyone can learn. They mentioned that if there was a problem and time after time of you making a mistake on the problem, and thinking to yourself, Why can’t I do that? or How come I can’t solve this problem? It just means that your brain is growing and getting stronger. They also mentioned how the brain is a muscle and just like a muscle, the more work you put into it that muscle gets stronger. This concept is similar for your brain, the more you work your brain, the stronger it gets. For example in my life, if I weren’t able to make mistakes, 1 I wouldn’t be the person I am today, and 2 I wouldn’t learn anything new, which means I wouldn’t have some hobbies I have now such as surfing, body boarding, etc. I am able to do these things since there isn’t anyone holding me back and because I have a growth mindset and am able to see mistakes as something not bad, but something that I can benefit and grow from.
Choose One Activity:
I am choosing the activity that we did on day 2 which was the penny one since I really enjoyed it and I felt like it was a good way to warm up and challenge my brain. My group came to a conclusion of having 3 stacks of 22 pennies, 5 stacks and one penny, 6 stacks of one penny, 7 stacks of 2 pennies, and 9 stacks of one penny. This adds u to 100 pennies total and perfectly uses up all the pennies we were given meaning we completed the challenge. At first, I thought visualizing the structure of pennies would be a good idea, but as my table group input their ideas, we all came upon the conclusion that it would be more effective to instead use trial and error with numbers, hoping that it would all come together after a few tries. What I did was write out the numbers and do the math, multiplying numbers by 3 and trying to solve it by using divison and subtraction with a bunch of random numbers, hoping at least one of the patterns I came up with would lead us to solving the challenge. Once those numbers were found, I added them all together with hope of getting 100 as the sum. Instead came out 106, a pretty close guess. Guess after guess, and working with table mates, found the solution of having 3 stacks of 22 pennies, 5 stacks and one penny, 6 stacks of one penny, 7 stacks of 2 pennies, and 9 stacks of one penny. This adds u to 100 pennies total and perfectly uses up all the pennies
Reflection
After the week of inspirational math, I reflected on it. I had fun but while having I definitely learned things and learned from my mistakes by making them. I also collaborated with my peers, physically, mentally and orally. Some traits of a mathematician I feel like i displayed throughout the week was learning from my mistakes, especially during the one cut triangle activity and the activity where we had to make shapes using a rope. I also displayed the skill of working as a team and collaborating others and sharing my ideas in all the activities since we could only do it if our whole group participated in the activities. Another skill that I feel like I displayed well was making educational assumptions. This skill was displayed during the activity with the 100 pennies. Like I said I thought there was a systematic way to do it, but the more efficient way would be to use trial error and educational guesses which is exactly what I did.
During the first week of school during Dr. Drew’s class we watched videos that taught us the simple traits of a mathematician and we were also given 4 different worksheets throughout the course of the 5 days we attended school. We were told to find ways to solve the problem creatively and “experiment”. I believe the reason we did these little assignments was so that we could break the ice between each other but also so we could warm-up our brain in the morning and get it awake. Also so we can develop a closer sense of community and being comfortable while sharing ideas along with working as a team.
Activities:
On the first day I worked together with my table mates to create shapes from a square to a tetrahedron. Once we made the assigned shape we were to call over a teacher who posed as a skeptic who tried to find flaws in our geometrical designs for each shape. At first I thought the activity would be simple since the first shape my group tackled was a square. Once we called over a skeptic he approved of our square making skills. We then went onto a star and our shape making streak came to a halt. We for some odd reason could not make a perfect star. We tried tracing a star after we drew it on a white board, but that didn’t work. Then as we were just messing around with the rope we made a pentagram. We called over a skeptic and the skeptic did not approve so our group tried to make other shapes, but they ended similar to the star.
The second day, we were given multiple patterns and we were to explore those patterns and find some similarities. Then on the back side of the paper we were given a task to figure out how to fit 100 pennies into a figure of 3, 5, 6, 7, and 9. But on the sheet there was a layout for the stacks of pennies we would have to make. For example, the 3 stacks made a triangle and we would have to make the pennies stack according to the shape each figure posed as.
On the third day, our class was given the challenge of cutting a scalene triangle out using only one cut. I found this activity to be quite challenging, after multiple trial and errors, I wasn’t able to find a way to cut out the scalene triangle using only one cut. The hope for this activity was so that we could learn from our mistakes and hopefully learn from them. But some of my classmates figured it out and went on to solve the more challenging ones such as cutting out shapes like parallelograms and octagons. It was interesting to watch them do it, I observed them and their strategy they used to solve the triangle problem didn’t work so they were back to trial and error.
Then on Friday which is the last day, we were assigned a worksheet where we were supposed to find squares within a rectangle. At first this task seemed simple and very basic, but as I observed, I found many little squares that would make up a bigger square. And I found this activity to be quite challenging. But more confusing than anything. With all my pencil marks, and numbers over the diagram marking the square it made it hard to tell if there was a square.
Videos:
The videos we watched all had a common theme and that was that anyone can do math as long as you have a growth mindset and if you believe you can learn the subject. The cast in the videos went into the science behind why anyone can learn. They mentioned that if there was a problem and time after time of you making a mistake on the problem, and thinking to yourself, Why can’t I do that? or How come I can’t solve this problem? It just means that your brain is growing and getting stronger. They also mentioned how the brain is a muscle and just like a muscle, the more work you put into it that muscle gets stronger. This concept is similar for your brain, the more you work your brain, the stronger it gets. For example in my life, if I weren’t able to make mistakes, 1 I wouldn’t be the person I am today, and 2 I wouldn’t learn anything new, which means I wouldn’t have some hobbies I have now such as surfing, body boarding, etc. I am able to do these things since there isn’t anyone holding me back and because I have a growth mindset and am able to see mistakes as something not bad, but something that I can benefit and grow from.
Choose One Activity:
I am choosing the activity that we did on day 2 which was the penny one since I really enjoyed it and I felt like it was a good way to warm up and challenge my brain. My group came to a conclusion of having 3 stacks of 22 pennies, 5 stacks and one penny, 6 stacks of one penny, 7 stacks of 2 pennies, and 9 stacks of one penny. This adds u to 100 pennies total and perfectly uses up all the pennies we were given meaning we completed the challenge. At first, I thought visualizing the structure of pennies would be a good idea, but as my table group input their ideas, we all came upon the conclusion that it would be more effective to instead use trial and error with numbers, hoping that it would all come together after a few tries. What I did was write out the numbers and do the math, multiplying numbers by 3 and trying to solve it by using divison and subtraction with a bunch of random numbers, hoping at least one of the patterns I came up with would lead us to solving the challenge. Once those numbers were found, I added them all together with hope of getting 100 as the sum. Instead came out 106, a pretty close guess. Guess after guess, and working with table mates, found the solution of having 3 stacks of 22 pennies, 5 stacks and one penny, 6 stacks of one penny, 7 stacks of 2 pennies, and 9 stacks of one penny. This adds u to 100 pennies total and perfectly uses up all the pennies
Reflection
After the week of inspirational math, I reflected on it. I had fun but while having I definitely learned things and learned from my mistakes by making them. I also collaborated with my peers, physically, mentally and orally. Some traits of a mathematician I feel like i displayed throughout the week was learning from my mistakes, especially during the one cut triangle activity and the activity where we had to make shapes using a rope. I also displayed the skill of working as a team and collaborating others and sharing my ideas in all the activities since we could only do it if our whole group participated in the activities. Another skill that I feel like I displayed well was making educational assumptions. This skill was displayed during the activity with the 100 pennies. Like I said I thought there was a systematic way to do it, but the more efficient way would be to use trial error and educational guesses which is exactly what I did.