1. What was the purpose of this week of investigations and video-watching? In other words, why did we spend 5 days of class time on this?
We spent 5 days on watching inspiring math videos because they were tasked to help us to use deep thinking in math. The videos sent out messages that put the idea in our brains that Math is meant to for deep thinking and you shouldn’t feel bad by taking extra time to think through the problem. We also learned that having a growth mindset instead of a fixed mindset is crucial to becoming a good mathematician. Having a mindset that has the user being confident in their abilities and has them always striving to improve will definitely make the person a fine mathematician.
Over the first week, we worked on 4 major projects.
One project we did was called, “Building Shapes”. What we did in this project was to build a 3D shape from a rope. We had to make sure that everyone was participating and if the shape was completely accurate to the shape that we were suppose to build. Here is the pictures representing what we had to build with the rope:
We spent 5 days on watching inspiring math videos because they were tasked to help us to use deep thinking in math. The videos sent out messages that put the idea in our brains that Math is meant to for deep thinking and you shouldn’t feel bad by taking extra time to think through the problem. We also learned that having a growth mindset instead of a fixed mindset is crucial to becoming a good mathematician. Having a mindset that has the user being confident in their abilities and has them always striving to improve will definitely make the person a fine mathematician.
Over the first week, we worked on 4 major projects.
One project we did was called, “Building Shapes”. What we did in this project was to build a 3D shape from a rope. We had to make sure that everyone was participating and if the shape was completely accurate to the shape that we were suppose to build. Here is the pictures representing what we had to build with the rope:
Another project we did was the “Number Visual Pennies” problem. In this problem we had to have piles of 3, 5, 6, 7, & 9. In each pile, we had to choose a number of pennies to put in piles. Though, let’s say we have 3 piles of pennies. In those piles of 3, you’ll have to find a number of pennies that would be on each pile and for those 3 piles, it would have to be the exact same amount of pennies in each pile. It would be same for piles of 5, 6, 7, etc. Except, the piles of 5 can be different than 3 and 7 or any of them. It’s just the piles of 5 that have to be the same number. The challenge to this is that all these piles have to add up to 100. So you need to find a way to get all your piles to add up to 100 in the end and you’ll have a good solution. Here is the picture of the worksheet:
Here is the photo representing the groups I was referring to. The group of 3 I was talking about earlier is on the top right corner of the picture. The 3 circles. There is where you would place a certain amount of pennies in each circle and you would have to put the same amount of pennies in each of those 3 circles.
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I also made a extension of this problem. For my extension, I decided that I would try to use the same groups shown in the picture above but the goal would to try get 200 pennies instead. Here is what I got for the extension:
Here I decided to start off with 3 15’s which add up to 45. Then, I decided to have 5 7’s which add up to 35 and I added those together. I got 80 but I wanted to get around 100 so I knew I had to use a number around 20. I then attempted to use the 6 piles and I found out that 4 6’s equal 24. I then added everything up to get 104. After that, I only had piles of 7 and 9 left. I searched for the perfect combination that’ll allow me to end up with 200 and I found it. Finally, I found out that 7 6’s equals 42 and then all I did was add that to 104. I got 146 and I subtracted that by 200 to find out that all I needed left was the number 54. I realized that 9 x 6 equals 54 and all I had to do was to add everything up. I got 200 and I was confident that I had proven to have a good solution to this problem.
I chose this problem because it intrigued me on how many ways you could do this problem and even how you can change it up a bit to make it a bit harder. There is endless potential in this problem because it’s basically just combining numbers and having them work together to accomplish the same goal. There is a lot of different paths you can take and many objectives you can try to accomplish with this type of problem. That is why I decided to pick this problem to extend on.
Some approaches I tried were mostly me figuring out which numbers would work with each other the most to reach the objective that we were suppose to reach. I tried smaller numbers with the lower groups like piles of 3 or 5. Though if I tried that, then I would have to put high numbers on the higher piles which means there is more quantity of higher numbers. That could become chaotic quick and it would be harder to find a answer for a objective that is around 100 or 200 with circumstances like that. The same if you put too high of numbers into the piles of 3 or 5. The numbers in the future piles will have to be incredibly small to add up for the objective. The key to this problem is balancing, you need to balance out your numbers so that you’ll be able to arrive to your destination.
Something else you use in this problem is “Conjecture and Test” which is a habit of mathematician. In this problem, you have to balance out numbers to make sure you arrive to your goal but first you need to actually find out what numbers will actually be able to balance out with each other. To do so, you’ll have to learn how to “Conjecture and Test”. The secret to Conjecture and Test is to constantly think about how things work and ask why. When you ask why, try to “test” it out and try to actually find your answer. In this problem, you have to ask why and how some of the numbers balance with each other. You have to ask how they can add up to your objective. Then, you test this all out to hopefully find a solution that can get to your objective. That is how you Conjecture and Test, and you use it a lot in this problem.
One issue that came up in my extension was related to the balancing problem that I mentioned earlier. I tried things like 10 or 20 pennies for the stacks of 3 and it didn’t work out for me. It wasn’t large enough for me to get good progress to 20 and it didn’t really work for the solution that I was trying to pull off. Though I tried to change the pennies to 15 for the stack of 3 and I got 45. It then seemed to work well with my other numbers like 35 and I got 104 out of that which helped a lot to get 200. So basically Conjecture and Test / number balancing was the answer to get through the issues that I was coming across.
Anyways, the third project we worked on the first week of school was called “One-Cut Geometry”. In this project, we were tasked to make a scalene triangle in the middle of the paper and we had to cut it out from the rest of the paper in only one cut. As you can tell, this is actually pretty difficult and it forces you to use your thinking skills. You’ll have to think outside the box to even have a chance to figure out a solution for this problem. Here is an example of the instructions on how we had to make our scalene triangle:
I chose this problem because it intrigued me on how many ways you could do this problem and even how you can change it up a bit to make it a bit harder. There is endless potential in this problem because it’s basically just combining numbers and having them work together to accomplish the same goal. There is a lot of different paths you can take and many objectives you can try to accomplish with this type of problem. That is why I decided to pick this problem to extend on.
Some approaches I tried were mostly me figuring out which numbers would work with each other the most to reach the objective that we were suppose to reach. I tried smaller numbers with the lower groups like piles of 3 or 5. Though if I tried that, then I would have to put high numbers on the higher piles which means there is more quantity of higher numbers. That could become chaotic quick and it would be harder to find a answer for a objective that is around 100 or 200 with circumstances like that. The same if you put too high of numbers into the piles of 3 or 5. The numbers in the future piles will have to be incredibly small to add up for the objective. The key to this problem is balancing, you need to balance out your numbers so that you’ll be able to arrive to your destination.
Something else you use in this problem is “Conjecture and Test” which is a habit of mathematician. In this problem, you have to balance out numbers to make sure you arrive to your goal but first you need to actually find out what numbers will actually be able to balance out with each other. To do so, you’ll have to learn how to “Conjecture and Test”. The secret to Conjecture and Test is to constantly think about how things work and ask why. When you ask why, try to “test” it out and try to actually find your answer. In this problem, you have to ask why and how some of the numbers balance with each other. You have to ask how they can add up to your objective. Then, you test this all out to hopefully find a solution that can get to your objective. That is how you Conjecture and Test, and you use it a lot in this problem.
One issue that came up in my extension was related to the balancing problem that I mentioned earlier. I tried things like 10 or 20 pennies for the stacks of 3 and it didn’t work out for me. It wasn’t large enough for me to get good progress to 20 and it didn’t really work for the solution that I was trying to pull off. Though I tried to change the pennies to 15 for the stack of 3 and I got 45. It then seemed to work well with my other numbers like 35 and I got 104 out of that which helped a lot to get 200. So basically Conjecture and Test / number balancing was the answer to get through the issues that I was coming across.
Anyways, the third project we worked on the first week of school was called “One-Cut Geometry”. In this project, we were tasked to make a scalene triangle in the middle of the paper and we had to cut it out from the rest of the paper in only one cut. As you can tell, this is actually pretty difficult and it forces you to use your thinking skills. You’ll have to think outside the box to even have a chance to figure out a solution for this problem. Here is an example of the instructions on how we had to make our scalene triangle:
Finally for the fourth project we worked on for the first week of school, we did a project called “Square Mania”. For this project, we were told that there was either 17 or 20 squares in the picture but not all of them were clearly seen in the picture. You have to use your thinking skills and creativity to find the other squares and you have to explain why you know where the other squares are & how they count as being there. It is a quite puzzling problem but an interesting one as well. Here is the picture of the worksheet of this problem:
Other than the 4 problems we worked on, we did something else on the first week of school. We watched 5 different videos on 5 different days that were suppose to inspire us and makes us think differently about math. The first day’s video was about some strategies that you can use to learn math and how working together with others to figure out a problem. The second day’s video was about how moving slow in math is important and speed isn’t an issue. The third day was about how brains grow and change. The fourth day was about how you should believe in yourself and how changing your mindset can really help you. Then finally, the fifth day was about how mistakes can be powerful and it can help you learn better in the future.
I believe that these are all very useful and everything listed above is great advice. Not just for math but in life in general. You should always try your best and have confidence in yourself. You should always strive to improve yourself and have a good mindset on life. Also learning from your mistakes can really help you to prevent more mistakes to happen in the future so all these advice can really help you in different parts of life as well and I feel that this is important to learn.
This first week was just warming me up for the rest of the year. I have had some mistakes this first week due to me being a mess and sickness. Though, I’ll learn from my mistakes and I’ll get better in the future. I will become more focused in class and I’ll try to participate a little more instead of being sick in the corner unable to comprehend half of the things happening. I still did really well while I was unwell but I’ll do better later in the year and I’ll only be able to improve even more as time goes on.
I believe that these are all very useful and everything listed above is great advice. Not just for math but in life in general. You should always try your best and have confidence in yourself. You should always strive to improve yourself and have a good mindset on life. Also learning from your mistakes can really help you to prevent more mistakes to happen in the future so all these advice can really help you in different parts of life as well and I feel that this is important to learn.
This first week was just warming me up for the rest of the year. I have had some mistakes this first week due to me being a mess and sickness. Though, I’ll learn from my mistakes and I’ll get better in the future. I will become more focused in class and I’ll try to participate a little more instead of being sick in the corner unable to comprehend half of the things happening. I still did really well while I was unwell but I’ll do better later in the year and I’ll only be able to improve even more as time goes on.