Week of Inspirational Math
1. The purpose of this week's investigations were to teach us that there are many ways of solving a problem and it's okay to make mistakes. What I learned was that people solve solve problems differently and see things differently. For example, in the squares to stairs investigation, people saw the patterns in a different way. Also, when we had to figure out how much squares figure 55 would have, everyone did something different. Some people actually drew squares, I created a table, and other people created an equation. The way I learned that it's okay to make mistakes is when some people had to show their work in front of the whole class, lots of people had minor mistakes in their work, but they weren't judged for it.
I think the purpose of the videos were to teach us how everyone could be a math person. Although some people learn slower than others, or some people understand things better than others, there is no such thing as a "math person". Everybody could learn math and make it fun if they choose to be interested in it. Anyone could be a math person because everyone's brain grows and expands.
2. Activity Overviews:
Tiling a 11 by 13 Rectangle: With an 11 by 13 rectangle with an area of 143 squares, we had to create the least amount of squares possible only using the 11 by 13 rectangle.
I think the purpose of the videos were to teach us how everyone could be a math person. Although some people learn slower than others, or some people understand things better than others, there is no such thing as a "math person". Everybody could learn math and make it fun if they choose to be interested in it. Anyone could be a math person because everyone's brain grows and expands.
2. Activity Overviews:
Tiling a 11 by 13 Rectangle: With an 11 by 13 rectangle with an area of 143 squares, we had to create the least amount of squares possible only using the 11 by 13 rectangle.
Squares to Stairs: We had to solve problems using the 4 figures above.
Using these figures we had to figure out a pattern we see visually. Everyone had different perspectives on how they see the pattern. For example, I saw the squares increasing diagonally, but others saw them increasing from the right or left. Based on the figures, we then figured out how much squares figure 10 would have, and if it was possible to make a staircase with 190 squares. While trying to figure out the answer to these problems, we came up with an equation: x squared + x / 2. Using this formula, we figured out that figure 10 would have 55 squares, and yes, you could make a staircase with 190 squares.
Hailstone Sequences: Using these rules (1. If a number is even, divide it by 2 to get the next number. 2. If a number is odd, multiply it by 3 and add 1.) we had make 3 sets of numbers using any number we wanted as the starting number. Within these sets of numbers we had to find patterns.
Painted Cube: With a 3 by 3 by 3 cube with a total of 27 squares, we had to figure out how many squares would have 3 sides, 2 sides, 1 side, and 0 sides painted if the cube was dropped into a bucket of paint. As a visual we used sugar cubes and actually built the model to give us a better visual in order to solve the problem.
Video Overviews:
Video 1: Ways We See Math
Everyone can be a "math person". Although some people may learn slower than others, it doesn't mean they can't be a "math person". Everyone's brains are growing and changing.
Video 2: Mistakes are Powerful
Making mistakes isn't a bad thing. It's actually good because it works your brain. You should take risks so your brain grows and expands. What matters most is what you learn through the process of solving a problem.
Video 3: Importance of Mindset
When solving a challenging problem, you should always have confidence in yourself. If you believe in yourself, your brain will expand and the better chance you have at solving a problem.
Video 4: Speed
How fast you are at solving a problem isn't important. What matters is your thought and process on solving the problem. You should really focus more on patterns, observations, visualizations, and ideas. It's better to take time on a problem and understand what you're doing, rather than being quick and not knowing what's going on.
Video 5: Visualizing
Although people have been telling us to stop using our fingers to count, it's actually better to use them. When you're doing mental math, you are actually visualizing counting your fingers in your head. It's important for brain growth and math performance.
Using these figures we had to figure out a pattern we see visually. Everyone had different perspectives on how they see the pattern. For example, I saw the squares increasing diagonally, but others saw them increasing from the right or left. Based on the figures, we then figured out how much squares figure 10 would have, and if it was possible to make a staircase with 190 squares. While trying to figure out the answer to these problems, we came up with an equation: x squared + x / 2. Using this formula, we figured out that figure 10 would have 55 squares, and yes, you could make a staircase with 190 squares.
Hailstone Sequences: Using these rules (1. If a number is even, divide it by 2 to get the next number. 2. If a number is odd, multiply it by 3 and add 1.) we had make 3 sets of numbers using any number we wanted as the starting number. Within these sets of numbers we had to find patterns.
Painted Cube: With a 3 by 3 by 3 cube with a total of 27 squares, we had to figure out how many squares would have 3 sides, 2 sides, 1 side, and 0 sides painted if the cube was dropped into a bucket of paint. As a visual we used sugar cubes and actually built the model to give us a better visual in order to solve the problem.
Video Overviews:
Video 1: Ways We See Math
Everyone can be a "math person". Although some people may learn slower than others, it doesn't mean they can't be a "math person". Everyone's brains are growing and changing.
Video 2: Mistakes are Powerful
Making mistakes isn't a bad thing. It's actually good because it works your brain. You should take risks so your brain grows and expands. What matters most is what you learn through the process of solving a problem.
Video 3: Importance of Mindset
When solving a challenging problem, you should always have confidence in yourself. If you believe in yourself, your brain will expand and the better chance you have at solving a problem.
Video 4: Speed
How fast you are at solving a problem isn't important. What matters is your thought and process on solving the problem. You should really focus more on patterns, observations, visualizations, and ideas. It's better to take time on a problem and understand what you're doing, rather than being quick and not knowing what's going on.
Video 5: Visualizing
Although people have been telling us to stop using our fingers to count, it's actually better to use them. When you're doing mental math, you are actually visualizing counting your fingers in your head. It's important for brain growth and math performance.
3. Video 3: Importance of Mindset- The personal significance in this message is most people today, when they feel like they can't solve a math problem, they automatically give up. You should always have confidence in yourself. Believing in yourself and not giving up will help you move forward and will help you in many ways.
Video 4: Speed- Speed isn't important in solving a problem. It doesn't matter if it takes you hours to do a problem, what matters is how much you think about it and trying different ways to solve a problem. It will improve your solving skills and it will expand your brain growth.
Video 4: Speed- Speed isn't important in solving a problem. It doesn't matter if it takes you hours to do a problem, what matters is how much you think about it and trying different ways to solve a problem. It will improve your solving skills and it will expand your brain growth.
4. Painted Cube Extension
- I created a problem extended off the painted cube activity. For this problem, instead of a 3 by 3 by 3 figure, I used a 3 by 5 by 4 figure with a total of 60 cubes. Using this figure I had to figure out the amount of cubes that would have 3 sides, 2 sides, 1 side, and 0 sides painted if the figure were to be dropped in a bucket of paint.
- I chose to extend this problem because it was more interesting than the other activities, and I felt it would be a little more challenging than using the 3 by 3 by 3 figure, especially because the length, width, and height were all different sizes.
- The way I solved this problem was by figuring out which cubes would have which amount of sides painted, than taking an estimated guess on which cubes on the sides that I can't see had which amount of sides painted. The way I checked to see if my answer was correct is I added the amount of squares with the certain amount of sides painted together, and if the sum was the same as the total amount of squares, then I knew the answer was correct.
- A challenge I faced solving this problem is figuring out which cubes had 3 sides, 2 sides, 1 side, or 0 sides painted because I didn't have a 3D visual, so I had to use the picture I drew.
- The habit of a mathematician I used was to start small. I used it because it was hard finding which sides had how many sides painted without having a 3D model. So I first looked at the cubes I could see in the drawn picture. Then I made estimated guesses off that.
- I created a problem extended off the painted cube activity. For this problem, instead of a 3 by 3 by 3 figure, I used a 3 by 5 by 4 figure with a total of 60 cubes. Using this figure I had to figure out the amount of cubes that would have 3 sides, 2 sides, 1 side, and 0 sides painted if the figure were to be dropped in a bucket of paint.
- I chose to extend this problem because it was more interesting than the other activities, and I felt it would be a little more challenging than using the 3 by 3 by 3 figure, especially because the length, width, and height were all different sizes.
- The way I solved this problem was by figuring out which cubes would have which amount of sides painted, than taking an estimated guess on which cubes on the sides that I can't see had which amount of sides painted. The way I checked to see if my answer was correct is I added the amount of squares with the certain amount of sides painted together, and if the sum was the same as the total amount of squares, then I knew the answer was correct.
- A challenge I faced solving this problem is figuring out which cubes had 3 sides, 2 sides, 1 side, or 0 sides painted because I didn't have a 3D visual, so I had to use the picture I drew.
- The habit of a mathematician I used was to start small. I used it because it was hard finding which sides had how many sides painted without having a 3D model. So I first looked at the cubes I could see in the drawn picture. Then I made estimated guesses off that.
5. Working on the investigations we did this week, I feel like I learned many different things on being a mathematician. For example, I learned to be more confident in myself, and I also used trying different ways to solve a problem. I learned that I use some of the tools the videos showed us, but I also found out some new tools I could use when solving a problem. I also learned that our brains can grow in many different ways by doing different things.