Hailstone Sequence
1. What was the purpose of this week of investigations and video-watching?
I think that the purpose for doing these things and watching those videos in class was to make us, the students, feel more comfortable in class and more motivated to learning new problems in Dr. Drew's class. I also think that this would help students not only feel comfortable to ask questions in class but to explain to the class their way of doing the problem.
2. Give an overview of all the activities and videos.
3. Choose two messages from any of the five videos we watched. Explain the personal significance of those two messages.
Out of all the five videos that I've seen, I feel that the two messages that stuck with me the most was the fact that in one of the videos, the lady said that it wasn't okay to make mistakes but Dr. Drew said that we, the class, all have a different mindset then everybody else and sometimes it's okay to make mistakes because later on, you start to realize that you made a mistake and that sticks with you. Something else that
4. Provide a write-up of the problem you chose to extend. Include:
- a detailed description of the problem
- an explanation as to why you chose this problem
- a description of the approach(es) you took to solving this problem
- high-quality images of your work (diagrams, tables, equations)
- a description of at least once challenge you faced and how you overcame that challenge
- a description of at least one Habit of a Mathematician that you used in working on this problem
5. A reflection of your work and effort during the Week of Inspirational Math: how will this week inform your effort and participation in math for the rest of the year.
Problem Of The Week Write-Up: Checkerboard Equations
1.) Problem Statement:
For the Checkerboard Square problem, Dr. Drew had handed out a piece of paper to everybody in class and on the paper it had two checkerboards on the top. There was a square on the left and a square on the right. On the paper it explains, “the diagram at the right below shows a 3-by-3 square outlined with the checkerboard.” This helped out a lot after reading this. The main goal of this assignment was to figure out how many squares could make out of the box, whether it was a 1x1 square or an 8x8 square.
2. Process Description and Solution:
When the teacher told the class to try and solve the problem on our own, I was struggling because I didn’t know how to solve it on my own and I couldn’t ask anybody for help until Dr. Drew gave us the “okay” to do so. Since I didn’t want to just sit around and feel left out, I tried to just count the squares 1-by-1 but I still couldn’t figure out what I was doing wrong and after about 10 minutes of trying, I eventually had to give up and just wait to do the problem with my table group. When the teacher told us to explain what we got to our table members, I had to tell them that I couldn’t figure it out and they were able to understand it better than I could. I even had to ask my friend if she figured it out and she told me that her group had found an equation, it was:
x=1nx2
3. Extensions and Further Exploration
But the problem was we both, my friend and I, couldn’t understand how to do the equation that he got. I was ready to just give up and start doodling because I felt like there wasn’t a point to doing the work but, luckily, my friend said that her table group had figured it out but she didn’t understand it and neither did I. When class was over, I was like a deer standing in the middle of the street, lost, and only finished some of it. The next day, the teacher asked us to take out the problem and share what we got with the class, luckily I didn’t get picked on because I would have made a fool of myself.
Boxes
# of Boxes
1x1
64
2x2
49
3x3
36
4x4
25
5x5
16
6x6
9
7x7
4
8x8
1
At first, I didn’t understand it but as I was writing, I realized something. I was in the middle of doing 4x4 and 5x5 when I realized that 25 was the answer to 5x5 and 16 was the answer to 4x4. That’s when I started to feel really motivated to figure this thing out. I saw that 6x6 was the answer to the 3x3 box, it was 36. I tried to match up all the numbers with each other and that’s when everything started going backwards.
1x1 = 64 which was the answer to 8x8 which had only 1 square. I was frustrated because I no longer had a pattern. After a while of discussing this with my mom, I had finally figured it out and may I tell you that it helped me sleep at night.
If I did do an extension on this, I would’ve had try to figure out whatever the equation that my friend had found out from her table. Now I feel like an idiot because I didn’t feel like writing it down when I had the chance, but if I had a choice then I would have asked them and then I would’ve figure it out in class. It seem easy but let me tell you that it was not and I didn’t understand it for a while. I feel that trying a new approach wasn’t necessary since it was actually pretty easy figuring it out in the end
4. Reflection
Now looking back on this, I can see how easy it was to solve it. To me, I guess I was so confused and disheartened with this problem and the equation that my friend’s table group came up with. Next time instead of giving up and waiting for the inevitable, I will try to do the work by myself first before asking anybody for help. To be honest, I usually find myself in these situations and the only thing that I know how to do is copy other people's work and not actually listen. I need to work on that.
1. What was the purpose of this week of investigations and video-watching?
I think that the purpose for doing these things and watching those videos in class was to make us, the students, feel more comfortable in class and more motivated to learning new problems in Dr. Drew's class. I also think that this would help students not only feel comfortable to ask questions in class but to explain to the class their way of doing the problem.
2. Give an overview of all the activities and videos.
3. Choose two messages from any of the five videos we watched. Explain the personal significance of those two messages.
Out of all the five videos that I've seen, I feel that the two messages that stuck with me the most was the fact that in one of the videos, the lady said that it wasn't okay to make mistakes but Dr. Drew said that we, the class, all have a different mindset then everybody else and sometimes it's okay to make mistakes because later on, you start to realize that you made a mistake and that sticks with you. Something else that
4. Provide a write-up of the problem you chose to extend. Include:
- a detailed description of the problem
- an explanation as to why you chose this problem
- a description of the approach(es) you took to solving this problem
- high-quality images of your work (diagrams, tables, equations)
- a description of at least once challenge you faced and how you overcame that challenge
- a description of at least one Habit of a Mathematician that you used in working on this problem
5. A reflection of your work and effort during the Week of Inspirational Math: how will this week inform your effort and participation in math for the rest of the year.
Problem Of The Week Write-Up: Checkerboard Equations
1.) Problem Statement:
For the Checkerboard Square problem, Dr. Drew had handed out a piece of paper to everybody in class and on the paper it had two checkerboards on the top. There was a square on the left and a square on the right. On the paper it explains, “the diagram at the right below shows a 3-by-3 square outlined with the checkerboard.” This helped out a lot after reading this. The main goal of this assignment was to figure out how many squares could make out of the box, whether it was a 1x1 square or an 8x8 square.
2. Process Description and Solution:
When the teacher told the class to try and solve the problem on our own, I was struggling because I didn’t know how to solve it on my own and I couldn’t ask anybody for help until Dr. Drew gave us the “okay” to do so. Since I didn’t want to just sit around and feel left out, I tried to just count the squares 1-by-1 but I still couldn’t figure out what I was doing wrong and after about 10 minutes of trying, I eventually had to give up and just wait to do the problem with my table group. When the teacher told us to explain what we got to our table members, I had to tell them that I couldn’t figure it out and they were able to understand it better than I could. I even had to ask my friend if she figured it out and she told me that her group had found an equation, it was:
x=1nx2
3. Extensions and Further Exploration
But the problem was we both, my friend and I, couldn’t understand how to do the equation that he got. I was ready to just give up and start doodling because I felt like there wasn’t a point to doing the work but, luckily, my friend said that her table group had figured it out but she didn’t understand it and neither did I. When class was over, I was like a deer standing in the middle of the street, lost, and only finished some of it. The next day, the teacher asked us to take out the problem and share what we got with the class, luckily I didn’t get picked on because I would have made a fool of myself.
Boxes
# of Boxes
1x1
64
2x2
49
3x3
36
4x4
25
5x5
16
6x6
9
7x7
4
8x8
1
At first, I didn’t understand it but as I was writing, I realized something. I was in the middle of doing 4x4 and 5x5 when I realized that 25 was the answer to 5x5 and 16 was the answer to 4x4. That’s when I started to feel really motivated to figure this thing out. I saw that 6x6 was the answer to the 3x3 box, it was 36. I tried to match up all the numbers with each other and that’s when everything started going backwards.
1x1 = 64 which was the answer to 8x8 which had only 1 square. I was frustrated because I no longer had a pattern. After a while of discussing this with my mom, I had finally figured it out and may I tell you that it helped me sleep at night.
If I did do an extension on this, I would’ve had try to figure out whatever the equation that my friend had found out from her table. Now I feel like an idiot because I didn’t feel like writing it down when I had the chance, but if I had a choice then I would have asked them and then I would’ve figure it out in class. It seem easy but let me tell you that it was not and I didn’t understand it for a while. I feel that trying a new approach wasn’t necessary since it was actually pretty easy figuring it out in the end
4. Reflection
Now looking back on this, I can see how easy it was to solve it. To me, I guess I was so confused and disheartened with this problem and the equation that my friend’s table group came up with. Next time instead of giving up and waiting for the inevitable, I will try to do the work by myself first before asking anybody for help. To be honest, I usually find myself in these situations and the only thing that I know how to do is copy other people's work and not actually listen. I need to work on that.