1. What was the purpose of this week of investigations and video-watching?
There were multiple purposes in this week of math. The purpose of the videos was to tell us that no one is born a math person. Everyone can become a math person. Some of the activities were ment to show how different people can approach a problem. In one we saw how many different people formed the same figure using different methods.
2. Give an overview of all the activities and videos.
The videos had skits and a teacher stating what the skit is trying to say. Most of them talked about brain growth and how failures makes your brain grow. There was a message about how fast you can do a problem doesn't matter. One of the activities was called tiling a 11x13 grid. In that we had to fit the least amount of squares into a 11x13 rectangle. The second one we did was a few questions with a staircase pattern. Third, we had to use a set of rule to find a patter in the sequences using those rules. Third was the hailstone sequences. In this we had to finish here.Last we use sugar cubes to make a 3x3x3 cube and count how many individual cubes sides were on the outside of the cube.
3. Choose two messages from any of the five videos we watched. Explain the personal significance of those two messages.
The first message that I found personal was the video about speed. In elementary school we had these timed tests that I could never complete in time so I had to spend a bit of my lunch working on memorizing timetables. I hated them and I knew I was good at math but I wasn't fast at math. So that reminded me of that time. The other message was visualizing. I never visualize math problems that much but it can be useful to make a diagram of the problem. It helped me in a few cases.
4. Provide a write-up of the problem you chose to extend.
The problem I chose was the hailstone problem. The hailstone problem had us make hailstone sequences. Hailstone sequences got their name because, like the the creation of hail, the numbers go up and down. The sequence uses two rules. If the number is even then you divide by two. If the number is odd then you multiply by three and then add one. We had to apply these rules to thee numbers. I chose 31, 7,150, and 55. I will not list all of the numbers in each because I couldn't get to the end of 31 so I couldn't start 7,150 or 55. What I did to expand on the problem was test different ways to change the rules to see if different patterns arise. I found that if you change the even number rule you start to get decimals witch breaks the sequence. And if you change the odd multiplication to a even number then you get a odd number almost every time so those need to be odd. Last the addition part for the odd numbers just changes the pattern at the end. I chose this problem because I didn't really do too much on it. I tried to code something in scratch to make it easier but in scratch to show all of the numbers you would need to have as many variables on the screen as you can fit so I could only have seventy-two numbers. I can only see two approaches to this problem. Work out each number by hand or use a computer. I tried both and the computer is easier. One challenge I faced when doing this was making sure I was getting the numbers right. I think I did get them right but I still had a feeling that I messed up and that is why It was so long. I overcame it by checking it with the answers on the board and the ones I got on the program. I used the habit Be Confident, Patient and Persistent. I used this when I was trying 31. I had gone through so many and the only reason I stopped was because class was ending. i also showed that in the 11x13 problem. I would try and try so many times and even tried to use decimals.
5. A reflection of your work and effort during the Week of Inspirational Math
I feel like I didn't do too much. we didn't do a whole lot that was hard or challenging for me. I made it more challenging during the hailstone sequence but the sequence wasn't that hard. Just following it using a calculator got me thinking I messed up. The painted cube was really easy and could have been solved without a visual. The 11x13 was challenging but we never got a answer at the end so i feel like I could have stopped at two and would have been fine. Last the stairs problem. i did get help at lunch but really I just got a more efficent equation than my equation and I learned how to make equations for those problems now. I never gave up on a problem or just didn't do the problem and I put the effort in where I could.