Introduction This week in math we learned different habits of a mathematician. We learned how to have self confidence by understanding that making mistakes helps our brains grow. We were assigned a new problem everyday. On Tuesday we had a problem based on squares and stairs. Wednesday, we learned about Hailstone Sequences, and on Thursday we did the Painted Cube problem. For the squares and stairs, we had to identify patterns we saw in a stair sequence that kept growing up and outward. For the painted cube problem, Dr. Drew gave us 27 sugar cubes. He asked us to figure out how many of the sides would be painted if we dipped the cube, as a whole, into a bucket of paint.
How was I impacted? We watched videos teaching us that making mistakes is okay because our brains grow more through learning from mistakes rather than getting everything right. The videos that stood out to me the most were the ones describing that working through a problem is more beneficial than just knowing the answers or giving up. It helps your brain grow more because you've tackled the challenge head on.
Hailstone Sequences My favorite problem we did this week was the Hailstone Sequence. To start we chose any number, then used the sequence with the rules: if you get an even number, divide by 2 and if you get an odd number, multiply by 3 then add 1. I liked this problem because it took me a long time to figure out all the calculations. It gave me a challenge to go back and double check my work. I started with the number 107 and used the sequence rules. It took about 2 hours to get down to the number 1 which is the end of the sequence. A challenge I had was double checking to make sure I didn't mess up any of the numbers in the sequence because it was taking me a long time to get down to 1. I used the habit "looking for patterns" because each number had a set sequence to follow. I think that since I pushed myself in picking a higher number to start with, that I am going to be able to take on a lot of challenges this year. I am willing to continue to push myself in order to enhance my mathematical skills.
Extension For my extension of the sequence, I chose the rule of: if odd- divide by 3, if even multiply by 2. I started with the number 5. It started to get into very long decimal numbers. I went ten numbers in and realized that this was a very complicated rule. There were a lot of decimals to keep up with. I wasn't really seeing any patterns. I came to the conclusion that continuing to solve it would take a lot of time and was not really benefitting me in seeing how there are always patterns in math. For future sequences, I will start with a higher number because that benefitted me before, seeing a pattern that all the numbers in the sequence will end up at 1.