Purpose:
We learned this week that mistakes are good and that they help your brain grow. We watched five videos from Joe Boaler from Stanford University. She taught us how our brain grows and changes each time we make a mistake and learn from it and our brain grows. We also were taught that it doesn't matter your speed and how fast you finish a problem. If you take longer it just means your thinking about the problem deeper. We learned that everyone solves problems at their own pace. We did four worksheets in class; Tiling a 11x13 rectangle, Hailstone sequence, Squares to stairs, Painted cubes. Tiling an 11x13 rectangle is where we had to find the lowest amount of squares we could fit inside of the 11x13 rectangle. The lowest I found was 8 squares. The Hailstone sequence is where we had to pick one number and if it was even we would divide it by 2 and if it was odd we would multiply it by 3 and add 1. We did this multiple times with different numbers each time until we found a pattern. The pattern I found was that if you start with the number 1 you end with 1. Squares to stairs was about looking at a set of stairs growing one block at a time and finding your own way of how you see it grow. I see it growing diagonally going down. Painted cubes was were we put together a 3x3 cube made out of sugar cubes and mark all of the faces on the outside with sharpie. The question we were asked was: "If this cube was dropped in paint, how many faces would be covered in paint and how many would not be?" I chose to extend on the hailstone sequence because I thought if I looked more into it I would be able to explain it very well. After watching those videos I realize that my brain grows more when I struggle and when I make a mistakes verses me getting the problem right and not growing as much.
Hailstone sequence:
For example: 14; 7; 22; 11; 34; 17; 52; 26
The hailstone problem is a problem where we had to find a pattern in numbers after using a formula. The formula was to divide by 2 when it's a even number, when it's an odd number you multiply by 3 and add 1.
I chose this problem because I felt I could really explain it without having any lack of detail and I also really enjoyed it after having that "Ah-Ha Moment." I found out that when you start with one, you end with one because Its just a constant pattern of 1; 4; 2;........ and so on. I got this on my first try because I wanted to see if smaller the number the easier the pattern, all patterns ended in 1 some how. One challenge I faced was when I kept hearing my table saying "They all end in 16." I couldn't wrap my head around that because, how could they all end in 16 when I have proof that they all find it's way to 1. So, it was just confusing and made me question my work and how I did it. One habit of a mathematician I used was Looking for Patterns, this was one is so useful for this problem that I didn't really use any other because once I found that pattern I pretty much knew the answer.
I chose this problem because I felt I could really explain it without having any lack of detail and I also really enjoyed it after having that "Ah-Ha Moment." I found out that when you start with one, you end with one because Its just a constant pattern of 1; 4; 2;........ and so on. I got this on my first try because I wanted to see if smaller the number the easier the pattern, all patterns ended in 1 some how. One challenge I faced was when I kept hearing my table saying "They all end in 16." I couldn't wrap my head around that because, how could they all end in 16 when I have proof that they all find it's way to 1. So, it was just confusing and made me question my work and how I did it. One habit of a mathematician I used was Looking for Patterns, this was one is so useful for this problem that I didn't really use any other because once I found that pattern I pretty much knew the answer.
Reflection:
On all the other problems I would always get stumped on the last one. I think this is because I didn't feel confident in doing math because I've never been. After watching all these videos and doing worksheets I realized that I should always keep trying and never give up, be cause just finding another way, wrong or right can benefit to you by learning your mistakes and helping your brain grow. I tried putting a lot of effort into the problems but I feel like I am the one holding myself back. I hold myself back by telling myself that I can't do it and that I should give up. This year I feel like I will be able to stop doing that, I can just tell because of what we've thought about in class I will stop thinking that way.