Purpose: The purpose of this week's inspirational math was to prove that everyone can be a math person and that if you are struggling it's ok because that just means at the end your brain is growing. During this week we also watched multiple videos by Joe Boaler from Stanford University. From her we learned that everyone moves at their own pace in math and just because you take longer on a problem than others doesn't mean your dumb or not a math person, it just means you're thinking harder on a problem. I really took this into consideration because I am always one of the last people to finish a math problem so I always just thought I just wasn't a math person. We also learned that making mistakes in math is a good thing because that just means your brain is growing. Over the week we did four different problems; Squares to stairs, Tiling an 11 X 13 rectangle, Hailstone sequence, and painted cubes. Squares to stairs is a problem where we looked at a single block and looked at the steps to it building up to a set of stairs. We each shared out how we saw the stairs grow and we had multiple ways of seeing it. The way I see it is it's like building up adding rows next to each other that have one more block than the last. The tiling an 11 X 13 rectangle problem was trying to figure what the least amount of squares you can make inside of an 11 X 13 rectangle. I found that the least amount of squares you can make is 6. The hailstone sequence is you pick any number of your choice and if its even you would divide it by 2 and if the number you got from that was odd you would multiply by 3 and add 1. You would do this multiple times until you found a pattern. The pattern I found was that no matter what number you choose you will always end up with 1. Painted cubes was where we put together a 3 X 3 3D cube of sugar cubes. We were asked the question, if this cube was dropped in paint, how many sides would be covered in paint and how many sides would not be. After doing all these problems we were asked to pick one and extend on it. I chose to extend on tiling an 11 X 13 rectangle because I took the most interest in it and wanted to see what the least amount of squares I could find in different size rectangles.
Tiling 11 X 13 rectangle
Tiling an 11 X 13 rectangle is a problem where we had to figure out the least amount of squares that we could fit inside of the rectangle. We had to do multiple attempts even if we thought we already got the right answer we had to attempt it more so that we could prove that it was correct. I got it on my second attempt but I tried it 4 other times just to make sure i was right. I decided to further on this problem because out of the four this one intrigued me the most. I wanted to see how many squares I could find using different size rectangles so thats what I did. My strategy to this problem is I always make the largest square possible because I find when I do that it always seems to make it so I have less squares to fill in. I have at multiple times where I get it right on the first time but you always want to double check your answer. One challenge i had while doing this problem was that I would find myself going in the right direction and I was making the least amount of squares possible but when I got to the end the single squares always got me and they made that attempt a fail. So now I always make sure that when I am making the squares there is never just one row left open because that would mean there would be a lot of individual squares .The habit of a mathematician I used for this problem was conjecture and test. I asked myself what if I make the biggest square possible on all of the rectangles then filled in the rest, would that make it so I could find the lowest amount of squares possible? I tried that with all of my attempts that weren't fails and proved that to be right.
|
Reflection |
Going through these problems some were challenging and other were very easy. I find that if I take my time no matter how easy I find the problem there is always something I will be missing. If I make a mistake I shouldn't be ashamed as I was before and I should celebrate it because that just means my brain grew. In the future I will know that even if I am the last person to get a problem it doesnt mean Im not a math person it just means I think longer and harder on the problem and thats ok.