How many squared are in figure 55?
I chose this question to focus on because I felt like I understood it the most. I found it the most intriguing to me.
PURPOSE
I think the purpose of this week was to teach us that just because we might not be good at something or fail a lot we are still capable of learning. During this week we watched a few videos. In the videos they were teaching us about how the brain learns more when we make a mistake rather than getting it right in the beginning. A few of the other videos taught about how we are all capable of learning and there really is not such thing as a "math person". It also talked about how speed is not everything and actually taking your time is good because you are trying to deeply understand it instead of just doing it and being done to eventually forget it. Something I took away was that even though i might take a while to do my work it doesn't mean I'm not good at math.
Extended Problem
My biggest challenge was trying to figure out how to do this problem in the fastest way. The first thing I started to do was to try to find a formula I could use. I did this by using a smaller figure such as figure 10. I tried to see how I could find the amount of blocks in the figure without having to draw it. I ended up dividing it in half to see the difference between blocks and how much an actual 10 by 10 square would be. I realized that 10 times 10 is 100 and divided by 2 is 50. That only gets you to 50 but the amount of squares in figure 10 is 55. I figured out a formula which turned out to be x times x divided by 2 plus half of x gives the answer. This worked for all the other ones. It turns out that figure 55 would have 1,540 squares in it based of the formula I used. An extension I did was instead of the "stairs" going up only one row each time I would go by 2 times more than it usually increases. For this I drew how it would look for the first four of these. Down below is what it would look like.
Reflection
I think my biggest success was figuring out this problem by myself. I was really surprised when I figured out that I actually got it right. I actually figured it out by accident and ignored it at first because I thought it was wrong. I got frustrated and took the long but easy route and actually added all numbers starting from 55 ending at one to find the answer but I got the same answer as I got out in the beginning.