Week of Inspirational Math
The purpose of the investigations we did over the past week was to get us back into the swing of the school year and get our brains "woken up" so we will be ready to start doing math after the summer. Since Dr. Drew has been putting such a big emphasis on group work the videos we have been watching have given us insight into the group work we will be doing in class.
Day One
First, we watched a video about how being a "math person" is a myth. You can't be a "math person" there is no such thing. Then, we were given the task of drawing an 11x13 rectangle and seeing how many squares you can fit that rectangle. We were able to fit six squares in the rectangle without using fractions or having leftover squares.
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Day Two
We watched two videos, In the first video we learned that when your brain grows the synapses in your brain fire twice, once when you make a mistake and then again when you realize you made a mistake. In the second video, we learned that having a growth mindset can have a big impact on your perseverance. Then we worked on the stairs to squares problem where we looked at how a set of boxes shaped like squares grew.
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Day Three
Day Four
Personal Significance
The first message that has a personal significance to me is "there is no such thing as a math person." I have never been super strong in math so when math was easy for other kids in my class I always thought they were just naturally good at math. In reality, they had just had more practice than me. The second message that has a personal significance for me is that "visualization in math is a good thing." When I first started learning my time tables I did not know my 9's facts without using my fingers, so when my teacher told me using my fingers was bad I was shocked. Then when I started school at HTM I started to use my fingers and I still use them to this day.
Extension
The problem I choose to expand was the Hailstone sequence problem. In this problem, you are given steps to follow. First, you pick a number to start with, then depending whether you decide to start with an even or odd number the rule changes. If you have an even number you divide by two, if you have an odd number you multiply by three and add one. It would look like this: (24 ,12 ,6 ,3 ,10 ,16 ,8 ,4 ,2 ,1) I choose this problem because I thought it was very interesting how the sequence looks with the changing numbers. I was wondering if how the sequence would look if I changed if I changed the rule. When approaching this problem I made sure not to pick numbers that were too big, but I did not pick numbers that were too small to clearly show the pattern. When approaching the extension I did of the problem I tried not to change the problem too much. The challenge I came across when working with my new rules was that I could not get the rules to always get you back an even number. To overcome this I came up write new rules, but even with new rules I still did not figure out how to get the sequence to work. The Habit of a Mathematician I used the most to solve this problem was taking apart and putting back together, I used this the most when changing the rules because I kept the original format and just changed the numbers.
Reflecition
I think my work during the week was very strong, I put all my effort into each problem we did. I think this past week should be my goal for how I work every as we get farther into the school year. Even if the work that we did may not be the same as the work we will be doing for the rest of the year, I have to make sure I stay engaged. When we are working on POW's or SAT warm-up's I have to make sure I do my best in the silent work time and always try to understand what other people are saying when we work in groups.