Videos
In this week, we looked at several old videos discussing brain growth and such, and worked on several different activities. The names of them were tiling a 11x13 rectangle, squares to stairs, hailstone sequences, and a painted cube. There were five videos each with important messages like how no one is born a "maths person", and when you learn from your mistakes your brain grows. I believe this was important to watch so the class can feel better about themselves if they didn't think that they could do maths. I used to call other people who could answer questions quickly or understand the problem quicker a "maths person". But I now understand that it's never about how fast you understand or solve the problem, the point is to make mistakes and learn from them so that you can learn new strategies and approaches to the problem.
Reflection
In this overall week, I think I participated as much as I could have. Though I didn't participate in raising my hand to sharing my answer or solution in class, I did try to look for patterns, conjecture and test solutions on my paper. I did work with partners on just about all the activities because of course, two brains are better than one. Even though I did show a lot of my work on my paper, I definitely wasn't organized with it. I would like to work on organization throughout this year so I'm able to go back to my work and be able to read and understand what I wrote.
Activities
In the first activity we did, the tiling an 11x13 rectangle, we investigated on how we could create the smallest amount of squares into an 11x13 rectangle. There was lots of trial and error on this, but the smallest amount of exact squares the class and I could find was 6. I think the largest amount of squares I had was about nine, and I couldn't really tell from there if that was the smallest amount of squares or not. My partner keep pushing me to keep trying to make a smaller amount of squares and I did, and I got six squares. I checked with my table and mostly everyone got six squares as their exact amount too.
In the hailstone sequences activity, we explored a set of numbers and tried to find the pattern in them following along with generating a set of numbers ourselves. The set of numbers we all looked at first was, "20-10-5-16-8-4-2-1." Looks random right? Not too long after trying to find a pattern, Dr. Drew told us that we should make our own number strings by starting out with any number. If it was even, divide by two. But if it was odd, multiply by 3 and add 1. This was an interesting method, but if you continued along with it for a while, you'd find yourself ending the set with 4-2-1. The whole class was shocked to find that all of our data ended with 4, 2, and 1.
The last activity we did dealt with sugar cubes and counting. We went over questions such as, "If we dunked this cube in paint and took it apart (into 27 cubes), how many small cubes would have (x) sides painted?" The first question asked how many cubes would have three sides of the cube painted, and the answer would be eight. Because there's only 8 cubes out of the 27 cubes that create the whole cube that show three sides.
In the hailstone sequences activity, we explored a set of numbers and tried to find the pattern in them following along with generating a set of numbers ourselves. The set of numbers we all looked at first was, "20-10-5-16-8-4-2-1." Looks random right? Not too long after trying to find a pattern, Dr. Drew told us that we should make our own number strings by starting out with any number. If it was even, divide by two. But if it was odd, multiply by 3 and add 1. This was an interesting method, but if you continued along with it for a while, you'd find yourself ending the set with 4-2-1. The whole class was shocked to find that all of our data ended with 4, 2, and 1.
The last activity we did dealt with sugar cubes and counting. We went over questions such as, "If we dunked this cube in paint and took it apart (into 27 cubes), how many small cubes would have (x) sides painted?" The first question asked how many cubes would have three sides of the cube painted, and the answer would be eight. Because there's only 8 cubes out of the 27 cubes that create the whole cube that show three sides.
Squares to Stairs
The squares to stairs was a long activity. We used almost all of the Habits of Mathematician for this. We looked for patterns in the stairs, we started out small with the figures until we expanded to more squares, we tested out different formulas, most people tried staying organized with their work, and collaborated and listened with our fellow peers about the problem. This all started out with Dr. Drew showing us figure 3 on the screen for one second, and without counting each seperate square, see if we could recongnize how many squares were in the figure. The class showed on the white board on how their brains functioned throughout that one second of counting. It was interesting to see that some people shared the same pattern, and some were completly on their own. I personally recongnized the amount of squares the same way as two other people in the classroom. We saw that it was in a stair case form, and that there were three squares going horizontal and vertical, and then got to the conclusion that there was 6 squares in all. We were then showed four different figures that you can see at the top of the picture that's on the left. Our task was to find a pattern, guess how many squares figure ten would have, guess how many squares figure fifty-five would have, and to see if you can use one hundred and ninety squares to make a stair case shaped form. After two minutes of re-counting, I found that figure 10 has 55 squares. It wasn't until a little bit after that I found a quicker way to find the amount of squares in a figure. By adding the sum of the past problem to x to get your new y. (As you can see on the photo) After doing that pattern for a little while I also found that figure 19 has 190 squares, so yes, it is possible for a figure to have 190 squares. I chose to discuss this problem because I thought it was the most difficult activity out of the whole week, so I wanted to see if I was capable of writing a descriptive explanation on what this problem was and how I solved it. I also believed that I put a lot of effort and had a lot of work on my page showing I tried. One of the challenges I faced was finding the pattern in the figures. In able to overcome this, I had to ask questions and kept pushing myself to teste formulas until I created a table and had my eyes open to a solution.
To expand and further explore this problem, I thought it would interesting to see if it was possible for there to be a figure to have 2000 squares. To find this out, I had to to addition while messing up several times on the calculator, until I came to the conclusion that you cannot have a stair case made of exactly 200 squares. The closest number to 2000 was 2016 for figure 63. I honestly expected it to be figure 200 or something, but apparently the number didn't have to be that high to get to that. |