The Building Shapes lesson was where we were given a piece of rope which was tied so it created a circle, we were given the task of creating different shapes accurately and being able to describe them to a sceptic. Some shapes seemed simple, for example a square. You would think that you could do a pretty good job of eyeballing and exact square, but with this we had to be as exact as we could. Our solution was to fold the rope in half evenly twice and each grabbing a corner, this way we had equal amounts and we measured the 90 degree angles with a piece of paper.
2: Number Visual Pennies
The Number Visual Pennies problem was where we were asked to stack 100 pennies evenly into a certain amount of stacks. As simple as this seems, some of the amounts of piles were not divisible by 100 and therefore could not be distributed evenly throughout all of the different amounts of piles. We had a bit of trouble with this one, but eventually came to the conclusion of going up a number for each amount of stacks and distributing them evenly from there.
3: One-Cut Geometry
For One-Cut Geometry we used patty paper to cut out a triangle with only one cut, although we were allowed to fold as many times as needed, the triangle we were trying to cut out did not have even sides so it was difficult to fold it exactly right. Although we could’ve found some complicated folding pattern to get it right, some students decided that they would find the least amount of folds that would work. One of our classmates figured it out using only three folds.
4: Square Mania
In Square Mania we were given a sheet of squares saying that there were more squares than were actually there. At first we were confused, how could there be more squares there than we can presently see? Well, after some brainstorming we came to the conclusion that not only were the single squares counted, but the bigger ones were too, for example four tiny squares equals one bigger square. Some overlapped, but in the end there were exactly the amount of squares as previously stated.
Videos:
1) Why did we spend a week working on these problems?
We spent the first week working on these problems because they were good refresher problems to help us get back on track from summer. Their purpose was to refresh our memories and to help us to improve our group work skills for tenth grade. These problems were not too challenging, but not too easy either. They were perfect for us because as crazy as the first week is, it’s always best not to rush into things but to refresh our memories first, maybe by learning something new as well.
2) What was the purpose of the videos and what did they mean to you?
Video #1: Strategies for Learning Math
I feel that I really connected to this video because I myself am more of a visual learner and it helped me to see how others learn as well. I connected to the part where they talked about drawing it out because I think that that’s one of the things that I do in my notes a lot because it helps me visualize the problem instead of keeping it all in my head.
Video #2: Speed Is Not Important
I connected to this because whenever I used to do a math test or everyone would be working on an assignment I always thought that because I was taking longer to get it that maybe I was less intelligent. I now know that although it may take me a little longer than others to get a problem, that doesn’t mean I’ll never come to a solution.
Video #3: Brains Grow and Change
I have always not been the best in math, maybe average, but I used to think that some people were just better at it than me. In order to be better you have to practice and have a growth mindset in order to improve. Without a growth mindset you’ll stay at the same level because you didn’t think that you could do it.
Video #4: Believe In Yourself
This goes along the same lines of having a growth mindset in my opinion. In order to grow you have to believe that you can, if you don’t think that you can grow mathematically or in anything, then your brain won’t grow. It allows you to think more and be more determined to find an answer because you believe that you can. Not having a growth mindset can be discouraging and can often lead to giving up.
Video #5: Mistakes Are Powerful
In this video we learn about how when you make a mistake, you learn from it no matter the situation. In math especially, it is quite common to make mistakes. When you make a mistake it learns from it and adapts from there, giving you new ideas to solve the problem or to see it from a different angle.
One-Cut Geometry:
For the One-Cut Geometry assignment the task was to draw a scalene triangle in the middle of the square sheet of paper. We were then to fold the paper in any ways we could in order to cut it out perfectly with only one cut. This proved to be harder than it seemed because the sides are not even. Because the sides are not even on a scalene triangle, if you fold even folds you would end up cutting out a right triangle instead, which is how most of my previous attempts had turned out as:
For some, I had decided to fold the triangle into itself in hopes that the lines would line up equally, however since the scalene triangle is not equal, there was extra paper which resulted in some pretty funky, but interesting designs. I overcame this by working with my group and collectively sharing ideas as to how to fold it, when we all shared our ideas we helped each other get closer and closer to solving it. I chose this problem because I think that it’s one of the ones I was most invested in, I worked well with my group and we all came up with some pretty good ideas. Although we didn’t get the answer ourselves in the end, I think that if we had a little more time, we would’ve figured it out. It was frustrating at times, trying to get the folds right, but all in all it was nice having others’ input. One habit of a mathematician that I used was start small because at first I was just folding in any way I saw fit instead of using any kind of strategy. As I worked more with my group and attempted it over and over, the closer I got. Starting small really helps because it gives you the chance to learn from your mistakes and to slowly improve.
Folding instructions for a one-cut scalene triangle:
One:
Draw a scalene triangle onto a square sheet of paper.
Two:
Fold the top point onto the base line while creating a crease through the right base point.
Three:
Next, fold the top point down onto the base line while making a diagonal crease through the left bottom point.
Four:
Then, fold the right side down while making sure the all of the lines are lined up flat on the base line.
Experiment:
For an experiment, I tried to fold a different shape other than the one we folded in class, the shape I chose was a equilateral triangle. This basically follows the same idea of the scalene, except less folds are needed because it is a more simple, equal shape with equal angles and line lengths. I chose this as an example to show how it can be simplified if the shape has equal angles, if the shape’s angles are not all equal or the lines are uneven, that makes folding difficult.
Step One:
Draw an equilateral triangle on a square piece of paper.
Step Two:
Fold point to baseline with crease going through right point.
Step Three:
Fold point to baseline with crease going through left point.
Step Four:
Fold down right fold and crease down left fold so that all lines are matched up on the baseline.
Reflection:
In conclusion, I think that this was a pretty good way to start the year and I’m glad overall that we did some warm up problems beforehand so that we wouldn’t be too stressed throughout the beginning of the year. Going into a new grade, especially in high school, is challenging because with every new year the workload grows and that can sometimes be super stressful. For a semi-organized person like myself it can be a little hard to keep up with all the due dates. I’m just glad that we didn’t get a ton of difficult assignments at the beginning of the year without a chance to refresh our memories. I think that what I’ve learned this first week will definitely help me in the coming weeks as I know that some of these problems will relate to future assignments and it’s always nice to be prepared!