Figures are mathematically similar because their corresponding angles are congruent and they must share a scale factor. For triangles, if their corresponding angles are congruent, it means they automatically share a scale factor. This is because the angles decide the scale factor of a triangle. In order for corresponding angles to be congruent, it means that if two figures were to overlap, all of the angles would line up with each other. This means that for triangles, you only need to make sure their corresponding angles are congruent, because if their corresponding angles are congruent, they automatically share a scale factor. If triangles are the same type of triangle and share a scale factor, it means they are similar. In order for two figures to share a scale factor, you must be able to multiply all of the sides by one number in order to get the side lengths of the other shape. For example, a triangle with side lengths of 2 4 and 6 would be similar to a triangle with side lengths of 1 2 and 3 because you multiply 2 4 and 6 by .5 to get the side lengths of the other triangle.You can also use ratios. You can use ratios because if they share a cross ratio, it means they are similar. For rectangles it is very different. This is because every rectangle’s corresponding angles are congruent, because rectangles have four 90 degree angles, but not all rectangles are similar. This means that for rectangles, scale factor is very important. For rectangles, it is basically the opposite of triangles. If the rectangles share a scale factor, then they are similar.

Any two rectangles are similar:

False. Every rectangle’s corresponding angles are congruent, but there are many rectangles that don’t share a scale factor. This means that not every rectangle is similar.

Any two equilateral triangles are similar:

True. This is because every single equilateral triangle has all of the sides the same length. This also means that all of their corresponding angles are congruent. Since all of their sides are the same length, it means that every single equilateral triangle is similar.

 

My notes on the left are very good. I think they’re very good because they’re very neat and organized. I also separated the different notes from each other, so that when you’re reading them, you don’t get them mixed up. I also put a lot of space in between everything, and it makes it a lot easier to read. I labeled everything, and made it legible. Also, the heading is very easy to read, and very clear.

My notes on the right aren’t my best. First of all, I use abbreviations for enlarged and regular, which makes it very hard to understand. I also think it doesn’t look very pretty, and it looks very messy. They are not well separated, and are very hard to read. The heading is confusing, and blends in with the rest of the notes. It is just overall a very bad note, that I will definitely use to improve my future notes to make them as good as they can be.

In Math, we are learning about geometry. One thing we are mainly learning about is how to find out if to figures are ~ (similar), or not. We’ve discovered two different things two figures need to have in common in order for them to be similar. First, the corresponding angles must be congruent. In mathematical symbols, it would be the corresponding ‘s (angles) need to be ≅ (congruent). What this means is that each figure has an  that corresponds to another . If each  that corresponds to the other , then all of the corresponding ‘s are ≅. The next factor that decides weather or no a figure ~ another figure is the scale factor. The scale factor is one number that corresponding side lengths can be multiplied by to give corresponding side lengths to another figure. For example, a rectangle with a base of 5 and a height of 10 ~ a rectangle with a base of 10 and a height of 20, because the scale factor is 2 or 1/2. These two things you need to check are the ways you figure out weather or not a figure ~ another figure. Here is my worksheet. On the first page, we needed to identify which figures ~ other figures. On the second page, we needed to draw a rectangle that was ~ and NOT ~ the rectangle that was on the top of the page. Then we needed to do the same for triangles. Here is the check up:

 

In math we made math profiles about ourselves, and our relationships with math. I really liked the project because it helped me to think about how many different math experiences I have had. Here is my math profile:

I’ve always had a great relationship with math. When I was in pre-school, my parents would always read me books about math and counting. 365 Penguins, 10, 8 Apples on Top and a lot of others. To me, those books were always boring. I thought that if counting penguins was all math was, then I wanted no part of it. In first grade, when we learned math,  it was usually counting which, as I said before, I was not the biggest fan of. Slowly, math got more and more interesting and not only about counting anymore. While the other kids were counting on their fingers to figure out the answer, I used my hatred of counting to my advantage, and I tried not to count on my fingers and it’s a good thing because the very next week the kids were told they couldn’t count on their fingers. Now, there was multiplication, division, addition, subtraction, fractions and so much more! Soon, I was excited to go to math. By middle school, math was my favorite subject. And I liked it so much I asked for “extra math homework”. I love math and can’t wait to learn more of it, and find more reasons why it’s the best thing ever.

 

One thing I love about learning math is that I love how there’s not just one way to do it. You can use different strategies to figure out the answer, but there is always one way to do it that’s quicker than the others. I also love the problems that aren’t as big, but there are a lot of them. For example, multiplication, division, etc. I like doing those kinds of problems because once you get the hang of it, you don’t even need to think about it, you can just do it. Not to say I don’t like big problems. I really like big problems. I like how different they are from the small ones. With the big problems, you don’t even know how much or which of the small problems you need to do to get the answer, and that’s what you’re trying to figure out. These require a lot of thought, which is what I like about them. I like everything about math, but you would be here all day if I wrote down every single thing I like about math.

 

As I said before, I like everything about math, which makes talking about my dislikes particularly hard. The reason why I don’t have any dislikes is because whenever I get frustrated with math, or go completely off track with a really big problem, it just adds on to the VERY long list of reasons why I do like math. I like how you can get frustrated easily because that makes it very hard to become a great mathematician, because you need to have a very strong will power. Whenever you look at a mathematician who is excellent at math, you can tell that they got past all of the frustrating things and pursued their passion for math.

 

I would say I’m a good math student. I love math, and I find that passion is very important when you’re doing anything. For one, I really love to participate. I love to share my ideas and talk in group discussions with the class. I find that it helps everyone to understand the concept we’re learning much better. Also, when we have work time, I feel that I work very efficiently and in an organized fashion. I think I’m a really good group worker, but something I want to improve on is giving other people more opportunities to share their ideas when I’m working in a group.

 

When I’m doing homework, I really like to try and get as much done as possible the first night it’s assigned. That way the next day, when I get more homework, it doesn’t start to pile on and get really stressful. I have a lot of afterschool activities going on, so right when I’m home and finished with those activities, the first thing I do is get my homework done. I love math and am so excited to learn more of it this year.