Category Archives: Boehm

What are Similar Figures?:

Figures are mathematically similar when all corresponding angles are congruent, they are related by a scale factor, and they have the same or relating ratios. Corresponding angles are angles that are in the same place on each figure. A scale factor is the number that two figures are related by. For example, if there is a 2×4 rectangle (rectangle a) and a 4×8 rectangle (rectangle b) the scale factor from a to b would be two because 2×2 is 4. Figures being mathematically similar means that they can be enlarged and shrunk in order to create each other.

True or False:

Any two rectangles are similar: FALSE! All rectangles have congruent corresponding angles because they have four 90º angles. Even though they have congruent corresponding angles, not all rectangles are related by a scale factor. For example, if there was a 1×4 rectangle and 1×6 rectangle they wouldn’t be similar. They would both have 90º angles, but they wouldn’t be related by a scale factor. 1×1=1 and 4×1.5=6. 1 and 1.5 aren’t the same number. Also, they wouldn’t have the same or related side length ratios.

Any two equilateral triangles are similar: TRUE! When two triangles have congruent corresponding angles they are automatically similar. Equilateral triangles have three 60º angles. Also, equilateral triangles have the same side lengths. This means that there will always be a scale factor because all the sides have to be equal. For example, if you have a equilateral triangle with the the perimeter of 9 units (each side is 3 units) and a triangle with the perimeter of 12 units (each side is 4 units), they will automatically have a scale factor. The scale factor from the first triangle to the second one is 1 1/3 and the scale factor from the second one to the first one is 3/4. Another way you can see that these two triangles are similar is by side length ratios. 3/3 and 4/4 are the side length ratios within each triangle. Now you just make sure it is a true proportion by multiplying 3×4 and 3×4. These both equal 12. This shows that these two triangles are similar.

This is an example of good notes in my math notebook. These are good notes because I wrote everything that was on the board, and I was really neat on my paper. This page in my notebook was used for my peers that are in math seminar to learn off. Even though Michelle added some things to my notes, I think I did a really good job. Overall, my notes have been extremely successful this year so far. 

I chose this page in my notebook to be an example of bad note taking because my heading isn’t good and I didn’t write everything that was on the board down. A better heading would have been which investigation we were doing and what it was about. For example Investigation 1 Finding Similar Figures 11/1/16 is a good heading. The things I didn’t write that was on the board was the scale factors in both directions. Overall, my note taking has been good so far.

These are images of a math assignment called Stretching and Shrinking Check Up 2. In this assignment we had to view seven figures and decide which ones are similar. When looking at the figures I decided which shapes were similar by checking to make sure their corresponding angles were congruent and that they had a scale factor. For the second page of the check up we had to draw figures that were similar and not similar to the triangle and rectangle provided. For the similar figures I made sure to draw a shape that had was a scale factor and that all corresponding angles were congruent. For the un similar shapes I made sure that there wasn’t a scale factor. After doing this work sheet I realized that I need to work on using correct notation at the right times. Overall, this assignment was a success and I’m so excited for the rest of the year in math.

While doing math I have had many successes, and disasters. Since I’ve been learning and doing math for a long time I have lots of stories from different times in my life. The first thing I remember about math is seeing six dots on a piece of paper. I don’t know why I remember this because it is kind of specific. In fourth grade we had to learn all of the multiplication combinations from 1-12. Although learning the problems was difficult at first I eventually I passed the multiplication evaluation and was very proud of myself. I’ve always loved KenKen, but certain puzzles are really difficult for me so when I finally solve them I feel satisfied with my work. In the beginning of sixth grade we studied percents. I could never remember how to order the numbers in the equation. At the end of sixth grade we started algebra and didn’t understand some of it. Other than that last year was a pretty good year for me in math.

I like learning math because it helps me with my everyday life. For example learning percents helps me figure out how much to tip. I also love the feeling I get when I finally understand something that I haven’t understood before. That feeling is similar to when I solve a problem that I never thought that I could solve. Those things are great, but my all time favorite thing about math is the fact that I get to keep learning more and more about the same subjects. For example when I had a unit about geometry in second grade it was very different then when I had a unit in sixth grade. That is interesting to me because geometry is always geometry, but as I get older I learn more difficult concepts and skills.

I dislike learning math because it can be very complicated and frustrating when I don’t understand something. I also hate when I get stuck while doing a problem. Usually when I feel stuck I take a step back and really think for a minute and if I still can’t get it I will ask for help. Another thing I dislike about learning math is that in most problems there is only one right answer. This means that if you mess up one thing you will probably get it wrong.

I do consider myself a good math student because I am organized with my work and I try my best at home and at school. Something that I struggle with is participating enough in class. I make it a goal to speak at least three times per discussion. This helps me because I am a competitive person and having a goal makes my brain think it’s a contest with myself.

I usually start my homework right when I get home from school so I make sure I have enough time to get everything done. I don’t have a certain place I like to work because things change day to day. While I work/study I can’t have the room silent. This also doesn’t mean I like it loud. What I usually do is put music on at a low volume so I can hear it, but it doesn’t distract me. Overall, I’m really excited for math this year.