Annenberg Symmetry Module:
In this module, I found Problem A2 very interesting.

I knew that each shape had many lines of symmetry, but I did not realize that there were as many lines of symmetry as there were sides on the shape. Hope, did you realize this to be true? I had never thought of it before reading the solution to this problem.
I also had a few problem with question B1…

After using the interactive board I could see the angle of rotation, but I would not have been able to see without that. Hope, were you able to solve this question without the interactive board? If so how?
Pentomino Activities:
I worked along with the activities from the power point. When finding the perimeter of the shapes, I was very confused. I could not figure out how the perimeter was twelve. Finally, I realized that you had to count the sides of the shape. Once I figured out that part of the activity, it was easy. I think this would be a fun activity to incorporate with students. I would show you how students are thinking at the time and if they have a grasp on perimeter.
I also thought drawing a title floor with the pentomino shapes was a fun activity. I had a pretty easy time fitting the shape I picked together. I think this would be a very fun activity for younger students to complete. Below is a picture of where I placed the pentomino shapes together.
(Sorry the picture turned out light)
Hope, what shape did you use to complete this activity? Did you have any difficulties with this or was it fairly simple for you as well?
I became very frustrated with the activity on the online website of trying to fit the pentominoes together to make a rectangle. I could not figure it out once! Not once was I able to make a rectangle! I feel like it should not be this difficult! Hope, were you able to make a rectangle? How did you do it if you did? Did you find it as difficult as I did? I am still trying to figure out this activity!
Pentomino Narrow Passage:
Below is a picture of my passage. I was only able to create a path with 13 spaces. I did find this activity much easier. Was this activity easier or harder for you than the others Hope?
Tessellating Tshirts Article:
This article was very interesting to me. I think I got the most out of this article when it discuessed how we cannot afford to wait until high school to teach students about geometry. The more this semester goes on, I find this more to be true. I have always had difficulties with math, and honestly do not remember learning many of the things discussed until high school. I think that we need to begin teaching students these conscepts, especially geometry, while they are in elementary school to help them grow further.
Tangram Discoveries:
Again, I had a really hard time trying to figure out this activity. Hope, how did you go about this? Do you have any advice to understand this better?
Ordering Rectangles Activity:
 I believe that rectangle C has the largest perimeter because the sides are so much longer than any other rectangle. I think rectangle B has the smallest perimeter just by looking. It appears to be smaller just based on my eye. I believe the order will go from smallest to largest rectangle B, rectangle A, rectangle D, rectangle G, rectangle E, rectangle F, and rectangle C.
 I believe it was harder to guess which rectangle had the smallest and largest area. I do believe just by looking at the rectangles, rectangle C has the smallest area and rectangle G has the largest area. Smallest to largest, I believe the area will be C, F, B, D, A, E, and G.
 The actual order, from smallest to largest for the perimeter was D, E, B, A, G, C, F. I did not do as horrible as I believed I had done and after measuring I can see now the correct order of the shapes.
 The actual order, from smallest to largest, for the area was C, D, E, B, F, A, and G. I also did not do as bad I as had believed estimating the area of these shapes. It is also a lot easier to see the actual order now looking at the shapes after measuring.
 I did much better at this activity than the previous activities in the module. It was very refreshing after doing so badly on the other activities. I am still somewhat puzzled at why I could see the area and perimeter but not enough to make the shapes in to previous activities.
Further Discussion:
This is actually a piece of artwork I have hanging in my house. I bought this when I was volunteering in Paraguay a few years ago. There were numerous artworks made like this. They used string and sewed these designs. All the designs used shapes and symmetry. I even had some earrings at one time from there that looked very similar but I cannot seem to find them now.
It sounds like we have a similar history of learning geometry. I remember getting to geometry 12 in high school and feeling quite useless as I barely could identify shapes nevertheless write proofs. We need to do more than help children to identify shapes in the early grades, we need them to be able to talk about the properties and also tie everything to measurement concepts.
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Yes, I definitely agree. I actually did very well in my geometry class in high school; however, I did not really understand the concepts. I knew this is what we are doing this week and then we moved to something different the next. Honestly, I barely remember anything from high school math now. I believe teaching more skills while in the elementary grades the better students will do in the long run.
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I was so excited when I actually came up with the same rule for A2. I experienced lots of frustration with the pentominoes during this module too. I feel so far behind when it comes to geometry.I don’t think there were more than four shapes when I was in elementary school (square, rectangle, circle, and triangle) lol…back in the stone age! These are the only ones I really remember learning about in great detail. I absolutely hated Geometry in high school. I just didn’t get it. Now, I see my nephew struggling in it. I definitely think that geometric concepts need to be taught and discussed in the early grades.
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