**Quick Images Video:**

I thought this video was very interesting and a great way to help students remember and draw shapes. I was not surprised when one student told the teacher the shape looked like the moon because that is the first thing I thought of when I saw the shape. It was very interesting to see how the students recognized the shape by things around them.

**Case Studies: **

I was very surprised at reading the case studies. I honestly do not remember learning about different triangles and shapes in school. I feel as if it was something I always knew and never really had a problem with. I see now how confusing learning shapes can be for students, especially triangles because there are so many different kinds. I was very impressed by Evan’s response in case study 19 that even if he is turned upside down or inside out, he is still a triangle. I think that really helped students make the connection that shapes can look different, but still be the same shape. I thought it was funny how Susannah in the same case study said there should be a rule that you might have to turn around a shape to see what it is. I think this showed that she was beginning to realize the same thing Evan had before. I believe that I will try and introduce more shapes, especially triangles, to students when I begin teaching (especially if I end up in a younger grade). I believe that this will really help students once they get older and focus more on geometry. In case study 18 many students kept saying the shapes were not triangles because they did not look like triangles they had ever seen before.

Hope, what ways do you think would be best to help students with these problems? Do you think introducing a variety of triangles to younger students would cut back on some confusion when they become older, or just confuse them more now?

**Annenberg- Polygons: **

In questions A2-A4 I was amazed at home many different shapes you could make. I did not realize all the different shapes. I think I just am in shock at how many there are because I have never really thought about it before. I realized that polygons were any shape with 4 sides, but I did not realize how many different polygons there were. Hope, how many different shapes were you able to come up with? Were you as shocked as I was at the many different shapes you could make?

Hope, were you able to fill out the chart for problem C6? I know that triangles make 180 degrees; however, I cannot figure out how to find the degrees of shapes with another number of sides. It seems to just have completely slipped my mind.

**Further Discussion: **

Geometry is everywhere around us in the world. We can see it in our homes, furniture, buildings, etc. I think you can see this used the most when looking at the structure of how things are made. We can see many triangles and many squares. It is important to understand how these shapes work to make sure we use them correctly in the world around us.

I thought Evan’s response was so clever! I think I will introduce a variety of triangles to my students. I definitely think this will reduce confusion as they get older. For me, once I get an image in my head of what something is, it is difficult for me to change those thoughts, and I think the same applies to young students. Just like with Susannah, she had a picture in her head of what a triangle looked like, and she struggled to accept anything but that image she had pictured. I believe that introducing different triangles earlier will help eliminate some of the occurrences of this happening in the future for my students.

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I definitely agree that once you have a picture or idea of something in your head it is hard to change it. I really do believe that by allowing students to see different triangles earlier, it will help them in later grades. I also thought Evan’s response was clever! He hit the nail right on the head. I think it was a great way of explaining things and it was at a level all of the students could understand.

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I like the thoughts of Dolores in case 18. It was very interesting to read the students’ responses. It seems that students are very distracted by the orientation of the shapes, one way to point out that orientation has no bearing on what a shape is could be to put 2 of each shape on a projector (especially the triangle, that seemed to be the most difficult). She could place one of each in the same way she previously did,upside down and sideways (as the students said) then place the other (exact same shape) right side up and then have students write about the shapes. I wonder if they would be aware that the triangles are the same and the rectangles are the same, or if they would correctly name one triangle but not the other. Then using the pictures on the projector, she could superimpose the upside down triangle on the “rights side up” one showing students they are the same and do the same with the rectangle. Do you think this would be beneficial for students? I would love to try this with my class, what do you think?

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