**Nets Activity and Mathematics Hiding in the Nets Article: **

I really enjoyed reading the nets article. I was able to complete the activity with little frustration. I was amazed at how well the students did with this activity. At first I was able to tell that all the cubes would have the same area, but I did not realize that would be the same for the perimeter. It did take me awhile to see this. I would really like to complete this activity with my future students. I remember completing something similar to this in school. After we discussed the difference in two-dimensional and three-dimensional shapes, we made our own three-dimensional shapes. I think that students would really benefit from discussion different issues and coming up with their own ways to make cubes. However, I think this activity would be very difficult for younger students. I believe you would have to make the discussion much simpler for students under third-grade. Do you agree with this Hope, or do you think that grades under third would still be able to come to these conclusions?

**Textbook Reading (Page 60 questions):**

- Describe van Hiele’s first three levels of geometric thought.

-Level 0- Students name shapes based on their appearance.

-Level 1- Students begin to think of shapes in classes rather than individual. For example, if students see a circle on their desk, they do not just think of it as a circle, they think of the class of circles.

-Level 2- Students begin to think about properties related to shapes. When a student thinks of a square, they realize that the angles must all be right angles.

-Activities at each of these levels would differ a great deal. Students in level 0 are just starting to learn shapes. They are understanding what a circle, triangle, square, etc. looks like and are able to name them. Activities would be focused on helping them learn the shapes and being able to recall them. Activities at level 1 would be focused on helping students understand that shapes can be classified together. The activities would have to do with having students identify the shapes and which shapes should be classified together, and which should not be. Finally, at level 2, students will be focusing on the properties of shapes. Activities will be focused on helping them realize why a square is a square and a triangle is a triangle (more than students just realizing they look similar).

-Hope, can you think of any other ways that activities would differ at these levels? This is all I could think of.

- Explore GeoGebra and explain how it can be used.

-GeoGebra was very interesting and I was amazed at how many materials were available. I believe that there are many activities for students at every van Hiele level. To incorporate this in the classroom, you could show the sight on the smartboard, or downloaded it on tablets if they are available to the class. I personally prefer using hand drawings and hands on materials when learning math. I feel as if I learn faster this way and remember longer. On advantage, however, to GeoGebra is that it is exiting and will catch student’s attention.

**Spatial Readings, Annenberg, and Building Plans: **

- Did you find any of these activities challenging? If so, what about the activity made it challenging?

-I had a very easy time with the “I took a trip on a train” activity. I was able to place the pictures in order correctly on the first try. I also had a very easy time with the “Shadows” activity. I was able to get the answers correct on the first try. However, I had a very difficult time with the “Plot plans and silhouettes activity.” I am not sure why I had such a hard time, but I was never able to solve it correctly. Hope, were you able to complete this activity? How did you do it?

- Why is it important that students become proficient at spatial visualization?

-It is very important that students become proficient at spatial visualization because it is a skill that will help them throughout the rest of their lives. I was honestly laughing so hard reading the spatial readings article. I cannot name how many times I have walked to my car from grocery shopping, only to realize I had no clue where I parked the car because I was not paying attention before I walked in. Also, my husband makes fun of me because I am horrible at directions. I would rather go a longer way to get somewhere because I know how, than try and learn a new faster way. It is so easy to use spatial visualization if we just take the time to do it. By students becoming proficient at spatial visualization, they are preparing for the future. Also, it will give them the knowledge they need to visually pick up on something to analyze it. Just as the article said Snow researched the virus and noticed that all the outbreaks were near a well and he discovered the one well was contaminated.

- At what grade level do you believe students are ready for visual/spatial activities?

-Students are ready for visual and spatial activities at the earliest of grade levels. By preparing them early and continuing to build on these activities, students will gain a great amount of knowledge that will help them throughout the rest of their lives.

- How can we help students become more proficient in this area?

-We can help students become more proficient in this area by challenging them to use their visual and spatial thinking through many different activities.

**Annenberg Tangrams Module and Creation of Manipulative: **

-I had no problem with question A1, creating the square. However, I did find it difficult to make a rectangle. Every option I came up with ended up being a square. Hope, were you able to make a rectangle or did you have a difficult time with this as well?

-I also had the same problem with question B1. When I cut the parallelogram, I could only form a square, not a rectangle. Again, Hope were you able to do this?

It’s interesting that you found the trip on a train and the shadows activity easy. I still can’t solve the train one but I found the plot plans to be relatively simple. Isn’t it interesting how our minds work? Were you able to locate any games or toys that involve geometric concepts?

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Amy,

I thought you did a great job of briefly describing van Hiele’s first three levels of geometric thought. I also could not make a rectangle with the tangrams. Even making a square was difficult for me. However, I stuck with it and was finally able to do it. For the three Annenberg activities I had the complete opposite experience than you did. I found the Silhouettes activity the least challenging and the shadow and train pictures more difficult. I too am spatially challenged. I was glad to learn that this can be improved. I would definitely like to learn how to be better at reading maps and following directions.

Thanks.

Allison Brown

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Allison, I have been playing around with the silhouettes and think I have finally gotten the hang of it, or at least I am getting better! I still have not been able to make a rectangle out of the tangrams. I am not sure why it is so hard for me, but I just cannot seem to figure it out!

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Yes, it is very interesting how minds work! I let my husband try the activities as well and he was the same as you. He could solve the plot plans very easily and could not solve the train trip activity. I was not able to find any games or toys that involve geometric concepts. I tried to research a few online and did run across a few interesting articles on how geometry is used in the making of video and computer games; however, that is all I could find.

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I originally thought that it would be much too difficult for younger students to complete the same activity mentioned in the article but I think using simplified languages as well as modifying the activity for younger students might help lead them to similar responses (probably not the same, but more similar than I initially expected) for the description of the nets. I noticed that the standard for Geometry for second grade, is for students to identify shapes (such as triangle, cubes, etc) as well as to recognize shapes having specified attributes (such as given number of equal faces). Maybe instead of having students identify how many nets could be made into a cube, the teacher could limit the activity by already having the eleven nets created and have groups of students work with them to figure out what characteristics each net has that makes it able to be made into a cube. After each group works with their net, as a class they could discuss and make a list of the characteristics that the students had determined their net had, and then test them out. She could also have a few examples of nets that don’t work to become cubes and work with the class on why these don’t work. Or do you think this would still be too difficult?

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I think that would be okay for a second grade level. You might have to help them along though. It is interesting that you brought up the standard for second grade is identifying faces on three-dimensional shapes. I used a book for my children’s literature assignment called “Mummy Math: An Adventure in Geometry.” The book is all about identifying faces on three-dimensional shapes and it is such a cute story. You should look at this book!

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Thanks…I haven’t heard of that book. I will definitely check it out.

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