**Coordinate Grids: **

I explored the website *Greg’s Grid Graphs*. One of the main advantages to this website is the information it gives. The website provides great definitions and examples for how to plot points on a coordinate grid. For example, the definition of how to plot the points would be *(x,y) = x how many times you move right from the number 0; y: how many times you move up from x*. I thought this was a great definition for younger students and they had great examples for students to complete. It was a great refresher for me. The only disadvantage I personally saw was that it taught students to write the ordered pair in parentheses, but when it came time to type in the ordered pairs you could not put parentheses in the blank. I felt that this could cause confusion. Also, the description of this site was to help Greg and his family plan their visit to the museum. I thought this was going to be a very fun and interactive site and it was only plotting points on a blank graph each time and it was pretty time consuming for me, so it would take quite some time for students to complete. Hope, do you think that since this activity can be time consuming it would still be worth using in the classroom? I would like to but I’m just not sure how to incorporate it because I’m estimating it would take each student around 20 minutes to complete. Do you think this could be used on student’s tablets if they have them?

**Miras and Reflections and Kaleidoscopes Article: **

I had never worked with miras before. I loved learning how to use this! I did have some trouble at first trying to get everything to line up, but once I became more familiar with moving the mira around it became easier. I loved learning how to use this to see if shapes and letters have lines of symmetry. I think this is such a great advantage and can really help students better understand lines of symmetry. Hope, have you worked with a mira before? I don’t know that I have ever even heard of one before this module! My husband was also amazed. He completed this activity after I did!

I also really enjoyed reading the article. I think it is so amazing that you can use items such as miras to create your own kaleidoscope to teach geometry. This is definitely a project I would love to complete in my classroom someday.

**Annenberg Measurement Module: **

During the Annenberg module, I was completely puzzled by problem B1 and B2. First off, I can understand why they are using tinfoil because it will wrap around the rock, but it this a reliable measurement source? What if the tinfoil is overlapping in some areas, wouldn’t this make a difference in your answer? Also, I do not understand what how the measurement is in cm^{2}. These two questions just had me very confused. Hope, do you think that using the tinfoil to measure would give you a number that is close to being correct? Also, do you understand how the answer would be in cm^{2}? I am just very confused with this.

**Case Studies: **

I really enjoy reading the case studies. I think it is so interesting how many factors go into us teaching our students about measurement. I was very impressed with how well the kindergarten students could measure using their feet and pick out that different students get different answers because their feet are various sizes. I was also a little surprised at how the older students seemed to always forget this step. It is very important, but I think it just relates back to when our brain sees a larger number we always think of something larger. I was also somewhat surprised at how the students were having trouble remembering how to use the rulers and tape measures. I think the teacher in this case study was correct in saying that we need to have students practice measuring more often.

**Further Discussion: **

The fifth grade teacher that believes he cannot teach his students geometry is truly mistaking. I have learned throughout these modules that students can learn different concepts of geometry at any age. By allowing students to learn a little bit at a time, the students will be able to connect different ideas of geometry and have them make more sense when they get up to geometry in high school.

After these modules, I really want to focus on teaching students more varieties of shapes so they understand that, for example, triangles can look different. I believe by just understanding this, they are on the right track to begin questioning other things and discovering how different geometry skills link together.

I really liked Greg’s Grid Graphs. It was one of my favorite websites out of all that were listed. Although time is an issue, I still think that you could use this with your students, especially if you think it will help your students.

I had never heard of a mira before this module either. I had fun playing around with it and checking to see if shapes and letters had lines of symmetry. How fun that your husband was able to get in on this activity with you.

In the Annenberg activity, I think that the tinfoil is a pretty good idea for determining surface area. I had never thought of it before. While I’m not sure if it will be 100% accurate, you would have to pay close attention (like the teachers in the video) and tear off any that is overlapping, I do think it can give you a measurement that is close to being correct. Also, from what I remember (I can’t get on the Annenberg page now to look at it again…so frustrating), area is the measurement of a 2 dimensional object or shape and is measured in units squared (in this case cm2) in the same way that the volume is the measurement of the 3 dimensions an object takes up and is measured in units cubed (I think this is correct :/). I hope that helps and I didn’t confuse you more.

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I agree that Greg’s Grid Graphs had a lot of great information! It was a great review even for me. I also loved the way it explained definitions. I feel like it would be a great review for students. Maybe because it is so time consuming you could have students that need extra review work on this site and have other students complete another that does not require so much time.

Your explanation of the tin foil for surface area does make sense. I feel as if it could give you a pretty close estimate if done correctly. When I first read this I just pictured all of the students in my partnership class trying to complete this and I could see them going crazy with the tin foil and having it everywhere! I was a little unsure how you could complete this with the goal in mind, but maybe you could break the class into groups and already have a square of tin foil cut tore off. That way you could cut down on the chance of too much tin foil being wasted and the students could work together to ensure that there is no extra. I think this does sound like a great way to get them used to the idea of surface area.

Thank you for explaining the units squared and cubed for me! It makes so much more sense the way you explained it. For some reason it was just not sticking in my head and I could not understand why one would be cubed and one would be squared. I just wanted to understand why!

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