**TCM Article: **

I found this article very helpful and a great resource. Throughout last week’s module, I wondered if having students begin measuring with different items effected their ability to use a ruler properly. The article discussed that this could lead to some confusion and inaccurate solutions. I think it was so neat to see how the students worked together to see that each ruler had different measurements. I think this activity proved that the students really did understand how to measure with a ruler. I would really like to complete this activity with students in my classroom to see if they can make the same connections. I think one misconception students may have when dealing with measurement would be counting the first mark as one instead of zero. I feel that this is a common mistake many people, especially children make.

**Angle Video and Case Studies: **

I was very impressed by the students in the video. Each student that explained seemed to have a very good idea of what an angle is. They also did a great job drawing and pointing out the angles on the chart. I believe that angles can sometimes be a difficult thing to understand. The case studies always show what the students are struggling with. I believe that many of the students were struggling with identifying the difference between obtuse and acute angles. The understood the definitions, but when it was time to draw the angle of find it, they had trouble. I feel as if this is probably very common throughout each grade level. What do you think Hope? I believe that most of the students had a great definition in their heads of what these angles are; however, just needed more practice actually using the angles and understanding the definitions.

**Annenberg Angles Module: **

I found section A in the Annenberg module very informative. The first part that I really enjoyed was learning that angles can be measured as a radian. I was not aware of that until this module. I just always assumed that angles were measured in degrees. Also, I really enjoyed seeing the activity of making angles out of bendy straws. I think this would be such a great and fun way to introduce angles to a class. I also liked that during the activity you cut the length of one of the sides and see that this does not affect the angle. I think this would be a great visual for the students.

I really enjoyed this module and did pretty well answering all of the questions. One question I did have a difficult time with was B7. When completing the chart by recording the angles degrees, I really wanted to measure and figure out exactly. I had a hard time just trying to use the polygons. Hope, how did you do with completing the chart? Did you have the same problem as I did or do you find it easier to measure with the polygons?

Another question I had a difficult time figuring out was question B12 part C. When I first read to find the sum of the measures of the vertex angles in the hexagon I became confused. I began to add the degrees of the triangles together to come to my answer. After checking the solution I realized that this was correct and felt better about the information. I felt just like I was back in geometry class when completing the Annenberg module. Thankfully, I remembered a lot more than I thought I did. What was some of the difficulties you had completing the Annenberg module Hope?

**TCM Article- How Wedge you Teach? **

I found reading this article very interesting. I always found it difficult to measure with a protractor and had to remember how to use one throughout reading this module. One of the biggest things I will take away from reading this article will be to have students describe angles without using the words acute, right, and obtuse. I feel that based on the students in this module, and from the case studies, students just memorize these terms without having a clear understanding of what they mean. I think it is so surprising how students can know terms, but not truly understand them. That is why I would like to take this away from the article to use in my own classroom. By having students explain without these terms, you really get an understanding of what they know and do not know.

I think there are many different misconceptions that students can have about angles. For example, one of the most common I have seen throughout the case studies and readings in this module would be recognizing how many angles are in shapes and different objects. I feel as if I have this same misconception at times. For example, in the case study, one of the students points out that there is an angle on the outside of the shape, as well as on the inside. I honestly did not even realize this until I read what the student had said. I think shows how it is important to ensure that students really know and understand the concepts, not just memorize definitions.

**Exploring Angles with Pattern Blocks: **

Green Triangle: each angle would be 60 degrees because it is an equilateral triangle. Each angle is equal and they must add up to a total of 180 degrees.

Blue Rhombus: clockwise starting from top left- 60,120, 60, 120. I honestly have no idea how we were supposed to do this using the mirror. I tried and reread the instructions and just became even more confused. I broke the rhombus into two equilateral triangles to solve the problem.

Red Trapezoid: Clockwise starting from to left- 60, 60, 120, 120. Again, I broke this shape into triangles to solve the answer. The trapezoid can be broken into three equilateral triangles.

Tan Rhombus: I am not sure how to solve this problem. I can see that it can be broken into two acute triangles. However, I am not sure how to determine what the angles would be.

Yellow Hexagon: I broke this shape into two equal trapezoids. They would be the same as the trapezoid I solved for before.

I was very confused on how to complete this activity. Hope if you can help I would extremely appreciate it!

**Further Discussion: **

My husband uses nonstandard measurements when cooking all the time. I am a very literal person and I like everything to be exact. He always argues that I take too long to cook because I do measure everything! I cannot just add things in the way he does, I need it to follow the exact recipe. I do believe that nonstandard measurement is preferred when cooking. It is so much simpler than measuring everything out and adds more flavor.

I did not do well with the chart at all. I found the polygons with 90 degree angles easy, but the obtuse and acute angles I found extremely hard to determine the measure of degree. I found it very difficult trying to measure the angle without the tools that I am used to. I also related to the children in the article How Wedge You Teach?. I also regard measurements by the benchmark terms of obtuse, acute, and right angles. I also use the 90 degree angle to determine other angles. Did you find that you did this too? I found the Exploring angles with Pattern Blocks showed me another way of measuring angles. The way I looked at each problem, I placed as many of the same angle from the polygon that I was working next to each other until they created a complete rotation. I divided 360 degrees (because a complete rotation creates a circle and a circle is 360 degrees) by however many of that polygon it took to create a complete rotation. For instance, it took 6 rhombuses (rhombi) to create a complete rotation, so that angle was 360/6 which mad e that angle 60 degrees. I’m not sure if my explanation makes sense. I hope it helps.

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Thank you for your explanation! It helps some, but I am still really confused. I just can’t make sense of how to measure something exact without measuring it with a ruler or protractor.

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Great work I am glad that I am not the only one that did not understand the Mirror thing but you did an awesome job anyway with you activity. Also I am he same as you my measurements have to be exact or i feel like it is wrong, But My Fiance can just dump thing in and be fine, I wish I could do that. I think measurement is very important though because it balances the flavor.

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That makes me feel better that others did not understand as well! I tried for so long and I just couldn’t make it make sense with the mirror! And I completely understand. I need everything to be exact and perfect or I feel as if it’s not correct!

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The activity I asked you to do didn’t use the mirror as I knew that you didn’t have one but it did ask you to use the square pattern block for a reference point. If you take three tan rhombi and lay them on top of the corner of the square, you’ll see that all three make a right angle which means that one tan rhombus (on the small point) is equivalent to 30 degrees. You can then use the square corner and the small corner of the rhombus to determine other angles.

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