Key Ideas in Geometry:
What are the key ideas of geometry that you want your students to work through during the school year?
When I first read this question, I was not exactly sure how to answer. I began by trying to remember what geometry was. I thought back to my high school class and my geometry teacher that I loved. I had struggled to pass algebra, but passed this course with an A. I was able to understand the shapes and equations so much better in geometry for some reason. I really felt as if I could have related how geometry was related to the other math subjects, especially algebra, I would have done much better. Because of this, I would want to work on how my students view geometry throughout the year. I want my students to see how geometry fits into other areas and math and in real life.
Van Hiele Levels and Polygon Properties Article:
There are four Van Hiele levels. Level 0 is visualization. In this level we think of shapes and what they look like. Students can name the shapes by how they look, but they cannot identify properties of shapes. Level 1 is analysis. In this level students are beginning to see shape properties, but cannot see how the properties of shapes go together. Level 2 is informal deduction. Students can understand some abstract definitions in this level, but the definitions should still be kept simple. Level 3 is deduction. In this level, student start to go beyond just identifying characteristics of shapes. This is usually taught at the high school level. Level 4 is rigor. In this level, students work in different geometric or axiomatic systems. This is at a college level.
I did not do so well with the interactive activity the first time; however, I completed it again and did much better. I think it just took me awhile to figure out all of the shapes. Hope, how did you do with the activity? I really enjoyed it and think it would be a great way to introduce geometry to many different grade levels. I would like to use this with my future students. I would especially like to use the activity with younger students to help them better learn shapes. Hope, how would you like to use this activity in your classroom?
Annenberg Triangle and Quadrilaterals Module:
I was incorrect in problem A5 from Annenberg, because I thought we were choosing one incorrect answer (I read through the directions too quickly…again). At first I could easily identify that it is not possible to have a right triangle that is also obtuse (choice D). An obtuse triangle is a triangle that has an angle larger than 90 degrees so that would not work. I was thrown off a little bit when choice C said an equilateral right triangle. At first my brain thought it made sense and was correct, but upon drawing it out I could easily see how this was not correct. Hope, did you have the same issues for this problem or were you able to know fairly quickly which choices would work or not?
I really enjoyed watching the video clip on building the towers out of toothpicks and marshmallows. It was a great example to show how strong triangles were. The groups that used triangles in their designs instead of squares had much taller and sturdier structures. I would love to use this activity with younger students. I think it would a great way for them to integrate shapes and start noticing shapes that are used in structures in the world around them.
Thinking about Triangles:
I think that this lesson is great and with a few modifications would be perfect for elementary students. I believe that for younger students I would have the triangles already cut out for them. Then allow them to see how they fit on the geoboard and have them draw conclusions from there. Hope what do you think? Do you have any other ideas that would make the activity a little simpler?
I did remember most of the vocabulary. For instance, I knew a right triangle, acute triangle, etc.; however, I did not really remember how to explain them. Hearing the definitions in this power point helped a lot.