Module 8
Hey Jess! I hope you had a great Spring Break!
What are the key ideas of geometry that you want your students to work through during the school year?
While I did answer this question before completing the module, I feel a little biased because I just went through these standards while planning my lesson. I know that it is very important to teach graphing coordinate points, parallel and perpendicular lines, types of shapes and triangles, and using graphs to solve word problems. I think the number one thing people think of when they hear geometry is shapes. The standards I was looking over were 5th grade standards since that is the grade I am currently working with, so I understand that this will vary with each grade. In first grade, I think it will be more essential to teach the types of shapes and their properties, such as the difference between a circle and a sphere, which shapes have how many sides, etc.
Van Hiele Levels and Polygon Properties
One thing that was super helpful was reviewing the math terms in this PowerPoint. Some of the vocabulary I was familiar and comfortable with, but other terms not as much. While the PowerPoint was very helpful, I found that the activities got more difficult as they went on. I believe that my instruction through grade school was a bit expectant, where the teachers expected us to know what was going on without thoroughly explaining, which made it very confusing and a lot harder when I moved onto college. Teaching geometry is very difficult and I can see that now, but hopefully I am able to help my students break it down in a way I never received from my teachers until the end of high school or college. When I teach it in the future, I think it is extremely important that I see what level my students are at without assuming and break things down for them as need be. While this may take more time, it will help them immensely in the long run. I would say I am at about a 4.
Jess, do you think it will be hard to balance teaching what we need to teach along with reviewing things that our students may not know, that they should know? I have no doubt that it will be worth it, because they cannot build off of a foundation that they do not have, but I am worried it will be difficult and possibly frustrating having students come into our classes who should be comfortable with certain concepts but are not. It would definitely have an impact on the progress we are able to make teaching.
Thinking about Triangles
What are the key ideas of geometry that you want your students to work through during the school year?
While I did answer this question before completing the module, I feel a little biased because I just went through these standards while planning my lesson. I know that it is very important to teach graphing coordinate points, parallel and perpendicular lines, types of shapes and triangles, and using graphs to solve word problems. I think the number one thing people think of when they hear geometry is shapes. The standards I was looking over were 5th grade standards since that is the grade I am currently working with, so I understand that this will vary with each grade. In first grade, I think it will be more essential to teach the types of shapes and their properties, such as the difference between a circle and a sphere, which shapes have how many sides, etc.
Van Hiele Levels and Polygon Properties
One thing that was super helpful was reviewing the math terms in this PowerPoint. Some of the vocabulary I was familiar and comfortable with, but other terms not as much. While the PowerPoint was very helpful, I found that the activities got more difficult as they went on. I believe that my instruction through grade school was a bit expectant, where the teachers expected us to know what was going on without thoroughly explaining, which made it very confusing and a lot harder when I moved onto college. Teaching geometry is very difficult and I can see that now, but hopefully I am able to help my students break it down in a way I never received from my teachers until the end of high school or college. When I teach it in the future, I think it is extremely important that I see what level my students are at without assuming and break things down for them as need be. While this may take more time, it will help them immensely in the long run. I would say I am at about a 4.
Jess, do you think it will be hard to balance teaching what we need to teach along with reviewing things that our students may not know, that they should know? I have no doubt that it will be worth it, because they cannot build off of a foundation that they do not have, but I am worried it will be difficult and possibly frustrating having students come into our classes who should be comfortable with certain concepts but are not. It would definitely have an impact on the progress we are able to make teaching.
Thinking about Triangles
Below are my "tri" words:
triangle
tricycle
tripod
triple
Is it possible to make a three-sided polygon that is not a triangle? No, because a triangle is a three-sided polygon by definition.
Is it possible for a triangle to have two right angles? No, a triangle can only have one right angle, but it doesn't have to have any.
How many different right triangles can be made on the geoboard? I was surprised to find that the answer was 14! I was only able to come up with 8.
How many different types of triangles can you find? I was able to find a scalene triangle, an isosceles triangle, an obtuse triangle, a right triangle, and an acute triangle. I thought that my acute triangle was equilateral, but after resuming the video, I realized that it was not.
Was this activity hard or confusing for you? I got a bit confused trying to count the triangles on the geoboard and making sure the triangles were different.
Follow Up Questions
How would you structure this lesson for students in an elementary classroom? Navigate to the Common Core website and determine where this particular lesson would fit within the different grade levels. Cite the standards in which the lesson could align. Standards should include both Content and Mathematical Practice Standards.
If I were to set up a lesson, I would begin by creating a strong foundation by introducing and reviewing the types of triangles before beginning. I had trouble remembering the names of the triangles before the video review. Even if they already know this information, this would be a good review for them. I think posing a question to lead to a discussion would help me see where each student was in this concept before starting out.
Standards:
CCSS.MATH.CONTENT.2.G.A.1
Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
What parts did you have issues with? Did you need to revisit some vocabulary words to remind yourself of their meanings? If so, which ones?
If I were to set up a lesson, I would begin by creating a strong foundation by introducing and reviewing the types of triangles before beginning. I had trouble remembering the names of the triangles before the video review. Even if they already know this information, this would be a good review for them. I think posing a question to lead to a discussion would help me see where each student was in this concept before starting out.
Standards:
CCSS.MATH.CONTENT.1.G.A.1
Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.
Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.
CCSS.MATH.CONTENT.1.G.A.2
Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.
Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.
Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
What parts did you have issues with? Did you need to revisit some vocabulary words to remind yourself of their meanings? If so, which ones?
I needed a review over the properties of a polygon. The vocabulary I had issues with were a few of the types of triangles, such as scalene and isosceles. I recognized these words but could not for the life of me remember which was which until the video explained. I think that students may get use out of a review like this, too, just to make sure they know all of the types.
Megan- Reading your first paragraph, I could not believe I forgot to write about things like parallel lines and perpendicular!! I think I have them grouped in my head with proofs so I did not specify, so I am really glad you did! I also seemed to have teachers expecting a lot from me without ever getting real break downs of the content. I think it is extremely important, as you said, to see where our students are at and go from there and not just expect them to be on a certain level because of their grade. I can definitely see how it would be difficult to balance what our students need to know/learn with what they need reviewing of. We cannot just move on to new standards or content because of a timeline of the school year, our students would never truly learn. I can definitely see getting pushed back because of trying to go help students understand before just moving on. I 100% agree that it would be completely worth it to make sure our students are caught up and conceptually aware before throwing in more difficult and new content. I think it is imperative. I also did get a little confused, especially with making sure the triangles were different and I was not counting the same one twice. I had to really look at them for a while to make sure I was doing it right! Really great post Megan I love all of the points you made!
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