Module Eight

Key Ideas in Geometry

What are the key ideas of geometry that you want your students to work through during the school year?

The key ideas of geometry I want my students to work through during the school is to better understand shapes and their attributes.Having my students be able to name different shapes just by knowing their sides or angles is a huge start. In my field experience class they just started working on this and some kids are having trouble, I never thought as just being able to name different shapes would be that hard for students but this has now proved me wrong. I feel as those for the other key ideas that I would want my students to learn would have to depend on what grade I end up teaching.

Are there key ideas that you think are more important than others?

Van Hiele Levels and Polygon Properties

I think that the power point was very informative. I never thought about students being at different levels to understand a concept. I just thought about different grade levels and most students in that grade level would understand that concept of that level, with a select few who don't understand it. In the activity I did pretty well figuring out the different shapes. I just had refreshers on these concepts in the class I am placed in. I think even if I didn't have a refresher I would of been able to do it. I can understand basic geometry very well, it was the geometry that we started to talk about in high school that I started to struggle with. It was really the only math class in high school I didn't do that well in. I think with geometry we as teachers need to make sure that our students understand the most basic concepts before moving on to the next. Just like all other math and most subjects you have to build the learning on the basics because if you don't do that you wont be able to understand the highest level. In the class I am in the teacher gave her students a worksheet that had riddles describing different shapes and as partners students had to figure out what the shapes use just by reading about their attributes. Once students understand 2-D shapes than you can move onto 3-D shapes but not before that, it will just confuse the students. 

Do you think geometry is an easy concept to understand?

Thinking about Triangles

Tri words:

Triangle, Tripod, Tricycle, Triathlon

Is it possible to make a three-sided polygon that is not a triangle?

No, a polygon that had 3 sides is a triangle.

Is it possible for a triangle to have two right angles?

No, a triangle needs to have obtuse or acute angles. A triangle can have 1 right angle but no more than that. 

How many different right triangle can be made on the geoboard?

I was only able to get 9, which I know it wrong because the in the power point it says there are 14. If I were to have my students do this I would allow them to do it in partners because I had a difficult time so I can only expect they will to. Working in pairs will allow them to use 2 heads instead of 1 and many times that brings more and new ideas.

Were you able to find more? If so how?

How many different types of triangles can you find?

I found 6 different types of triangles, The different types of triangles I found were the different types I remember talking about in school which were: Right, obtuse, acute, Equilateral, Isosceles, scalene

Did you find more? Was it easy for you to find the different types of triangles 

Follow-Up Questions

How would you structure this lesson for students in an elementary classroom?

I would start the lesson by talking about triangles and the different types of classifications. After talking about the characteristics of the different triangles I would ask students to come up to the board 1 at a time to draw the different types of triangles. We would talk about the different types of angles that triangles can have and what those types of angles mean for the triangle name. I would also if available let the students use geoboards, I think it would help them to better understand the different types. If not available I would use the geoboard paper like we used for the activity

Standards:

Mathematical practice standards:

CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.

CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively.

CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.

Content Standards

• CCSS.MATH.CONTENT.K.G.A.2: Correctly name shapes regardless of their orientations or overall size.
• CCSS.MATH.CONTENT.K.G.B.4: Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/”corners”) and other attributes (e.g., having sides of equal length).

• 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.
• 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.
• 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.
• CCSS.MATH.CONTENT.4.G.A.2: Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

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?

As far as the vocabulary I didn't have issues my issue was when using the geoboard paper I had a hard time coming up with different types of triangles that I hadn't already used. 

Do you think students would have trouble with an activity like this? What grade level do you think this activity would best fit?