Key Ideas in Geometry
What are the key ideas of geometry that you want your students to work through during the school year?I would think that the key ideas that the students should work through are knowing the shapes, finding the perimeter and area, knowing the different types of angles and how to identify them. But it would depend on the grade level I am teaching, I am still drawn too kindergarten, so I think geometry for them would be knowing shapes for the most part.
Van Hiele Levels and Polygon Properties
For the PowerPoint activity I did well, I was prepared and had the shapes printed and cut out. I already knew the many of the terms used and was successful in removing the specific groupings that needed to be removed. I was able to get 3/3 on the activity. How about you Aubrey, was this a hard task?
What I didn't know was the classification of levels using the Van Hiele levels, I have never heard of him before this lesson. I think I would rate myself at a Level 2 or 3, I get confused with the reflections and rotations of shapes about creating a certain number of triangles, but that was from the Triangle activity.
Understanding the levels are essential so that we as teachers are not over teaching before our students can relate what they already know. It also helps having school-aged children at home.
Thinking about Triangles
I wasn't able to come up with many words with "tri", I have tripod and tricycle. I feel silly not knowing more, but the words were just not coming to me last night.
Is it possible to make a three-sided polygon that is not a triangle?
No, because the shape must have three lines that intersect the only possible polygon with three-sides is a triangle. Does this reasoning make sense to you?
Is it possible for a triangle to have two right angles?
No, the triangle is three-sided with three-angles, the total size of an angle is 180 degrees. If two angles were inside the triangle that would equal 180 degrees and would not create a triangle. How about this one?
How many different right triangles can be made on the geoboard?
I wasn't sure on this one, I created 11 or 12 myself and then got lost. So when I went forward on the PowerPoint and Dr. Higgins said 14, I decided to look them up. However, when I looked it up they said 17 could be made. I am interested in finding the 14 hat were mentioned to know where the others came from on the website I found. I decided to add the picture I found with the 17 right angles. Dr. Higgins and Aubrey, can you see any mistakes on this picture? Did you get 14 Aubrey? Dr. Higgins, will you show use the 14 that we should have gotten?
How many different types of triangles can you find?
I was able to create 5 types: right angle, obtuse, acute, isosceles, and the scalene. My children might have helped me a little :) The scalene was the difficult one for me, I created it but couldn't remember what it was called. I almost put equilateral, but I had my ruler and measured it, what about you Aubrey, did you find the different types?
Follow-Up
How would you structure this lesson for students in an elementary classroom?
I think one thing I would do is have partners, so that it is a little easier to keep track of the different triangles being made, it was difficult to come up with the right angles myself and ensure that I didn't just rotate one I already had. I'm still not sure I didn't, LOL. I think that having the geoboards for each students is great too, and maybe more different colored rubber bands, that way many bands can be on the board at once. What age level would you introduce this activity to Aubrey?
Common Core:
Kindergarten:
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).
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.K.G.B.5
Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.
Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.
First Grade:
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.
Second Grade:
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.1 Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.1 Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
Third Grade:
CCSS.MATH.CONTENT.3.G.A.1
Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
Fourth Grade:
CCSS.MATH.CONTENT.4.G.A.1
Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
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.
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.
Fifth Grade:
CCSS.MATH.CONTENT.5.G.B.4
Classify two-dimensional figures in a hierarchy based on properties.
Classify two-dimensional figures in a hierarchy based on properties.
What parts did you have issues with?
I had to remember the different types of triangles at first, I knew the right, obtuse, acute, equilateral, and isosceles, but I had to read about the scalene. After the review I knew all the shapes and could make them.
Hey Tracie! Good Morning. On the activity with the shapes I got 1/3 correct, but I think that was due to the fact that I was not as familiar with the vocabulary. I felt proud of myself for getting the first one that I thought the next two should be easy, but it got harder. I should have had my kids help me too, but I ended up going to the library to work alone.
ReplyDeleteWith the thinking about triangles questions I knew the answers to the questions but I wasn't sure how to explain why I knew that was the right answer. Your reasoning made sense to me. When I made the triangles on the geoboard I must of misunderstood what she meant, because I thought she meant using the whole board how many could you make and I only got six. Now I can see it was supposed to be different. When I did the six triangles I made on the geoboard I was able to make right and obtuse triangles.
As far as introducing this to an age group of students. I would love to do this with third graders and see if they are able to get all three correct.
Since I didn't take the math class last semester, I feel like I am trying to play catch up this semester in this class.
Hi Aubrey,
DeleteI did well on the activity, I would have liked to rate myself higher on the levels, but I am not sure I am that proficent. As I mentioned in my blog the only triangle I couldn't remember was the scalene.
I was hoping that we would have one of those puzzles to put together that are geographicial shapes, do you know what I mean? I like shapes and I like making shapes on the geoboard, but it is difficult to create the different angles without repeating.
I am glad that my resasonings made sense, I wasn't sure if I was articulating exactly what I was trying to say.
Your doing well Aubrey, as long as you go step by step with the checklist you'll be successfull in the blog postings :)