Table of Contents

1. Overview2. Concept Cards

a. Shapesi. Kite (1)ii. Antiprism (2)

b. Anglesi. Reflex Angles (3)ii. Supplementary Angles (4)iii. Alternate Interior Angles (5)iv. Corresponding Angles (6)

c. Trianglesi. Congruence Condition of a Triangle (7)ii. 30-60-90 Triangles (8)iii. Isosceles Triangles (9)iv. Equilateral Triangles (10)v. Acute Triangles (11)vi. Scalene Triangles (12)

d. Segments and Points of a Trianglei. Altitude of Triangle (13)ii. Orthocenter of a Triangle (14)iii. Angle Bisectors (15)iv. Centroid of Triangle (16)v. Circumcenter of a triangle (17)

e. Circlesi. Circumscribed Objects (18)ii. Circumference (19)iii. Chord (20)

3. Choice Pieces of Worka. Problem Solve- The Tukatoome Tileb. Communicate- Frame Upc. Connect- Segments and Points of a Triangled. Reason- Geojacket

Overview

The pages to follow are a sampling of my work in geometry. Included are definitions that I either struggled with grasping or learned more about that I wanted to add to my memory bank. Also are samplings of pieces of work that I felt were most relevant to my growth as a geometry teacher in the areas of problem solving, communicating, connecting, and reasoning.

Each of these activities was unique and challenged me in a different way. With the Tukatoome tiles, I referred back to my problem solving strategies learned last semester. In the Frame-up activity I had to work at explaining a concept I understood well, but found challenging to verbalize. The next activity, really a sequence of activities, came to a culmination when I wrote out the concept cards for each. I struggled with understanding the differences between a centroid, circumcenter, and an orthocenter, but upon creating the concept cards, they all became clearly separate in my mind. Lastly is a selection of my ability to reason- the geo jacket activity. This activity hinged on the ability to identify patterns and continue them with larger sized boxes.

This portfolio is a great way for me to reflect on my learning, see areas that I have strengths in and areas that I am growing. I have certainly had many geometric concepts refreshed; as well as, learned concepts in a different way. I feel this portfolio is a good reflection of a variety of geometric concepts that are pertinent to teaching K-8 geometry. I hope it will be a resource for the future.

Problem Solve The Tukatoome Tile

The Tukatoome Tile activity was about finding shapes within shapes. This activity called for some systematic way of counting shapes within the larger shape. I very much enjoyed “hunting” for shapes. This activity took looking at something in different ways. I decided the best way to solve it would be to draw around each shape as I found it and tally on the side the shape that it was. After finding the correct answer, I drew each shape on graph paper to prove what I had found.

This activity helped me to take problem solving to another level. Not only did I have to solve the problem, but then I had to prove what I found and explain my answer.

Communicate Frame Up

This activity was about making triangles given certain lengths of sides. (In some combinations a triangle would not be possible because some sides would be too short.) Right off the activity seemed pretty simple, but I thought this would be a great introductory activity for students learning about triangle conditions.

I did explain this activity to another peer who was confused that not all the lengths could make a triangle. I felt confident that my peer understood when I was done explaining it to her.

Connection Segments and Points of a Triangle

I gave this activity the name above. It was actually a whole group of activities in class about folding triangles at certain points to find certain points in relation to the triangle. Each different way of folding showed a different point (centroid, circumcenter, or orthocenter).

I was having a very hard time keeping them straight. Then I made the concept cards and it all made so much more sense to me. Being able to draw triangles and label each separate kind of intersection in relation to the triangle clarified which was which. In this section, you will find the activities we did in class. The concept cards for each of the three points listed above can be found in the concept card section of this portfolio.

Reason Geo Jackets

This activity was working on experimenting with the volume of blocks. In this activity, you start with a block and find other blocks that could fit inside it. Then you keep decreasing the size of the blocks you are trying to fill it with to get more blocks in the same amount of area. As you descrease the size of the block you are putting in, you see patterns based on the prior blocks that were filling that space. During this activity we worked with table groups (4 people to a group). Some time during the activity I turned and realized that other table groups had found other patterns to work for the same blocks we were working on. At that point, I realized this too would be a great activity to do with students- to see what variety they could come up with.

As I stated above, there was a pattern in how blocks replaced prior larger blocks. Because we were working in a team, we had to establish our sequence in changing larger blocks for smaller blocks, but it was easier to identify the pattern when there were four peoples’ eyes on it. We figured out which blocks could be removed and replaced with two blocks (or three, or four) to get the next total of blocks required.