Geometry: Polygons and Angles in Regular Polygons,

I heavily relied on the CSCOPE curriculum, End of Course prep book, and online resources to guide me through this unit. This is my first year to get this far journal wise and thoroughly teach properties of two dimensional figures.

Pg 1. Unit 7 Properties of Two Dimensional Figures

When I get the whole Youtube thing figured out, I will try and share some paper-folding lessons I've learned in workshops and used in my classroom. They strongly support the unit on two dimensional figures and they are fun!!

Pg 2. Polygons

This is an unusual foldable, but I love how it organizes the concepts I'm trying to get over to my students. It's folded into fourths. The right side is folded two times into itself and the the left flap folds over top to the right. (Sorry if this explanation is terribly confusing; hopefully the pictures make more since.)

Again, there's some gray area as far as complex polygons go, and I informed my students as such. Any opinions or suggested resources, please share.

Next year, I plan to use color to compare corresponding categories.

Complex vs Simple

Concave vs Convex

Irregular vs Regular

Pg 3. Angles in Regular Polygons

I enjoy teaching this lesson because students need multiple ways to determine angles and experience deriving the formulas from building patterns.

We started with a large polygon on the front and illustrated what is considered the interior and exterior angle. Next, I asked them to make a conclusion based on what they know. They concluded that the interior and exterior angles are supplementary! We added that statement to the top. We then went to the inside and completed the gigantic table to derive the formulas. We finished by writing the important formulas and ideas on the front inside the large polygon.

Students struggled with remembering the formula for the measure of an interior angle. They found another way - determine the measure of an exterior angle (easy), and subtract the measure of exterior angle from 180 to determine the measure of the interior angle. A much longer process (to me), but I was so excited that they could figured an interior angle measure out based on concrete prior knowledge.

 

Posted with Blogsy

Geometry: Quadrilaterals

This is one of my favorite units out of geometry now, but it wasn't the first time I taught. My secret... I will reveal in a later post. ;)

Pg 1. Unit 6 Quadrilateral

Pg 2. Map of Quadrilaterals

This is my original organization and understanding of quadrilaterals. Some students like the Venn Diagram feel of this graphic organizer. This notes page does not include the trapezium and also leads to the misconception that legs of trapezoids always extend outwardly. I added that small trapezoid image to remind me about that misconception (and that trapezoids should also be seen 'upside down').

Pg 3. Properties of Quadrilaterals

This page is used to define and list the attributes of quadrilaterals. This foldable is a collaboration of my second year project from my students.

 

There has been some controversy over whether or not the complex are actual polygons or not. Some of my resources are

• http://www.mathsisfun.com/geometry/polygons.html
• http://www.math.com/school/subject3/lessons/S3U2L1GL.html
  
• http://mathworld.wolfram.com/Polygon.html
  
• http://www.mathopenref.com/polygon.html

I always try to use multiple resources along with different curriculums and textbooks. When get to a gray area, I let my students know, provide them with the references, and tell them to keep an open mind because math is up for interpretation. (And I am not always right. :))

Pg 4. Flow Chart of Quadrilaterals

This page was a result of a tutoring session with a student at Sylvan. This student wanted to look at my class journal to compare my information to the information from her teacher. After viewing my Map of Quadrilaterals page, she disagreed with my graphic organizer and drew up the following flowchart on a scratch sheet of paper. My students really like the flow and relationships that this graphic organizer gives. I used this graphic organizer to visually notate the critical attributes of each quadrilateral. As we went shape by shape, I encouraged students to reference our previous notes page.

 

During my second year of teaching, I had students write a paper analyzing the relationships of quadrilaterals or depicting the relationships through fiction. My favorite result was the student that wrote about the rhombus and the rectangle that stayed out late one night, and nine months later, there was a square.

Pg 5. Properties of Trapezoids

This is an important page as far as properties go. I didn't know how to go about this journal page, so I went with my go to half page fold. I need to find another foldable or way to help organize and emphasize each property. Suggestions?

 

 

NEW: I viewed these in an amazing geometry workshop and I can't wait to try them out next year.

Who am I? Puzzles:

Read the lines one at a time to students. One teacher suggested giving students whiteboards to draw their guesses as each line is given. If a student makes a guess, then they are required justify their guess using attributes and definitions.

 

 

 

Posted with Blogsy

Geometry: Parallel Lines, Transversals, and Special Angle Pairs

It has taken me about three years to grasp the point of this unit. The angle relationships are later used in Unit 6 Quadrilaterals and Unit 7 Properties of Two Dimensional Figures.

Pg 1.

Pg 2. Transversals and Special Angle Pairs

OR

Diagram of Lines and Transversals

 

Pg 3. Special Angle Pairs

OR

 

 

 

 

 

I have noticed in the past that students sometimes struggle with all the numbers assigned to the angles. A fellow teacher at a math and science symposium shared this star-dot labeling she has used in the past. She said that this is to be used once an exploratory is complete where a student builds an understanding of congruent and supplementary angles. This allows the students to quickly relate two symbols with location instead of dealing with the numbers.

 

Posted with Blogsy