Geometry: Non-Central Angles, Interior and Exterior Angles, and Secant and Tangent Relationships of Circles

Pg 5. Non-Central Angles (Need to rethink the title now that I think about it.)

This page consists of a half page fold of two pages glued together with four half page folds on each page. This entire page is pulled from the CSCOPE curriculum and tweaked just a bit.

First, we completed a page/lesson using paper folding and making conclusion based on what we know. When complete, the students would make a conclusion based on the evidence. We wrote that on the front off that page. After we completed all four pages, we went to the front and wrote three summarizing conclusions. I think it went pretty well and soundly build and understanding.

First section:

Left side:

I drew up a general diagram for the following three pages. We then completed the lesson with the same diagrams.

Right side:

Second Section:

Left side:

Right side:

 

Pg 6. Circles, Lines, and Angles

I want to find a better way to present and organize the following two pages. My students understood, but it didn't make a lasting impact.

 

 

 

Pg 7. Secant and Tangent Relationships

 

 

 

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Geometry: Properties of Circles with Paper Folding

Pg 4. Properties of Circles

We began with taking a half sheet of construction paper and glueing down a pocket. The pocket is used for the three paper folding diagrams we created for the terminology. Next we took three quarter sheets of paper and stapled them together like a magazine to create mini books. (We glued each one down after we completed it.)

I find all the properties and relationships of circles to be quite overwhelming. I decided to take these next few journal pages slow and make them as hands on as possible. I learn so much from my students that much of the written statements are conclusions students made.

With each term that could be applied to a paper fold, we used a printed circle to apply the term. There is a printed circle page for each mini book.

Mini Book 1: Circles and Angles

We used a compass to construct the circles for each term.

The original definition did not include equidistant. It used 'equal distance', but my student love their new word 'equidistant' this year.

 

 

:) Student's conclusion and addition: Concentric circles and all circles are similar! I never realized this detail. I cherish it now.

When I remember, I try to always identify and notate a term within the diagram.

 

Here's the first folded circle. We began with folding the circle in half to identify the center. Point out that the center of the circle doesn't have to be found with perpendicular diameters. It's a go to strategy for most people and can build a slight misconception.

After the center was identified, we located two points ON the circle and drew a central angle. Next, we located a third point ON the circle and drew an inscribed angle.

 

Mini Book 2: Segments and Lines of Circles

 

 

 

 

At this point, if I didn't initiate notating the term in the diagram, the students would prompt me on it.

I tried to make a fold for each term to make it more hands on. The paper folding was the favored part of this journal page.

Mini Book 3: Arcs of a Circle

 

 

 

 

 

 

 

I like this journal page. I learned a lot from my kids!!

 

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Constructions!

I LOVE CONSTRUCTIONS! I plan on teaching them as an ongoing concept.

Last summer, I was introduced to them at a workshop. I was never taught constructions when I was in high school or college. This was brand new. I went home and completed a detailed step by step and guideline for myself. I will share this. If it doesn't make since or you have another way or constructive criticism, please let me know. I did teach some this past year and the experience went really well. The students loved them and it helped build a stronger connection and understanding amoung the fundamental concepts of Geometry.

 

I begin constructions with a diagram and a few 'rules' or guidelines for myself and my students.

I couldn't tell you how I folded and glued these ten pages togther, but this is the coolest document that I think I've ever done. It is front and back and about 9 feet long.

One side is my initial attempt and additional practice. The other side is my detailed steps and constructions. I hope that these make sense, and if not, you can find a lot of great videos on youtube!

 

 

 

 

 

 

 

 

This last one is a confusing combination of my discovery and the presenter's approach. I always knew that SSA was not a postulate/theorem of triangle congruency. How? "Because you don't say ASS in class!" is what my high school teacher told me. It wasn't until my third year of teaching that I figured it out. I actually learned this through Khan Academy and of course put it to paper. The way the presenter approached it, you would never have a problem with the 'a-word' in class, but I couldn't tell you what or how she said it.

 

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