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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Geometry: Triangle Congruency and Similar Triangles

Pg 13. Congruency and Similarity Relationships

This is a half page book fold with half page extensions on the inside.

We first wrote and diagramed all triangle congruence theorems.

We then briefed over similar and non congruent.

Finished with CPCTC and two proofs.

 

 

Pg 14. Proof Patterns of Congruent Triangle Proofs

The first year I taught, I noticed that students struggled with proofs. My third year, I decided to focus on building a pattern/strategy for proving congruent triangles.

1. Label what is given.
2. List the triangle congruency theorems/postulates we could use.

3. Start with the given.

4. Prove by listing the needed information (side, then angle, then side). This began to vary as the diagrams and proofs changed.

5. Prove statement.

 

Pg 15. Proof Book

This was a collection of about eight proofs. The students would complete one to two proofs each day as warmups. Any down time we had, the proof book would be used.

 

Pg 16. What Makes Triangles Congruent

This was originally a warm up quiz that turned into an impromptu lesson and journal page. As I graded their completion immediately, I noticed that many students struggled with number eight.

IMPROMPTU LESSON: I grabbed some patty paper (awesome stuff) and we traced the two triangles from the given statement and labeled the congruent segments. Once the triangles were separated, students saw the relationships and congruency.

We folded the paper in half (my go to impromptu journal fold) and glued the patty paper to the front.

Pg 17. Similar Triangles

 

Pg 18. Similar Postulates, Theorems, and Proofs

This was a new area for me this year so it's going to be a little rusty.

The statements on the front are actually students conclusions based on our warmup discussion while prepping (passing out papers, getting journals, etc.).

 

 

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Geometry: Transformations on the Coordinate Plane

Pg 12. Transformations

 

I pulled the information from the given website and typed this assignment.

Pg 13. Translations

Pg 14. Reflections

 

Pg 15. Rotational Symmetry

Pg 16. Rotations

During my third year, I implemented a new strategy for transformations.

Materials needed:

• paper coordinate grid
• coordinate grid on a transparency
• push pin
• piece of cardboard

Plot the original image on the paper grid.

 

Layer materials:

1. cardboard
2. paper
3. transparency

Using a dry erase marker, copy/trace the original image; then using the transparency, complete a selected transformation. For translations, slide the transparency. For reflections, flip the transparency about the line of reflection. For rotations, turn the transparency in the desired direction and degree. Use the push pin to poke holes through the transparency, paper, and cardboard to mark the resulting image coordinates. Remove the transparency, and replicate the pre-image.

Pg 17. Dilations

Pg 18. Transformations Booklet

OBJECTIVE: This is another one of those 'create your own' projects. Students are given a grid and asked to plot a triangle of their own. I always use points that create a scalene triangle that does not have horizontal or vertical sides. I love watching students throughout this project because they see other's results and begin to connect patterns.

One year, I completed each section after each lesson and practice for the four transformations. The next year, we completed the entire booklet after all four lessons and practices were done. I'm not sure which had a better result. I think that the sequence depends on the level the students are performing at.

We then wrote a translation statement and completed a table using notation. I think students graphed first and then we completed the table. Graphing is easier for students because it it visual and kinesthetic.

We completed dilations after reflections and rotations.

I do remember stating at the beginning, that if you feel daring, then plot across the axes; however, if you are not sure, then keep it in a single quadrant.

 

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