Geometry: Midpoint Formula and Distance Formula

Pg 5. Discovering Midpoint Formula

 

Pg 6. Midpoint Formula

 

Pg 7. Midpoint Formula: Working It Backwards

 

Pg 8. Where does the Distance Formula Come From?

 

Pg 9. Distance Formula

 

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Geometry: Angle Relationships

Pg 15. Angle Addition Postulate

The bottom half is a manipulative used to physically demonstrate the Angle Addition Postulate. The yellow rectangle was glued down 'like a pocket' for angles 1 and 2.

Pg 16. Angle Relationships

 

 

I use the layered flip book quite a bit.

 

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Geometry: Angle Basics, Protractor, Compass, and Types of Angles

Pg 10. Compass: What, How, and Use

It was important to diagram (trace) and label the components of a compass. We took a few minutes and practiced constructing circles with the compass on scratch paper to discuss the essential task of a compass.

I felt that it was critical to have students write out the steps for each concept. By writing the notation and terminology, students used them when teaching and working with others. Even though arcs haven't been officially introduced, I still used the term and notation for the diagram. This was a good experience for them. They began to observe and identify arcs as they came up throughout the year.

The independent practice problems that they store behind the notes previously completed by glueing the notes down 'like a pocket'.

FAVORITE: One of my perfered methods of teaching is to introduce the concept, complete a guided example together, and finish with one independent practice problem that day. Then on a seperate day, I have them go back and do one more. When they finish four days later, students either have it down, or we complete another set every other day. This helps them retain the skill over a period of time. There are some days when my students are independently mastering a series of concepts. I enjoy those days.

 

Pg 11. I begin angles with a page called Angle Basics. This page focuses on the components of an angle. I feel that in geometry it is very important to know and continually recognize angles.

 

Pg 12. How To Measure an Angle

For this page, my students are given a regular plastic protractor an angle, and together they are to build a set of three to four step instructions on how to measure and angle.

Then we take an envelope, cut it half and use it as a pocket for their own personal protractor that I print off on a transparency.

EXCELLENT IDEA: Print reusable tools like rulers, protractors, and grids on transparencies. Templates can be found through google. I use the grids for transformations of shapes and functions, and I also discovered that they are a great tool for layering and comparing systems of equations (especially those with infinite solutions because students then understand when we say the two equations are the same line - one over the other) from a list of four to five equations.

Pg 13. Angle Construction

Each student constructed their own angle and completed a set of sentence stems.

I really like the idea of students individualizing their experience-creating diagrams, writing problems for given information, etc. This encourages students to collaborate with others about their findings and allows them to teach each other without cheating tendencies.

Next year I plan on inserting a page of Angle Construction using the compass to copy angles, bisect angles, etc.

 

Pg 14. Types of Angles

This page is a half fold consisting of five flaps.

 

BETTER IDEA:

I pulled this diagram from a SmartPal template book. Using a push brad and straw, we created a reusable took for types of angles. We used the straw to physically demonstrate each type of angle and then we defined them under the 'area' for that angle.

LESSON SEQUENCE:

1. Engaging: Read Sir Cumference and the Great Knights of Angleland to my high school students. (They actually enjoyed it!) As I read they were given post-its and asked to write down any words or phrases they thought were important to the world of Geometry. From here, I knew that they caught the cute geometry references along with the important vocabulary. They demonstrated a significant prior knowledge for angle types (which I should expect). They then posted and organized the class post-its into some form of organization. Discussion ensues.

2. Exploring and Explaining: We complete the foldable.

3. Evaluating: I would ask them questions that required them to demonstrate a certain angle measure and type using their foldable and hold up their journals when asked. (Surprise(Elaborating): Disscussion of the two angles that actually exist each time came up!)

It just so happened that I ended up with a unannounced evaluation that day. It couldn't have gone better. I will never forget that lesson.

 

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Geometry: Types of Lines and Relationships

Pg. 7. Lines, Line Segments, and Rules

Original Foldable: Pocket Book

This foldable takes a looooonnnnggg time to complete. I suggest finding another strategy. Suggestions?

QUICK CHECK FOR UNDERSTANDINGS: Book foldables may be time consuming, but they can be reusable. I had my students pull out all cards from the books, mix them up, and match them back to the correct pocket. It is easier to have them compare to a neighbor and monitor their results closely. I really like the disscussions that arise from who's right and wrong.

QUICK AND EASY: 'Types of Lines' foldable:

Line

Segment

 

Ray

Perpendicular

Haven't figured out how to work parallel into this.

This is one of my favorites. I had a student struggling with this concept at Sylvan. We created this foldable in under two minutes, had a one to two minute reteach, and she mastered the concept. She still has this in her folder and enjoys teaching other students that struggle.

This is paired with another trifold foldable in my journal.

 

Pg. 8. Relationships of Segments and Distance

 

Pg. 9. Segment Bisector (this is a trifold)

 

 

 

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