## Friday, June 28, 2013

### 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.

### Having Trouble With Protractors, Angles, and Polygons?

TOOL TO USE: Anglegs!

I have had students struggle with how to use a protractor in the past. The main issue for students was "Where do I put the center?" and "I can't line up the center and the base at the same time!".

Anglegs can be used for angles, triangles, quadrilaterals, etc.

My students call them click sticks. :)

ANGLES:

Students can lay them flat.

Students can stand them up and rotate the extended side to watch the change in degree measure.

TRIANGLES:

Use Anglegs to discover the Triangle Angle Sum. (Can also discuss that the length of the side relates to the degree of the opposite angle.

These are an excellent tool for students to use to discover and explore quadrilaterals. I, myself, made a discovery regarding trapezoids.

This is just a small look at the possibilities of Anglegs!

### 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.

## Thursday, June 27, 2013

### Geometry: Finding Distance, and Applying Coordinate Geometry to Quadrilaterals

Pg 10. Finding the Distance

This is a foldable that I wrote as a template.

Pg 11. Rectangle Analysis

FAVORITE: This is an individual project that we paced ourselves through as a class.

GEOGEBRA: We used Geogebra to graph a rectangle. This required students to be able to enter in two sets of parallel lines perpendicular to adjacent sides. Each student was required to create their own individual rectangle (no two projects were alike). This required some thinking and reworking. Once graphed, printed, and pasted, students had to justify that the shape is a rectangle. On page one, they listed the equations, intersections/ordered pairs, slopes, y-intercepts, and the parallel/perpendicular relationships.

We discussed the other critical attributes needed to justify the rectangle; they came up with midsegments and lengths of each side.

I tried my best to focus on notation, and I wish that we had written a final summary justifying the rectangle. Writing is an important component on math.

This kind of activity allows students to collaborate without copying another's work. They see multiple rectangles and help others troubleshoot.

### 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