Saturday, July 20, 2013

Geometry: Special Right Triangles

Pg 10. Rationalize Square Roots

Before we dived into Special Right Triangles, I though we'd go over rationalizing square roots. This went much smoother this year than in the past because my students were familiar and comfortable with square roots and simplifying them. Surprisingly, most of the students took this very well and rationalized square roots like it was nothing! (Still amazed!) It has been such a struggle in the past.


Pg 11. Special Right Triangles

This has always been my toughest area to teach to my students, until this year. When it was all said and done, I confessed to my students that this is one of the hardest concepts/lessons for me to teach. Then, they blew my mind. My students told me this was the easiest thing they've done so far and loved it. Throughout the rest of the year they chose to use the special right triangles method to solve most other problems over trigonometry!!

I think that part of reason for this is the method I used to teach this concept. I pulled several resources for notes, guided practice, and independent practice. I worked all problems myself to identify a pattern to the differing levelss of questioning. After this, I taught each question type as a lesson by itself.

For 45-45-90, I focused on finding the legs first and then the hypotenuse.

For 30-60-90, I began with the questions that required simple mathematical relationships in order to solve and then we worked up to the questions involving rationalizing.

We would work out an example with extensive explanations, then complete a student let guided practice. For the independent practice, I encouraged them to work as a team and I graded them immediately. I actively monitored for independent and collaborative work and I made sure to intervene when I saw attempted cheating.

Special Right Triangles


Deriving the formulas:

Lesson examples:
Guided Practices: These were folded and tucked behind the above notes that were glued down like a pocket.
For each question, you'll notice a select number of homework problems. I assigned what my students thought was randomly selected problems. I would assign a small two to three problem practice and then the next day come back and do one to two more or the same. In the end, we completed the worksheet.

Honestly this whole journal page probably took us four or five days to complete. We looped through lesson, guided practice, and independent practice for each type of question. I felt that this was an important tool needed later for properties and measurement of two and three dimensional shapes.

Usually, the lesson using trigonometry to solve right triangles is introduced here. However, this lesson hit right before Christmas break. I looked through upcoming units and decided that I could make up the lessons and concept in Unit 8 Measurement of Two Dimensional Figures. It turned out great! Not sure if I will keep it this way next year or not. I guess it depends on timing.

This is a page from my second year journal.

Optional Pg. Right Triangle Solving Strategies

This foldable was used after the lessons on Trigonometry to summarize the strategies used to solve right triangles.