Wednesday, May 28, 2008
12.3 Quiz
I have a quiz covering 12.1 - 12.3. At first I worried that the quiz would be too long, but after my first hour I am much more confident that students will be able to finish the quiz in the time provided.
12.3 Law of Sines
This lesson was split over two days.
On a Friday, when most of the students were gone on a field trip, I went over the derivation of the SAS Triangle Area Conjecture, and the Law of Sines. After the derivation I gave students time to catch up on past assignments.
Many students were able to follow the proof, and I didn't expect all to understand the proof fully.
On the second day I quickly reviewed the Law of Sines and SAS-Area-Conjecture. After a couple examples students began working on homework in class.
On a Friday, when most of the students were gone on a field trip, I went over the derivation of the SAS Triangle Area Conjecture, and the Law of Sines. After the derivation I gave students time to catch up on past assignments.
Many students were able to follow the proof, and I didn't expect all to understand the proof fully.
On the second day I quickly reviewed the Law of Sines and SAS-Area-Conjecture. After a couple examples students began working on homework in class.
12.2 Problem Solving with Right Angles
This is mainly a word problem chapter. We spent one day and went over a couple examples in class. Students had time in class to work on homework and ask for help.
12.1 Trigonometric Ratios
This lesson was split into two parts.
Day 1: We looked at the basic trig functions: sin, cos, and tan.
To introduce the tangent we looked at the ratios between the legs of a right triangle that I drew. The drawing was by hand so the ratios weren't perfect, but they were close to a constant. Then I told them that this ratio is important so it has a special name "tan", I let students guess what "tan" was short for and most classes had a student who would guess "tangent".
Then we went over the names for other ratios, i.e. the sine and cosine.
Our angles are in degrees so we need to check our calculators are in degree mode, then we went over how to use the sin, cos, and tan buttons on the calculator.
Day 2: The arcsine, arccosine, and arctan.
I mainly refer to the arc-functions as "inverse sine/cosine/tangent". This is easier, and worked with my explanation of how the inverse functions undo the sine/cosine/tangent.
We went over how to enter these in the calculator and began working on some problems.
Day 1: We looked at the basic trig functions: sin, cos, and tan.
To introduce the tangent we looked at the ratios between the legs of a right triangle that I drew. The drawing was by hand so the ratios weren't perfect, but they were close to a constant. Then I told them that this ratio is important so it has a special name "tan", I let students guess what "tan" was short for and most classes had a student who would guess "tangent".
Then we went over the names for other ratios, i.e. the sine and cosine.
Our angles are in degrees so we need to check our calculators are in degree mode, then we went over how to use the sin, cos, and tan buttons on the calculator.
Day 2: The arcsine, arccosine, and arctan.
I mainly refer to the arc-functions as "inverse sine/cosine/tangent". This is easier, and worked with my explanation of how the inverse functions undo the sine/cosine/tangent.
We went over how to enter these in the calculator and began working on some problems.
Practice Test, Review, and Test
I did another practice test. Students didn't try as hard on this one, but I think it was still benificial. We also did some review from the book.
Many students have been late to take the test and procrastinating. It may be due to the end of the year, or extreme laziness.
Overall students are doing well on the tests.
Many students have been late to take the test and procrastinating. It may be due to the end of the year, or extreme laziness.
Overall students are doing well on the tests.
11.5 Proportions with area and volume
This is a lot to cover in a single lesson so I split it into two parts.
First we looked at proportions with area. This lead to the proportions of length squared (m/n)^2.
Then we looked at proportions of volume. (m/n)^3.
This lead to an interesting propoerty that the exponent is just the power of how many dimensions we have. I think that when volume and area came together with dimension the students understood this better.
First we looked at proportions with area. This lead to the proportions of length squared (m/n)^2.
Then we looked at proportions of volume. (m/n)^3.
This lead to an interesting propoerty that the exponent is just the power of how many dimensions we have. I think that when volume and area came together with dimension the students understood this better.
11.4 Corresponding Parts of Similar Triangles
This is true for any polygon (or any shape really), so we talked about triangles, then thought about how it is true for any shape in general.
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