Today Matthew and I drew a unit circle on a coordinate plane and we started with the obvious coordinates (1,0), (0,1), (-1,0), and (0,-1). Next we labeled the multiples of 30 degrees, 45 degrees, and 60 degrees. We considered what those angle measures were in radians and labeled those as well. Next, we proved using the Pythagorean theorem, the coordinates of the multiples of 45 degrees. Matthew was then able to complete the unit circle. Then we related the unit circle back to the x and y values of each point. Matthew recalled that sine goes with y, x goes with cosine and tangent is y/x. He was able to answer questions like sin(pi), cos(300), tan(-45). We will continue with this tomorrow.
We looked at solving probability problems involving or, and, and conditional probabilities. We went over the concept of odds and compared odds to probability. We also started the work to be able to find expected values of situations. This is a part of decision theory.
Assignment
Problems
Session Minutes
90
Minutes Student Attended
90
Lesson Comments
The lesson went very well. Jackson has a good understanding of probability and its applications. We covered a variety of topics to get him closer to completion of the course.
Today Josh and I first went through the Free Response Questions he had for homework. The first one he got all 9/9 points. I was so proud of him! The second he got 6/9 points which is still really good! Next, Josh asked me if we could go through some ACT Math practice since he is taking it on Saturday. We discussed a trig problem requiring us to set up triangles within a triangle. Next we discussed a polynomial problem where we had to find the coefficients. They were quite tricky but we got through them.
Today JPaul and I discussed the Unit circle, its angles in degrees and radians, and its x/y coordinates. JPaul and I did something simliar to this in Algebra 2 this past summer, so parts of this was a review. So instead of me instructing him, I had him stand up at the board and do the teaching (with my help). He drew a unit circle on a coordinate plane and we started with the obvious coordinates (1,0), (0,1), (-1,0), and (0,-1). Next we labeled the multiples of 30 degrees, 45 degrees, and 60 degrees. We considered what those angle measures were in radians and labeled those as well. Next, I proved to JPaul using the Pythagorean theorem, the coordinates of the multiples of 45 degrees. JPaul was then able to complete the unit circle. Tomorrow we will relate the unit circle back to the 6 trigonometric functions.
Instead of moving on we decided to spend one more day reviewing the content from yesterday. These problems are a bit challenging. We first have to use the given trig ratios and their signs positive/negative to determine which quadrant we are in. Once Matthew did that, he was able to label the sides and use SOHCAHTOA to determine the trig ratios. Matthew asked me WHY the signs are positive or negative. We went back to discuss how in the coordinate plane, depending on where the point is, the x's or y's will be positive if they're up or right, but negative if they're down or left. Matthew reached his Ah-ha moment in understanding why the signs are what they are.
Today JPaul and I reviewed some of the concepts that we've been covering lately since they can be a bit challenging. HE did a great job recalling how to do them. The first problems we practiced were giving us the coordinates of a point in the x-y plane. We plotted the point, labeled the sides and then came up with the other trig ratios. Next we were given one trig functions values and the sign of another. Using that info, we had to determine which quadrant we were in first, then we could set up the triangle to find the missing sides.
Today Joshua and I started by finding a reference sheet for all of his "need to know" formulas for the AP Exam. Then we went through his homework. He got an 80% on it. We went through all of his incorrect answers and determined where the mistakes were made and then we made the corrections. We covered polynomials, sequences, trig ratios and more. Tomorrow we will focus on FRQs.
Today Matthew and I focused on finishing up the last Trig Chapter. Using a given trig ratio and the sign of another, we first had to determine what quadrant our reference angle was in. Then we drew a triangle with the x axis and labeled the sides appropriately. To find the third side we used the pythagorean theorem. Then we used SOHCAHTOA to find all the remaining trig functions. This was a bit difficult at first. Matthew had to recall sine is y, cosine is x and tangent is y/x. He also had to rationalize the answers when they were not in simplest form. I guided him through the problems at first, but toward the end of the class he was able to do them correctly on his own.
