I showed Joshua various trigonometric identities and techniques for proving them. We used the cofunction, Pythagorean, and negative angle identities to prove that one expression was identical in value to the other expression. This exercise helps students to understand the way different trigonometric functions are related. There was no assignment.
Assignment
See Lesson Outline
Session Minutes
45
Minutes Student Attended
45
Lesson Comments
Joshua was as obstructive as he could be. This usually happens when he is trying to slow down the overall progress.
I introduced Matthew to the procedures required for simplification of complex fractions which consist of rational expressions divided by rational expressions. I showed him how to simplify both denominators after factoring them and then multiplying the upper numerator by the reciprocal of the overall denominator. There was no assignment.
Assignment
See Lesson Outline
Session Minutes
90
Minutes Student Attended
90
Lesson Comments
Matthew was not able to follow most of the lesson and I feel that he is missing an important part of understanding in the lesson.
I worked with Joshua to produce the missing trigonometric functions of a triangle given one of them and the domain of the angle. He was able to determine the placement of the opposite or adjacent sides given either the sine or cosine values and using the Pythagorean Theorem. We were able to finish two of these problems. There was no assignment.
Assignment
See Lesson Outline.
Session Minutes
45
Minutes Student Attended
45
Lesson Comments
Joshua was very obstructive and accomplished about half of what was possible. He does not seem to appreciate that he still has to do a lot of work to finish the course. There are less than 5 full weeks before he has to finish the chapter we are in.
Adding and Subtracting Fractions with Unlike Denominators
Lesson Outline
Students participated in an all-day field trip. Matthew was among the students traveling. There was no assignment.
Assignment
See Lesson Outline.
Session Minutes
90
Minutes Student Attended
90
Lesson Comments
The choice to go on the field trip was an unfortunate choice on Matthew's part since he is so far behind. I would have expected a student who is so desperate to make up lost progress to have forgone the trip.
Simplifying trigonometric expressions using trigonometric identities
Lesson Outline
I worked with Joshua who was online to demonstrate how to use trigonometric identities to simplify more complex expressions. We used a group of identities from pythagorean identities to cofunction identities. There was no assignment.
Assignment
See Lesson Outline.
Session Minutes
45
Minutes Student Attended
45
Lesson Comments
Joshua worked with less distractions than usual so we were able to make more progress.
Adding and subtracting rational expressions with unlike denominators
Lesson Outline
I worked with Matthew explaining examples and doing guided practice problems about adding and subtracting rational expressions with unlike denominators. In most of the problems, the denominators had to be factored to find the least common factor. There was no assignment.
Assignment
See Lesson Outline.
Session Minutes
90
Minutes Student Attended
90
Lesson Comments
Matthew worked hard today but was still confused about the procedure for addition and subtraction of fractions. I was surprised that he still elects to take the 15 minute break at the end of one of the classes built into the schedule, which he could elect to skip in order to accomplish more work. He has expressed an interest in going faster through the material in the last week.
translating the graphs of trigonometric functions both vertically and horizontally
Lesson Outline
I showed Joshua how to translate the graphs of sine, cosine, and tangent of x both vertically and horizontally. I showed him how shifting the sine or cosine of x can change the sine of x to resemble the cosine of x or even the negative sine of x. I also showed him vertical transformations. There was no assignment.
Assignment
See lesson outline.
Session Minutes
90
Minutes Student Attended
90
Lesson Comments
Joshua was a little less obstructive today and so the lesson was more productive than previous lessons.
I reviewed problems with Matthew about simplifying, multiplying, and dividing rational expressions. I then introduced the topic of adding and subtracting rational expressions with the same or different denominators. We looked at an example of how to find the least common multiple. There was no assignment.
Assignment
See lesson outline.
Session Minutes
45
Minutes Student Attended
45
Lesson Comments
Matthew worked hard today and we made a lot of progress. He asked me if there was extra work he could do on his own to finish the four remaining chapters before the school year ends. I told him it would be difficult for him to work ahead because algebra is cumulative and requires a step by step approach. He understood.
graphing the sine, cosine, and tangent of functions with different amplitudes and periods.
Lesson Outline
I demonstrated to Joshua how to graph various trigonometric functions with different amplitudes and periods. I also showed him the tangent function graph with various amplitudes and periods. I pointed out that the tangent function has a period of pi instead of two pi. There was no assignment.
Assignment
See lesson outline.
Session Minutes
45
Minutes Student Attended
45
Lesson Comments
Joshua continued to resist all instruction that I offered. I introduced many distractions to stop me from teaching. It is very frustrating to have such strong resistance.
Simplifying, multiplying, and Dividing Rational Functions
Lesson Outline
I worked with Matthew to practice problems involving simplifying, multiplying, and dividing rational functions. I mentioned to him that some fractions cannot be simplified and I reminded him that in division, he should always multiply by the reciprocal of the second function. We did several representative problems. There was no assignment.
Assignment
See lesson outline.
Session Minutes
45
Minutes Student Attended
45
Lesson Comments
Matthew worked hard all period long trying to finish the curriculum by the end of the school year.
