I worked with Joshua to use several standard trigonometric identities to simplify complex trigonometric expressions to simple ones. I also taught him the meaning of verifying trigonometric identity equations so that both sides become equal. I gave him an assignment due on Monday: P. 928 # 10 - 20 evens, and 28 - 34 evens.
Assignment
See Lesson Outline
Session Minutes
90
Minutes Student Attended
90
Lesson Comments
Joshua continues to be obstructive using various distractions to avoid making too much progress.
I showed Matthew how to solve rational equations using cross multiplication. I also showed him how to get all the denominators in a rational equation equal and then cancel the denominators. I gave him a homework assignment to reinforce his learning. The assignment is due on Monday and is: P.591 #6,8 and P. 593 # 4,6, 8, 10, 12.
Assignment
See Lesson Outline
Session Minutes
45
Minutes Student Attended
45
Lesson Comments
Matthew worked very well during the session. He copied down the assignment.
I led Matthew through some simplifications of complex fractions and showed him the steps that are always necessary when the parts of the fraction have unequal denominators. We did five problems of increasing difficulty. There was no assignment.
Assignment
See Lesson Outline
Session Minutes
45
Minutes Student Attended
45
Lesson Comments
Matthew seemed somewhat sluggish in following examples. He needs to take notes during each session.
Joshua and I worked on using trigonometric identities to find the different parts trigonometric functions of a triangle. The Pythagorean identities were also used to find the cosine of a function when the sine was provided. There was no assignment.
Assignment
See Lesson Outline
Session Minutes
45
Minutes Student Attended
45
Lesson Comments
I missed most of my session with Joshua due to my attendance in the meeting with Matthew's mother. He worked a difficult problem in a novel way in my absence.
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.
