Hunter was still able to recite the quadratic equation today! I gave him a 10 question assessment on solving quadratic equations and simplifying imaginary and complex numbers. He was able to use the formula to solve the equations, and even recognized that one of them were easier to solve by factoring than by using the quadratic formula. I was impressed that he was able to make the distinction. He struggled a bit with making arithmetic errors.
After a short discussion regarding Hunter's football banquet/dinner the previous night, we viewed a video of major construction engineering disasters. The first was a tower that was not properly built with the correct substructure foundation. The second was a nuclear power plant in Utah in 1961 that had a major melt down due to improper construction. Good session.
This morning we focused on updating our stock portfolio and researching some of the causes behind recent swings in the portfolio. We focused our attention on Ligand Pharmaceuticals which reported excellent quarterly financial results and yet the per share price of the stock dropped considerably. We determined that one of the company's affiliates reported less than favorable performance of one of its products which caused an over reaction in the stock market. Lesson learned is that the quality of your research is very important when making decisions on when and how to buy.
I showed Hunter how to derive the quadratic formula by completing the square. We did several examples of solving quadratic equations using the formula. I told him that we can always use the quadratic formula to solve a quadratic equation. He did 11 problems from a worksheet where he solved quadratic equations using the formula. I then taught him about the discriminant. The value of the discriminant tells us how many solutions a quadratic equation has. This can also tell us whether the parabolic graph of the equation crossed the x axis in one, two, or zero places. Hunter is starting to see the connection between the equations and their graphs. He was also able to recite the quadratic formula by the end of our session. I was very proud of him!
We cannot always factor a quadratic equation when we need to solve it. There is a method called completing the square that changes the quadratic equation so that it can be factored and solved. The method is lengthy and involved. I showed Hunter a visual example of it, then we worked through several exercises using the method. Hunter was able to do the problems, but had some difficulty. I mostly wanted to give him exposure to the process. He completed p. 278 (41-46) p. 281 (4-9), p. 285 (7-12) and p. 285 (1,3,5,13,15,17,19)
The square root of a negative is not a real number. In order to take the square root of a negative number, we use the imaginary number i. It is defined as the square root of -1, and i squared equals -1. I taught Hunter how to reduce radicals that had negative numbers by taking out the imaginary number i. We talked about complex numbers, which are comprised of an imaginary number and a real number. I taught him how to add, subtract, and multiply complex numbers. He did p. 278 (1-39 odd)
Today Hunter adds the dimensions to his orthographic projection (three view drawing). He first locates the hole from two directions and then adds the diameter. Following this he shows all the measurements that would be needed for a craftsmen to make the part in a shop. Lastly, he neatly adds pertinent information to the title block such as his name, date, and location that the drawing was made. Excellent session.
Hunter read last night to page 167. He continued in class with a writing assignment and chose a quote for Parts Two and Three to respond to and write about. I re-printed guiding questions for him to answer while reading. He completed an exercise identifying literary techniques based on the reading. We began reading Part Four together in class. HOMEWORK: Read to page 196 and choose a quote to write about.
Hunter today learns what the term orthographic projection means in terms of a mechanical drawings. He first watches a video and then he does an actual drawing with what he has learned on the video. Great session.
Hunter brought in his book today. He began the writing assignment by finding a quote from each part of the book and writing why it spoke to him, why it was significant, and identifying the figurative language used. He completed this for part one and began looking through part two. I assigned HOMEWORK - to read to page 167 and to look for a quote in this section, which is part three. He also submitted his resume for a job during our class!
