Today JPaul and I took notes on 1.5, regarding radicals with negatives, and rationalizing complex numbers. First we discussed how to factor out a negative root by making it imaginary. Then we used radical properties to combine terms. JPaul did well with this section. He is good at doing calculations in his head. However, I encourage him to write out the steps so in the event he makes a mistake, we can retrace his steps to find the error. Lastly, we covered rationalization of complex numbers. We discussed how it's considered improper to leave i's in the denominator. So to clear them, we must multiply by the conjugate to rationalize them.
Run the lab exercise used to estimate a population by the capture, release, and recapture method. Apply the formula to obtain the estimated population by using marked and unmarked lima beans. When finished, review briefly population ecology
As JP has been absent for over a week, today I briefly reviewed our prior study of transitions and cohesiveness. We then reviewed JP's homework answers analyzing assigned textbook essays. By focusing on the details of the studied passages, I explained the shortfalls in his homework responses and provided examples of how to improve his essay analysis. Additionally , I distributed a list of transition words and a list of subordinate phrases that can be incorporated into an essay to add cohesiveness and logic. I explained when and how to use these words and phrases to create a contrast, or to explain a claim ie, introduce commentary.
Today we discussed changemakers. JPaul created a list of teenage changemakers around the world. On Friday, he will create a PowerPoint presentation that displays his chosen change makers, with a picture and description.
It's been a while since JPaul and I have had a class, so I tried to catch him up without going too quickly. Today we covered most of 1.5 on Powers of i. We went through the pattern of i^1, i^2, i^3, i^4, etc. JPaul recognized that after a while the terms begin to repeat. So we can use that pattern to determine large powers of i, like i^73. We would take the power, divide it by 4 and the remained becomes the new power. Since 73/4 is 18 with remainder 1, then i^73=i^1. Next we practiced adding and subtracting imaginary numbers. JPaul combined like terms, keeping the real parts separate from the imaginary parts. Tomorrow we will finish the section.
