We are both getting excited as we are nearing the end of the curriculum. Today we discussed graphing polar coordinates and how their shapes look like flowers. Worked with the polar functions and graphed points. We could see in the cosine function, the graph creates a circle that opens right if its positive, left if negative. For the sine graph, we could see it creates a circle that opens up if positive, down if negative. This lesson was long and we were unable to finish it today, so we will see what happens tomorrow when the circles divide to become "flowers" with multiple petals.
Today PJ and I worked in his textbook on word problems involving inequality signs. PJ has been doing extremely well with this content, so we are moving through it quickly. PJ read word problems, set up an inequality, and then solved it. Right now we are working on one step inequalities like, "Mason is selling plushies for $10.25 each. How many plushies will he need to sell to collect at least $100?" PJ set up the inequality 10.25P>100. He divided to get P>9.75. Then he realized that Mason would need to sell at least 10 plushies, since 9 would be too low.
Today Carson and I continued with our review of linear functions. We reviewed what we did last class on the different ways to find a slope, write the equation of a line, and graph a line. Today we started by writing the equation of a line passing through two points. Carson recalled to find the slope first with the formula. Then he was stuck. So I showed him the parts of the slope intercept form of a line and how we know the x and y values. He realized he could substitute those in, to find the y-intercept and correctly write the equation of a line. We practiced this with a few examples. Next we saw what happens when the slope is 0 or undefined. We discussed how these would produce horizontal and vertical lines, so their equations won't look like y=mx+b. It will just be x=Number or y=Number.
We began today by starting with a problem like we have been working on the last few classes. I wanted to see if Andrew could do it without any assistance. He got started by converting the given angle that was in degrees to radians. He did that successfully. Then he thought the problem was done. It made me realize Andrew is beginning to memorize steps instead of understanding the WHYS behind what he is doing. So I tried to break it down for him. We discussed the entire distance around the circle is the circumference, however all we are looking for is part of the circumference, just the arc length. Andrew is also having trouble with recognizing the radius, so I will "quiz" him on that each class so he learns the importance. Andrew put in a good effort today.
Aiden and I moved onto the next lesson: setting up and solving two-step inequalities. Aiden did an excellent job with this section. He was asked questions like "Last year the club raised $658.35. This year they want to exceed that goal. They are selling coupon booklets for $17.95 to help reach their goal. If they have already raised $498.75, how many coupon booklets do they need to sell to exceed their goal?" Aiden set up the inequality 498.75+17.95b>658.35. He used inverse operations to solve and reached the conclusion b>8.89. Aiden and I discussed how you can not sell 8.89 of a booklet, so how many booklets would they need to sell. We agreed 9. Aiden is ready to move into multi-step inequalities tomorrow!
Today we started by discussing what it means to be "like terms". I wrote out a few examples of like terms, and a few non-examples as well. Ben picked up on the concept quickly. Then I wrote out a problem with two polynomials and asked Ben to add them and then classify. I showed him how to do it first. We started by collecting terms with the highest degree first, and added them. Then we moved to the next terms, combining them one at a time. I wrote it down while Ben told me what to write. Once we added them, I asked Ben to classify them. He did a great job recalling the names, monomial, binomial, trinomial, polynomial. He needs more practice with the degrees: constant, linear, quadratic, cubic, etc. Ben did an excellent job participating today.
