Today Carson and I continued with the concept of Greatest Common Factor (GCF) of polynomials. First we practiced finding the GCF by considering the largest number and variable that divides all of the expressions. Carson did a great job with this. Next we practiced separating the factors. Carson saw problems like 32x^5-16x^3 and was successfully able to factor it as 16x^3(2x^2-1). After Carson showed me that he has mastered this content, I showed him some random problems involving exponents. I asked if he was able to simplify them. He ran into some difficulty. This shows me that he could use some time reviewing these concepts. So we will dive into this tomorrow.
Today JPaul and I discussed the Unit circle, its angles in degrees and radians, and its x/y coordinates. JPaul and I did something simliar to this in Algebra 2 this past summer, so parts of this was a review. So instead of me instructing him, I had him stand up at the board and do the teaching (with my help). He drew a unit circle on a coordinate plane and we started with the obvious coordinates (1,0), (0,1), (-1,0), and (0,-1). Next we labeled the multiples of 30 degrees, 45 degrees, and 60 degrees. We considered what those angle measures were in radians and labeled those as well. Next, I proved to JPaul using the Pythagorean theorem, the coordinates of the multiples of 45 degrees. JPaul was then able to complete the unit circle. Tomorrow we will relate the unit circle back to the 6 trigonometric functions.
Instead of moving on we decided to spend one more day reviewing the content from yesterday. These problems are a bit challenging. We first have to use the given trig ratios and their signs positive/negative to determine which quadrant we are in. Once Matthew did that, he was able to label the sides and use SOHCAHTOA to determine the trig ratios. Matthew asked me WHY the signs are positive or negative. We went back to discuss how in the coordinate plane, depending on where the point is, the x's or y's will be positive if they're up or right, but negative if they're down or left. Matthew reached his Ah-ha moment in understanding why the signs are what they are.
Kaitlin was 20 minutes late arriving. We will not do spelling words this week since we have testing Thursday and Friday. She commented that she would rather do the MAP testing all in one or two days instead of spread out. I explained that we have to share the use of computers.
Christopher wrote his spelling words in his journal and highlighted letters to remember. He read material to help him think about what to write. He typed on his script.
Richard will do word assessment (Dibels and Orton Gillingham). With Play Doh, he will practice his spelling words. I will show him words with sub, un, and pre prefixes. He will read books with words he can read.
Today Andrew and I completed the activity we began last week on cross sections and nets of polyhedrons. He did a great job. He was asked questions where he was given a net for a dodecahedron and asked to find how many edges it has. We counted them up and then considered that some edges would be touching so we subtracted those we've counted twice. We realized it had 30 edges. We also practiced slicing polyhedrons with a plane and considering what shape the cross section would be. Lastly we discussed a plan moving forward on how we will prepare for the SAT Math.
