Today JPaul and I practiced working on the unit circle to find reference angles and coterminal angles. We used the white board to draw an angle like 150 degrees. I asked JPaul how to get to that location going in the negative direction. JPaul tries to do a lot of math in his head. I encouraged him to do a quick sketch, so he could actually SEE what quadrant he was in, and how far he would need to go in the negative direction. He complied and realized that it WAS actually helpful to see it. Then we practiced finding the reference angles - the angles formed with the x-axis (which is what we will need to find in the next lesson).
Today Carson and I worked on using the Pythagorean Theorem to derive the Distance formula. We started with two points. Carson plotted them on the coordinate plane. I asked him to estimate the distance between them. He guessed 9.5. Then I drew the horizontal and vertical distance between them. I asked him to calculate those distances (he got 6 and 8). I asked how could he use those distances to find the distance between the two plotted points. He knew that he could apply the pythagorean theorem. He found 6^2+8^2 as 100 and realized the distance was 10. So he was pretty close. We did a few more examples like that and then we derived the formula. I showed Carson that while the Pythagorean theorem is helpful, the distance formula might even be a better tool to use depending on the given information.
Andrew was here today but he came to me at the beginning of class and asked if he could use our class time to work on his art piece. He said he feels like he might not finish in time for the art show. I made sure it was ok with his teachers. I used the class time to prepare material for our upcoming lessons.
Today Matthew and I took notes in the new section on Trigonometry. The first section is regarding angles. We discussed how we rotate around the coordinate plane, counterclockwise is a positive angle and clockwise is a negative angle. Then we discussed how degrees and radians are related. We practiced converting 60 degrees to pi/3 radians (and vice versa). Matthew did a great job counting around the unit circle.
Christopher wrote his spelling words in his journal and highlighted letters to remember. We read The Watsons Go to Birmingham and discussed it. He typed on a story he is creating.
