Today we started with an ACT question type. I drew a picture of a bird in a tree 24 feet above the ground and a guy taking a photo of it from ground level 7 ft from the base of the tree. I asked him what the angle of elevation must be to get the perfect photo shot. JPaul considered the triangle, labeled the sides. I asked him what trig function relates the angle and the 2 given sides? Since we were given opposite and adjacent, we used tangent. We set up the equation and discussed how inverse trig functions would be needed to solve for the angle. We used our calculator and found the inverse tangent of the sides to get the angle measure. Next we worked in our notes on solving for missing side lengths. We used a similar approach, setting up trig equations and solving.
Today we started with an ACT question type. I drew a picture of a bird in a tree 24 feet above the ground and a guy taking a photo of it from ground level 7 ft from the base of the tree. I asked him what the angle of elevation must be to get the perfect photo shot. Matthew considered the triangle, labeled the sides. I asked him what trig function relates the angle and the 2 given sides? Since we were given opposite and adjacent, we used tangent. We set up the equation and discussed how inverse trig functions would be needed to solve for the angle. We used our calculator and found the inverse tangent of the sides to get the angle measure. Next we worked in our notes on solving for missing side lengths. We used a similar approach, setting up trig equations and solving.
Today Andrew and I reviewed what we've been covering for the last few classes on arc length and area. We started by going through the formulas and discussing each part and how it is determined. Andrew was more engaged today. He asked good questions for clarification. I told him he was doing great and he said, "Well I don't want you to be mad at me like you were on Friday." I said, "So you are trying harder today because you are in fear of me being angry?" and he said, "No, it's because I want to learn. But I also don't want you to be upset with me." I said, "Andrew, what happened on Friday was disappointing because I have high expectations of you. Not only were you extremely late but you were not showing much effort in what we were doing. When you don't meet the potential I know you have, it's disappointing." He said, "I know, when you tell me that it makes me want to try harder and work harder because you care." I was happy he told me that because I want him to know where I'm coming from, and I think he does. He started to be able to complete the problems that I asked him on his own. I think with a little more practice he will be able to do it on his own.
Kaitlin spent a lot of time talking about her horses and the show she is going to this week. I think it is important to allow some of this conversation because this builds our relationship and helps her work harder for me.
Christopher took his spelling test on last week's words. He wrote the words for this week in his dictionary. We looked at a paragraph of his story to discuss appropriate punctuation. He typed more of his story.