Today Aiden and I moved on to discuss the Area of the circle. Aiden already is familiar with this formula. I explained to him in an Honors Geometry class we derive the formula, but in middle school math we just familiarize ourselves with the formula and how to apply it. Together we discussed a problem where given the cost of floor material as $3.95 per sq foot, how much would it cost to cover a circular room with a diameter of 18 ft. Aiden knew right away to use the formula A=Pi*r^2 then multiply it by $3.95. This problem led us to discuss how we write units in feet, square feet, or cubic feet. Aiden demonstrated that he understands its relation to dimensions. Next we discussed a problem where the area was given as 78.5 sq.feet and we had to determine the length of the circle's diameter. Aiden set up the problem correctly, as 78.5=Pir^2. He divided both sides by Pi to get 25=r^2. Aiden and I have never discussed the inverse operation of squaring. So Aiden thought about it like "What times itself is 25?" and he easily found r=5ft therefore the diameter d=10ft. I told Aiden tomorrow, I'd like to discuss this more. He agreed and said, "What if it was a number I didn't know times itself?" I said, "It involves sq. roots." And he said, "I knew it!! I was going to say square root!!" We will tap into this tomorrow so he knows what to do if the problem was r^2=40.
Today PJ and I worked on graphing ratios. We started with the example that 3 balloons cost $2. We then used that ratio to predict the cost of 6 balloons, 9 balloons, etc. We started with a table and listed the values up to 15 balloons. Then we created a coordinate plane and plotted each of the points. I asked PJ to explain to me in the context of the problem what the coordinates (6,4) meant. He was able to explain that it meant 6 balloons would cost $4. We did a few examples like this. I asked him challenge questions like "Would it be possible to buy 8 balloons for $5?
Christopher wrote his spelling words in his journal and highlighted letters to remember. He worked on typing his script.
Session Minutes
45
Minutes Student Attended
45
Lesson Comments
Christopher said he might go to Baldwin next year. When I asked why he wants to leave, he said, "I don't want to leave. That's just the way it has to be."
Kellan wrote his spelling words in his journal and highlighted letters to remember. He read Dog Man, and we discussed it.
Session Minutes
45
Minutes Student Attended
45
Lesson Comments
When Kellan asked what he is going to do all summer without our class, I suggested that he write his ideas in a journal so he will be ready to write when school starts.
