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.