While I was out, I gave Aiden some practice problems on area and circumference. They were surprisingly challenging. Aiden did really well on them, though he told me he freaked out at first. For example, he was given the circumference of a circle and asked to find the area. He had to work backwards to find the radius, then use that to find the area. He did great! One question asked Aiden, "If given the area, how can you find the radius?" Aiden wrote, "First we would divide by pi and then divide by 2." The first part was correct, but it opened up a discussion of why we don't divide by two. I showed him with an example. I gave him the Area of a circle as 254.469 ft. We divided by pi to get r^2=81. Then I explained to him how dividing by 2 would not solve for r. We discussed inverse operations. I asked him "What is the inverse of squaring?" He thought about it and said, "that line thingy!!!" He was right, the square root is what he was looking for. He has not had thorough practice with radicals/roots, yet the text expects him to understand it in this chapter. We discussed Sqrt(49)=7, Sqrt(100)=10 and why, because 7^2=49 and 10^2=100. I could relate to why he said we would take "half", showed him that we are not quite "halving" anything, but we ARE thinking about what times itself would give us that value. It seemed to click with him. Our next section is on cross sections. We did not have time to dive into the lesson, so I just gave him an introduction on the board. I drew a picture of a cylinder and asked Aiden to consider if we sliced it horizontally with a piece of paper, what shape would it create on the paper? Having a visual aid helped him to see that it would form a circle. Then I asked him to consider if we sliced it vertically. This was a bit more challenging to "see". I gave him the example of a coke can. If we sliced it top to bottom and opened it up, what shape would we see on both sides. He then decided it would be a rectangle. So we defined cross section as the shape created when a figure is cut by a plane.