On Tuesdays I upload an update of what we did in math for the week.

RightStart Geometry:

Lesson 24 Square Centimeters. First you eyeball a couple of rectangles and guess which has the greater area. Then, it’s simply a matter of dividing up rectangles into square centimeters, then finding the area of the rectangles. KidV1 doesn’t bother using the centimeter cubes as a manipulative. The lesson is over very quickly.

Lesson 25 Square Inches. Same as yesterday, but with inches rather than centimeters. I am fascinated by how at ease she is with the drawing equipment. She is chatting away about an unrelated subject while drawing her precise squares -- quickly ticking off the inches, then confidently zooming the pencil along the triangle to make the lines.

Lesson 26 Area of a rectangle. The lesson starts off with a discussion of the word “formula”, and shows the formula for the area of a rectangle A=w x h. Then the algebraic version is given (putting the w and h side by side with no intervening x), with a bit of explanation of various other ways this may be written.

The problems are fairly straight forward. The first asks for the area of a figure -- it looks like a rectangle with a square taken out of a corner, making a 6 sided figure. The book shows a couple of ways to find the answer. A couple of problems crop up while working on the worksheet. First, the problems require remembering the multiplication table for 9, yet KidV1 seems to have forgotten this somewhere along the line. Oops. Also, she is unsure about whether she is supposed to subtract the small rectangle inside the big rectangle ... I reply that it wouldn’t be a “rectangle” if you took out the other bit, so they must mean the entire big rectangle without subtracting anything ... she points out that in the book some of the 6 sided figures are called “rectangles” even though they aren’t ... hmmm, you know, she’s right, and "isn't that annoying?" I look at the answer sheet to figure it out -- it’s the big rectangle with nothing taken out.

After she finishes the sheet she reviews her 9s multiplication.

Lesson 27 Comparing Areas of Rectangles. The sheet in the book has a picture that looks like the Gateway Arch at the bottom -- the sidebar mentions that “the shape of this graph is called a parabola.”. It also mentions the word “calculus”, as in “this type of problem is easily solved with a branch of mathematics called calculus.” There is much balking at these scary images and words. I decide to stay available for questions. The first question is along the lines of, “In the book this says this math is really for middle school students, so should I be doing it?” We discuss. I think the bottom line is that she chose to do this math this summer; I’m okay with her deciding not to complete it right now. So far everything has been well within the capabilities of an average 10yo, particularly one who has used RightStart before.

Okay, with much trepidation she moves on with the lesson, which is calculating the area of rectangles with a constant perimeter. It’s given as a story-problem -- you have

*x*amount of gold edging to put around a rectangular frame; you want to maximize the area within the frame. What dimensions should you use for the perimeter? (The problem in the book is written more clearly for students, but that’s the gist.) I point out that the arch/parabola is made on the graph by drawing points on the graph and simply connecting the dots. She starts filling in her own graph; I gently correct her when she starts labelling the x axis incorrectly (“I think it will work better if you put the numbers at the base of the line, see? LIke they did in the book. It’ll be easier for you to draw the final figure that way.”)

She survives. I don’t know if she feels a sense of triumph. Maybe it’s more a sense of surprise at how easy it was once she got started.

RightStart B is on hiatus. We’re going to do some Waldorf-based math, then take a math-break for summer.

## No comments:

Post a Comment