The continuing saga of our adventures using RightStart Geometry and RightStart B. I have a 10yo and a 6yo who have average math ability.The 10yo has done Miquon, Singapore, RightStart Transitions, Level D and Level E; RightStart has saved her from a life a math phobia.

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

RightStart Geometry:

Lesson 40 Area of Octagons.

Lesson 39, area of hexagons, took a long, long time -- over an hour. Lesson 40, area of octagons takes minutes. The student is simply to demonstrate ways it can be done -- no actual measuring takes place. It’s a fun lesson, stretching the imagination as Kid1 tries to come up with various ways to divide an octagon into triangles and rectangles.

Lesson 41 Ratios of Areas.

This gets off to a rocky start, as Kid1 is to draw a rectangle the same height as the one given, but twice the area. I pause to demonstrate how I would do it, a skill honed through years of laziness (“I would just take my T-square and draw a long line here ... and here ... see, I don’t even measure, I just use the lines they used for the top and bottom of their rectangle as my guide ... okay, now you’re ready to figure out how to make the area twice as large”).

I notice she has learned that tick marks can denote equivalent lines. Cool.

Lesson 42 Measuring Angles.

Kid1 is measuring the angle of her elbow with the goniometer. “This book is a lot less stuffy than a lot of textbooks, Mom.” Later she is flipping the goniometer around carelessly. I ask her to stop, not wanting her to ruin it. She replies that the book tells how to put it back together if it breaks. Yeah, well, it’s still not a good idea.

Lesson 43 Supplementary and Vertical Angles

Kid1 come bouncing into the room: “I thought this was going to be a long, boring hard lesson, and I was going to have to ask you for help, but it wasn’t. It was really good.“

“So, was it good because it was easy, or short, or what?”

“It wasn’t exactly easy ... it was just really fun. It wasn’t the most fun of any lesson -- I liked the lesson that was 2 worksheets where you had to name figures better.”

She shows me the worksheet. “Look, here I had to figure out this angle without measuring.” The picture shows various lines which would add up to 360 degrees; I can see that you could easily figure it out using the idea of supplementary angles. “My explanation of how I did it was a little different than their’s. I didn’t understand that I was supposed to write it out step by step as I went through it.” Yes, the students are supposed to be writing out how they arrive at some of their answers. And, yes, this one sounds like an informal proof.

I comment, “Someday you’ll learn to do this in a formal way ... it’s called a ‘proof’. You’ll prove that this angle is a certain measurement.”

She softly sighs, “Oooh,” her eyes shining with anticipation.

## 22 August 2006

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