RightStart Geometry

The continuing saga of our adventures using RightStart Geometry and RightStart B. I have an 11yo and a 7yo who have average math ability.The 11yo has done Miquon, Singapore, RightStart Transitions, Level D and Level E; RightStart has saved her from a life a math phobia.

I try to update our adventures on Tuesdays, although sometimes it doesn’t get done until Wednesday. And sometimes we really haven’t done that much math, so I skip it entirely.


RightStart Geometry:

(I think we have skipped some lessons here in my chronicle of our time with RightStart. I suspect Kid1 did them last June and I never got around to commenting on them.)

Lesson131 Basic Trigonometry

Day one:

I am not prepared to be “back to school”, but Kid1 has decided to bustle around doing school this morning. Her resolve to get into the school groove starts to crumble as she reads through the RightStart explanation of trigonometry. I read through it -- it’s thorough and succinct. I help her through the first problem, finding sine, cosine and tangent of a 45 degree right triangle, showing my work on the chalkboard (I love doing math on a chalkboard -- whiteboards just don’t cut it for the tactile satisfaction). Her eyes are glazed, she keeps asking why, as in why the heck would anyone DO this? I suggest we drop it for today and try a different approach tomorrow.

Day two:

I have googled various websites on the uses of trigonometry, trying to choose ones that will interest her. She is unimpressed. Next we get out Zaccaro’s Challenge Math and read through the chapter on trigonometry in it. I point out the exciting concept that triangles can be different sizes yet have the same ratio of opposite side/adjacent side. She rolls her eyes at this -- it is such old news. But she starts to realize that this isn’t some weird new branch of math someone dreamed up just to torment innocent young students -- this is a logical outgrowth of things she already knows.

We look at a few of the word problems in Challenge Math but decide against doing them. I like the way RightStart approaches trig better, mostly because it’s the way I learned trig many years ago.

Day three:

Ready to tackle the RightStart worksheet again. We work through the sine, cosine and tangent of a 30-60 triangle together, using the chalkboard. Then she starts filling the The Chart -- it’s a chart of sine, cosine and tangent of 5 degrees, 10 degrees, 15 degrees, etc. on up to 85 degrees. She is to measure triangles on the second worksheet, then use her measurements for her calculations. No indication is given whether it would be better to measure in metric or inches, but she decides metric would be more accurate.

I am on alert, since I’ve noticed that this business of measuring can turn into disaster -- sometimes the reproduction of the worksheets is a scootchy bit off, leading to different interpretations of length. Since she’s going to be using millimeters to calculate, she could rapidly end up with an answer that’s fairly different from what it should be (especially since she’s to use the table she’s making for the next lesson). We hit on a strategy -- first of all, I look at the answer sheet and discover that every hypotenus is 10 centimeters. Aha -- I figured there would be some constant somewhere, since that’s the way elementary math books tend to work. Plus “10” is easy to divide by, so it makes oodles of sense that every hypotenus would be ten.

I keep the answer sheet out. She measures the sides of each triangle, then tells me what she gets for the measurement. I tell her what the answer sheet says. We quickly ponder the difference (can she see why they called it what they did?), then she uses the “official measure” for her calculations. I draw traingles on the chalkboard for her and label the angles and sides with A,B,C,a,b,c. She soon sees the patterns that are forming with her answers (which is why it’s so cool to do this exercise, and why I wanted to do it instead of just doing the Chalenge Math -- you can discover the relationships between sine, cosine and tangents of the various angles as you calculate them).

The lesson took 3 days and plenty of parental involvement, but in the end she is confident that trigonometry is something she can deal with.

Lesson 132 Solving Trig Problems

Kid1 zips through this lesson, using the chart of trig ratios from lesson 131. She feels good about this.

The discussion of Problem 1 comments that “your answer may not quite agree with the solution. Trig ratios cannot be calculated very accurately by measuring as you did.” Umm, I feel like we’ve been caught cheating on yesterday’s chart!

Lesson 133 Comparing Calculators

MrV’s scientific calculator uses Reverse Polish Notation, so I decide to spring for the calculator specified in the book instead of making do with his. I bought our Casio fx300MS from Amazon since our local Target didn’t have it and I was able to get free shipping (driving around town looking for one was going to use up as much gas as the price differential).

It looks rather like a Star Trek data pad, which makes it a very satisfying addition to our household. The kids quickly figured out how to use it. Kid1 didn’t make it all the way through the worksheet, though, as she started feeling woozy, heralding a fever. She'll get back to this lesson after she recovers.