Wow, is this getting harder to wrap our brains around. My daughter and I are struggling. This feels light years ahead of Right Start E.

We're at lesson 38-1, and we have no idea how to answer the question in the middle. I kind of see what's happening, that essentially we have one height, that's constant for both triangles (except it doesn't look like it when you divide it into triangles, and that's really confusing, and I don't think my daughter understands what I mean), but that answer typed out makes absolutely NO sense to either of us, in the answer book.

"When you copy a trapezoid and flip it vertically, it makes a parallelogram. The width of a parallelogram is W1 + W2. The area is (w1 + w2)h. So divide by 2 for area of one trapezoid."

I beg your pardon? None of that made sense to us.

My daughter says, what difference does it make which direction it's pointed - a parallelogram doesn't have to be any particular orientation.

We don't make any sense of "the width of a parallelogram is w1+w2.

To me, essentially, it seems like we're finding the average of 2 widths, times the height. That appears to me to be why it's divided by 2, but it seems to me that I should be explaining it to her in terms of triangles, following these prior principles.

When we finally unravelled it and made sense of it, to ME, it felt like I should be telling her this:

(w1+w2) divided by 2 (because of the need to average out that width.

Take that AVERAGE and then multiply it by the height.

It comes out the same either way, but we don't understand the explanation the other way, not at all. It's like a foreign tongue.

I'm getting scared. She can't do this independently, and it hurts my brain to wrap around trying to help her.

I find myself longing for algebra, and wondering if we can handle this...

Kristina,

You're right the answer to #3 isn't clear without referring to the figure in #2. The answer should state:

The width, or base, of the parallelogram is the "bottom" of one trapezoid and the "top" of the other trapezoid. That's why the base of the parallelogram is w1 + w2. The height is h.

Note that Lesson 38 addresses one way of calculating the area of a trapezoid using triangles and Worksheet 38-1 uses a second way to calculate the area. Personally, I like the second method better. I thought it was really cool to see that two identical trapezoids, one "turned upside down", snuggled into the second makes a parallelogram! (Just you just love my technical geometric terminology ??) And since I know the calculation for the area of a parallelogram, width x height, from Lesson 31, I can figure the area of the trapezoid (remembering that two trapezoids make one parallelogram, therefore the area one trapezoid is half the area of the parallelogram).

When I was talking with Joan about this, she commented that your method of averaging the two widths then multiplying by the height is actually a THIRD method of calculating the area. EXCELLENT!! I know you probably aren't as excited as we are that you got this third method, but once the confusion wears off, you should be.

One final thought for your and your daughter --> this curriculum IS the next step beyond Level E. In Level E, you are teaching and your daughter is following. In RightStart Mathematics; A Hands-On Geometric Approach, she is reading and learning. You are facilitating. This IS a switch. And it can be hard on both of you (sometimes harder on the teacher than the student). We are starting her on the path of independent learning. So, will she need to read and re-read and re-read the lesson and/or worksheets again? Absolutely! Just like you and I read and re-read and sometimes re-read again when we are learning something new.

Have your daughter email Dr. Cotter directly at JoanCotter@ALabacus.com when she has any questions. Have her put "Math student" in the title and Joan will get to her as quickly as possible.

Remember, Kristina, we are here to help. Let us know what the questions are and we'll get it worked out for you.

Kathleen

That is such an encouraging response! Thank you, Kathleen!