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Geometry Lesson 38 and Worksheet 38-1

Kristina,

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

First flip one trapezoid vertically and put it next to other trapezoid. The two trapezoids make a parallelogram. The width of the parallelogram is w1 + w2. The area is (w1 + w2)h. So divide by 2 for area of one trapezoid.
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

Re: Geometry Lesson 38 and Worksheet 38-1

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