Wednesday, January 23, 2008

Connected Mathematics G6 Circle Area and Circumference leaves out ...

What do you think would be the most amazing bit of information leftout of the student textbook on a 6th grade unit on area culminating in circumference and area of a circle?
(Hint: remember that the book on adding fractions does not contain any summary explanation of a correct way to add fractions)
How do you develop a formula for area? Draw a square around the circle,so that it covers 4 radius-sized squares.
Now the following is ONLY in the teacher book:Cut out the scraps outside circle on 3 pie sections, and chop them up. Fill the 4th pie sectionwith scraps, you won't be be able to fully fill it in. Based on this, students will all discover that that the area of a circle is slightly more than 3 radius-length squares, or 3 r squared. Last time we sawa number a bit more than 3 it was PI, so it might be pi r squared.
The students are asked to develop a method to compute the area basedon radius, and the correct answer is pi r squared, but...
Same with 2 * PI * r
Now get this.
How do you find the radius if you know the area?
The answer in the teacher book is simple, just divide by pi and take the square root.
Can anybody spot the problem?
Square root isn't in the index.It's not in the book.It's not covered in connected mathematics until GRADE 8.
What sort of a student is going to figure out the right answer?
I just got this from visiting the math office at the Lake Washington resource center, but they chased me out when they needed the table for a meeting. Library hours are 8:30 to 11:00 am, and they don't have the complete connected series. You really need to see the teacher manual to see if any actual teaching is taking place, but the parents can't see the teacher's manual to help with homework in case suzie didn't figure out pi r squared on her own and wasn't paying attention.
What kind of idiots write these texts and review them, and why do 95% of teachers give Pearson an excellent review???

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