Thursday, March 14, 2013

Math problems of the week: Circles in 6th grade Everyday Math vs. Singapore Math

In honor of Pi day, I wanted to find some comparison problems involving circumferences and areas of circles. 6th grade Sinapore Math has a whole chapter devoted to "Circles," so I turned next to the 6th grade Everyday Math curriculum. To my surprise, there isn't a single problem in the entire curriculum involving circle area and circumference. Only within the sections on "data" does the circle make a brief cameo--but without its transcendental straight man:

I. The only circle-related problems in the 6th grade Everyday Math workbooks (Student Math Journal, Volume 1, pp. 41-42; p. 190):

II. The final problem set in the Circles chapter in the Singpoare Math Primary Mathematics 6B Workbook (pp. 36-37):

III. Extra Credit

Is it right to prefer "data" to Pi?

Should circles in 6th grade be restricted to straightforward, single-step Percent Circle and protractor problems?


Auntie Ann said...

EM does areas of circles in 5th grade (and I think 4th. Our kid had it introduced mid-second semester 4th, they spiraled back to in 5th.) It's in Lesson 10.9 of EM's 5th grade Student Math Journal. And volumes of circular cylinders and of cones are in 11.3 and 11.4.

But, they don't have anything like the problems in the Singapore curriculum. Just a couple simple area problems, a couple simple cylinder problems and a couple cones and done.

I'm surprised they don't spiral back to it in 6th.

Anonymous said...

How old is the EM book? Aren't we approaching our seventh billion soon?

Crimson Wife said...

California's 6th grade math standards specifically call for students to be able to calculate areas and circumferences of circles, so I'm surprised that EDM won state approval without the topic being in their 6th grade book.

Auntie Ann said...

EM's 5th grade Math Journal starts off pretty well, I think, by having kids measure various circles and then calculating C/d to get pi. I remember suggesting to the 4th grade teachers that this would be a good thing to do in the gym, since there are three large circles painted on the floor, and it would only take some string for the kids to do the project.

Then, EM has one page with one circle on a grid which kids use to calculate pi (and do data crunching with the circles all the class has measured in the previous task.)

They do something similar for the area, where they trace circles onto graph paper and count squares to estimate area. Then the formula is presented and a problem is offered. Kids then compare the calculation to their graph-paper estimates. They calculate 3 more circles before being asked whether graph paper or the formula are easier.

I suppose if a student says that tracing onto graph paper and estimating the answer by counting squares is better, the teacher will validate that response. I wonder if you can design an airplane or a pipeline by calculating areas with tracings on graph paper?

Cynthia812 said...

The most ironic thing is that the Singapore problems look interesting and fun to work on, while the EM questions are deathly boring.