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Hi Bill,
We are laying out our MS curriculum for next year and we have a question about the percent proportion. When is the percent proportion introduced? Should we use the percent proportion as a method to teach 6.RP.2c or wait to introduce it in 7.RP.3?
I’d like to take a crack at this one before Bill does if that’s ok.
It seems to me that our treatment of proportion in the past has been setting 2 ratios equal to each other and “solving” (maybe relying heavily on the magic of cross-multiplying), but now the standards are asking us to analyze proportional relationships, i.e testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin (7.RP.2a).
I think “percent proportion” falls into the former way of thinking about proportion rather than what we are being asked to think about in the Common Core, so I worry about using it at all. If it is to be used, I think it would be limited to 7th grade since proportional relationships are not introduced in 6th grade, but more importantly, how does it support the ideas of proportional relationships as outlined in the standards? Those ideas being: testing for equivalent ratios in a table, graphing on a coordinate plane and observing whether the graph is a straight line through the origin, and using the unit rate to write equations of the form y=kx.
Yes, I think abieniek has it right. Although, I confess, I’m not completely clear on what is meant by “the percent proportion.” In the Common Core a percent is a rate per 100, so anything you would do with a rate you can do with percents. This includes, in Grade 6, understanding that 5% of 200 is 10 because $\frac{5}{100} \times 200 = 10$, and, in Grade 7, being able to express the statement “the sales tax is 5% of the price” using an equation such as $T = 0.05P$.
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