Name: Lori Thomas
Who is asking: Teacher
36 is 20% less than _____?
Thank you so much Lori
I think this illustrates some interesting problems about the use and abuse of %. There is an interesting article by two English Math Ed folk Celia Hoyles Richard Nossand and Stefano Pozzi who followed nurses around to see how the ACTUALLY did calculations with ratios, etc. It was NOT what we teach in school, but was something that worked, and that they were confident with in terms of avoiding overdoses etc.
So there are two ways you might try to read this question.
36 plus 20% of 36 = 36 + 7.2 = 43.2
Or 36 + 20% of X = X. Therefore .8 X = 36 and X = 9/2 = 45.
Careful analysis of '20% less than' would suggest that the second is the correct reading. (Besides, this is a text book and a whole number answer is what students will expect ;-/)
However, I would complain that the entire question is silly and unnatural in any practice for your students, in their field. It is a 'word problem' to drill some algebra and some use of vocabulary, but nobody would really talk that way in practice.
Over the last few years, I have concluded that many uses of % are what I would call 'sabre tooth curriculum'. Stuff left over from the ice ages, but having nothing to do with how people calculate using calculators or how people think using almost any techniques from visual to mental calculations.
As an example of absurd use of % I would cite lines on the Canadian Income Tax form such as 'multiply by 17.15%'. Nobody multiples by such a %. Onto the calculator, you enter .1715 - so why not write this? Habit (bad habits) and some wierd perception by people who wrote the law that this will 'feel right' to the people who are computing their taxes! People like that give numbers a bad name.
Given that this is in a program for practitioners, one might well be able to look at the practice within the field, and narrow down to ways of communicating, calculating and thinking that match what people do well, what calculators do well, and what is needed.