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Hi everybody. Had a question about how best to approach this standard. Let me know where I’m wrong, because I’m sure I don’t have this completely right.
This is the first introduction of percents, so teaching a percent as a ratio out of 100 is a must. I’m thinking a graphical representation like 10×10 grids. Maybe even some estimating percents with some pie charts, horizontal bars partly shaded.
I see this leading to things like 8 out of 25, and having students change them to ratios out of 100, and then making a percent.
That’s where I get a little confused on where to go. You could do more complex examples, like what percent is 7 out of 12…but if the whole point of the standard is to build on proportionality, this seems too complex. Dividing 7 by 12 and making a decimal is a 7th grade standard. So do I only deal with denominators of 2, 5, 10, 20, 25, 50, 100? You could change 7/12 to 56/96 and conclude that it’s a little more than 56% and estimate, which might be the farthest you’d want to go in 6th grade?
As far as finding percents of numbers, like 30% of 45, I envision (30/100) x 45. Is the expectation that this should be solved as a fraction question? That would lead to 1350/100…is the expectation then that students should divide that to get 13.5? Does that mean this standard should come after some of the 6th grade NS standards that deal with division and division of decimals? I’m trying to stay away from simply converting to a decimal and multiplying (though even that would probably put this standard after some of the NS standards).
An alternate way I’ve seen is to say that if 45 was broken up into 100 pieces, each would be worth .45, and you would then multiply this by 33. To get that you’d have to divide 45 by 100, so aren’t you essentially teaching students to move the decimal twice to the left (but perhaps with more meaning I guess). Is that really any different from dividing 30 by 100, and multiplying .30 x 45? That would be a fraction to a decimal, which is more of a 7th grade thing though.
And finally the standard says, given a percent and the part, find the whole. I’ve seen the example 30% of a class is 6 students, how many in the class? Those numbers work beautifully to do 30% – 6, 30% – 6, 30% -6, and then the final 10% – 2. Does that mean students aren’t expected to do something more complex like “35% of a whole is 17?” which would obviously result in a decimal. I know in 7th grade we could do .35x = 17, but is the standard in 6th grade supposed to be fairly simple?
I know the progression document isn’t out yet, so a lot of this might get answered in there, but I thought I’d ask! Amazing how something as simple as this standard can make me feel like I know nothing about percents, haha. 🙂
It seems to me you are doing a good job of thinking this through. Yes, you are right, 7/12 doesn’t come until Grade 7. All your ideas for 30% of 45 sound good to me. But I don’t see why you are trying to avoid 0.30 x 45, that is also covered by the NS standards. You are right also that the NS standards have to be interwoven with the RP standards in the appropriate way.
Thanks for the reply Bill! I’ve always taught students to move the decimal twice to the left. I try and show them why that happens (divide a few numbers by 100 and show what happens), but most simply remember “move the decimal twice to the left” and they have no idea why.
The standard itself says to put the percent over 100 and multiply, and I’ve seen it taught that way, as if putting it over 100 is a more “meaningful” representation than changing it to a decimal.
But like you said, the 6th grade NS standards go quite deep into division with decimals and multiplication with decimals, so 0.30 x 45 would certainly be possible.
Thanks for the website and your time it takes to respond. It is much appreciated!
I know this is an older post and I have also looked through the progressions document. I don’t see a solution to this part of Nathan’s question.
“I see this leading to things like 8 out of 25, and having students change them to ratios out of 100, and then making a percent.
That’s where I get a little confused on where to go. You could do more complex examples, like what percent is 7 out of 12…but if the whole point of the standard is to build on proportionality, this seems too complex. Dividing 7 by 12 and making a decimal is a 7th grade standard. So do I only deal with denominators of 2, 5, 10, 20, 25, 50, 100? You could change 7/12 to 56/96 and conclude that it’s a little more than 56% and estimate, which might be the farthest you’d want to go in 6th grade?”
I don’t see that as part of 6.RP.3c because you are not finding a percent of a number. Nathan notes that an initial part is to determine the percent but the standard doesn’t say that.I am replying to myself. Upon a better reading of the standard I see this as the first part of the standard. Find a percent of a quantity as a rate per 100. Sorry.
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