This is from my 4th grader’s online homework assignment (the achieve3000.com assignment on St. Augustine History, for those of you in Gainesville). For these assignments they answer the same question before and after completing a reading and homework assignment. At the end they give you the results shown in the picture below:
Achieve 3000 is confusing the shit outta my kids.

**My response when I saw this was: “huh”?**

1) One explanation is they meant “10% of the total student pool changed their mind”, e.g., 10 students changed their mind – some going from the “agree” to the “disagree” column and some going from “disagree” to “agree” column, with a net gain one one student in “agree”. But that’s not possible, because if you assume:

X = kids who voted “agree” in round one who voted “disagree” in round two &

Y = kids who voted “disagree” in round one and voted “agree” in round two

then you can set this up as a system of two equations with two unknowns:

81-X+Y = 82

19-Y+X = 18

that you can solve for (and only for) X = 0 and Y = 1. So only 1% of the sample could have possibly moved. This makes sense logically – there is only one combination of the sum of the numbers from 0-10 that sum to ten but have a difference of one are 0 and 1.

2) They could have meant “there was a 10% increase in the number of kids that agree” But that’s obviously not true because 10% of 81 is 8.1. 89.1 != 82.

3) The only possible explanations I can imagine is that they actually meant “there was a 10% decrease in the number of kids that disagree”. but even that is a mess because But 19->18 can be interpreted two ways: 1% of the total sample moved (which is correct but not 10%) or 10% of the kids in the “disagree” column changed their mind. 10% of 19 is 1.8. If this is the explanation, it only works if they round down the fraction of a kid such that: 19-1.8 = 19 – ~1 = 18.

If this is indeed their logic, this is insanely lame. “10% of the students changed their opinion” means “10% of the total number of students taking the before/after poll”. They should have said “approximately 10% of the students that disagreed the first time changed their mind the second time”.

We are doomed as a nation.

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From Facebook my friend James Umbanhowar came up with the following ridiculous and rounding-heavy possibility:

“I’m not sure, and it doesn’t work without rounding, but 77% agree before and after, 5.5% disagree before and agree after. 14% disagree before and after, 4.5% agree before and disagree after. I know it doesn’t quite add up, but you could figure out some decimals to make the rounding work.

The algebra: 81-n+m=82=>m-n=1; m+n=10=> m=5.5, n=4.5”

80.8+5.4-4.6=81.6 19.2-5.4+4.6=18.4

I see. But since you are multiplying percentages, it must be a preety small number of potential population sizes where 80.8% will give you a whole number of kids to take the test. Put another way, you can make it work with your math if you assume the population of kids is can be a continuous and non-negative integer, but you require it to be discrete then the number of population sizes that fits the condition is limited.

No way. I refuse to even admit this as a possibility. S-T-R-E-T-C-H.

James responds: 73/17 =>74/16 m=5 n=4 works.

EB: so there is at least one solution if you accept the premise of James’ totally ridiculous solutiuon. Any others?

Perhaps my pre-Christmas brain is missing something subtle, but from a first glance both equations solve to Y-X=1, which means that any combination of Y and X that satisfy this are fine. E.g., 81-5+6 = 82 & 19-6+5=18.

Yeah, but that means 11 kids changed their mind: 5 from agree to disagree and 6 from disagree to agree. That’s 11%

Ah, sorry, I see this is all there in the post now. Time to turn off the computer 🙂

Someone clearly needs coffee. Do you need me to bring over the good stuff?

I don’t think it’s going to help at this point :(. Just need to make it through these last 10 things and then take a little break so that I can, you know, get my brain to actually read the full text of a short blog post again.