Yesterday I was helping my granddaughter with her 8th grade algebra. The assignment she was working on was working with fractions and order of operations. It was an online quiz where it would display an equation and then four answers at the bottom and you had to pick the correct answer.
There was one question that we both worked out independently, and got the same answer, but the answer we got was not one of the four options given. We worked through it together a couple of times and got the same answer, I also plugged the equation into the calculator on my phone and got the same answer. So basically I’m looking for a sanity check that we were right and the online quiz was wrong.
The equation was: 8 + (4)^2 ÷ (7/2 - 2)
The answer we got was
18 2/3. Of the four options given, three were whole numbers and one was a mixed number with a 5 as the denominator. I didn’t think at the time to try to get a screen shot, so I don’t remember what the exact responses were, other than that none of them were the answer we got.
If you got a different answer, explain how you got it?
If ÷ is to be read as a long fraction with everything to the left on top and everything to the right at the bottom, you get 24 / (3/2) = 16 ; a whole number.
I’ve never heard of that interpretation. To be used that way, the 8 + (4)^2 should be enclosed in parentheses.
The “÷” symbol, originally called an obelus, has been used in other cultures to mean things other than division. To avoid confusion, SIO has a standard for math notation that recommends only using the “/” symbol (called a solidus) to indicate division.
The existence of the extraneous parentheses around 4 in 4^2 tells me that they aren’t following normal order of operations. Also, they’re using a division sign and a slash, which is weird. So, they’re probably looking for 16 – (8+4^2)/(7/2 - 2), or 24/1.5.
ETA: I agree that the answer is 18.6666… if you follow the normal order of operations.
18 2/3rds is correct based on standard order of operations. However we can be clued in to the fact that something strange is going on here because we have two forms of division: / and ÷.
Now, just because you sub ÷ for / doesn’t mean you get to ignore parentheses. But, I would guess your daughter is learning from home, due to the pandemic?
It’s likely this is the first time the teacher is digitizing this assignment, and on paper it’s easy to put the whole first half of the equation on one line, underline it, and put the whole second half of the equation on the next.
In the new digital format the teacher didn’t have this option, so they replaced the “two lines of text, with a numerator and denomenator” format with the ÷ sign. But, in num/den format, parentheses are implied. You do the whole top, then the whole bottom, then divide. This was lost in the translation.
I’d pick 16 as the intended answer but send the teacher feedback so they can correct their assignment.
Because on the original paper assignment it probably had the digit 4 with an exponent of 2. But the teacher didn’t know how to enter that format into the software either (or it is straight up not possible), and (4)^2 was the best they could do.
A couple of clarifications. One, checking my notes again the 4 being squared was not in parentheses. They’ve been throwing in a lot of extraneous parentheses and negative signs and whatnot to make the problems more tricky, but I guess this wasn’t one of them. Although it really shouldn’t matter.
Second, the 7/2 is actually a fraction, 7 over 2, I just wasn’t able to write it that way, and did the best I could.
My granddaughter will be back with us today so I will ask her if she can still get to that online quiz and maybe I can get a screenshot.
Nitpick: This is not an equation. There’s no = in it. An equation is a statement that one thing is equal to something else.
Yes, this is the same sort of thing as in those math problems that have gone viral on social media, based on the controversy over how to interpret the ÷ symbol.
Let me just say that any mathematician who wrote that expression without parens would be disbarred. Yes, I know there is a standard order for applying operations, but we don’t count on it being done correctly.
And I will add that this sort of nonsense is a great ad for RPN. Using that, you are forced to write either (I use , for enter, ^ for power, and / for divide)
8,4,2^7,2/+ which is 18 2/3
or
8,4,2^7+7,2/ which is 16.
The term ‘standard’ used here only means one of many ways of implementing operator precedence, including no precedence what so ever. For a homework assignment that should be known, but in the random internet problem it is not known and usually more than one answer. In this case it’s homework and there should be just one answer, assuming it’s a student in the US probably PEMDAS, and the superfluous parentheses around the ‘4’ are just a distraction. It would behoove 8th grade students more to learn there is no universal standard, and for the foreseeable future understanding how to use different orders of precedence is an important skill.
Back to the OP: Any time you see a multiple choice math question and you compute an answer not available as a choice, you can safely assume somebody who’s math-illiterate was involved in re-writing the question, the answer(s), or both. And garbled something. The problem is not you.
For darn sure due to COVID a lot of people are being asked to do things outside their normal expertise and under time / workload pressure.
But crappy work is crappy work. A math illiterate wouldn’t even think to consider teh possibility they’d injected an error. A more math-literate person would be aware of the possibility and guard against it.
A sloppy worker is a sloppy worker in any case math skills or no.
My wife is a teacher so I have a bit of insight into what is happening right now. There are two groups:
teachers like my wife who are working their ass off to convert every single lesson to being online, which means going through last year’s lesson and completely changing it if needed.
far more common teachers who just copy-paste last year’s lesson onto a PowerPoint slide, whether or not it is suitable for the digital format.
I admit that my first reaction was assuming option 2. But after thinking about it I don’t think that just because this teacher botched one math problem we can put them in category 2.
To be fair… It’s probably more likely, especially because IME cat 1 teachers are the younger ones who were probably already making heavy use of computers in class before COVID.
My niece who lives nearby is a kindergarden teacher. We talk often. Or perhaps I should say “She vents often while we listen and try to help.”
Have you ever tried to teach 5 year-olds to sit quietly and cooperate as a group via Zoom? Darn hard. And even more so when most of them are only children of comfy-class SAHMs who expect the world to revolve around them 24/7/365.
Try teaching them to hold a pencil via Zoom? All but impossible.
And yet she and her fellow teachers struggle on gamely. While being pretty continuously crapped upon by admins and by parents alike.
Clearly many teachers have been handed new tasks they’re ill-trained to handle. And no more hours have been added to the day; 24 is all there is.
So don’t mistake my displeasure with the results for shooting the worker. Bad work is being done. Sometimes by bad workers, but more often by OK or even good workers placed in a bad situation.