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Look at the equation below.
y/7 – 5 = 4.
Part A
What is the value of y in the equation?
Show your work.
Part B
On the lines below, explain how you found the value of y.
I'm seriously back on track with checking the math homework, let me tell you.
Christopher solved the equation easily enough. But then, for "explain how you found the value of y," he wrote "I guessed and checked." Which he manifestly had not done, seeing as how he'd scribbled some calculations on the paper that clearly revealed the fact that he had added 5 to 4, then multiplied 9 by 7.
I wanted to bean him.
Apparently adolescence gets worse before it gets better. Lately Christopher has taken to imitating me and hurling challenges such as "Do you ever think about anything except math?" my way on a minutely basis.
That's "minutely" pronounced min - et - lee, by analogy to "hourly" or "daily." I am experiencing challenges to my authority on a minute-by-minute basis, as opposed to an hourly or a daily basis.
I don't like it.
Of course, it's true that my grim determination to get math inside Christopher's head tends to provoke hostile imitations.
I know this because this morning I imitated myself.
I did.
I said something math-obsessed, such as "You have to practice math to be good at it," and then I imitated myself saying "You have to practice math to be good at it."*
So, along with driving everyone else crazy I am now officially driving myself crazy.
"I guessed and checked" is the wrong answer
What is the right answer?
What should he write for Part B?
_________________
* Did this ever happen to Erma Bombech?
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19 comments:
Whatever makes the teacher happy.
hahahaha
seriously, what would he say as a justification for each step...??
I don't see much difference between "show your work" in part (A) and "explain how you found the value of y" in part (B). Actually, I don't see any difference. But, clearly, they are looking for two separate answers.
I think that there is a reasonable chance that Christopher is "correct" to put down "I guessed and checked" in the sense that this may be the answer that gets the highest grade.
Seriously.
-Mark Roulo
really?
That seems wrong to me....can't he do something like say he used the....additive-whatever?
Am I going to have to look this stuff up???
What if he said he simplified the equation and then solved it?
(That's mathematically correct, right? First you simplify; then you solve ?)
Would that work?
I agree that the question is ludicrous. If he's shown his work (he didn't do that well enough but I'm INSISTING)...an "explanation" is superfluous.
But I'm thinking he could justify each step as Saxon does & as Russian Math sometimes asks students to do.
I must say, often Saxon doesn't precisely "justify" each step, but simply describes it.
He'll say "subtracted" by the line where he substracted, then "added" by the line where he added.
I doubt the state test would look favorably on that.
A guaranteed winner, although a little long:
"I used inverse operations. I added 5 to both sides of the equation because addition and subtraction are inverse operations (y/7 - 5 + 5 = 4 + 5, so y/7 = 9). Then I multiplied both sides by 7 because multiplication and division are inverse operations (y/7 x 7 = 9 x 7, so y = 63)."
That sounds too mathy.
The answer the teacher is looking for no doubt will have the words "tally marks" and/or "repeated addition" figuring prominently with a "guess and check" thrown in for good measure.
I used inverse operations.
THAT'S IT!!!
I used inverse operations.
I used inverse operations. I added 5 to both sides of the equation because addition and subtraction are inverse operations (y/7 - 5 + 5 = 4 + 5, so y/7 = 9). Then I multiplied both sides by 7 because multiplication and division are inverse operations (y/7 x 7 = 9 x 7, so y = 63).
The whole thing is terrific.
Thank you!
It's not too mathy - this isn't the teacher, anyway; it's the state test, which I assume is looking for something real.
I just couldn't figure out how to describe what you do solving a simple operation - I kept thinking about "addition and subtraction" identity properties....(I've forgotten the terms).
"Inverse operations" is exactly right.
It's something a kid his age could know (ought to know), and it simply describes what he did to solve the problem.
PLUS I keep trying to get him to see that when he solves these problems HE IS USING INVERSE OPERATIONS.
His knowledge is so fragmented that it's been VERY hard to get him to see that he can use inverse operations to find the measure of one of two supplementary or complementary angles.
I imagine they ask these questions in the hope of catching students who just work on a patterns basis - for this question try these actions.
I imagine they ask these questions in the hope of catching students who just work on a patterns basis - for this question try these actions.
I really have no idea.
The actual state test, the one 7th graders took last year, has no such questions.
This is from the test-prep booklet, so I don't even know if such a thing is likely to be on the test in the first place.
HOWEVER, since he was asked, I want him to be able to say something intelligent about why he did what he did whether it's going to be on the test or not.
"I used inverse operations."
I think the whole thing needs to be preceded by a statement of aims. It needs to be said why these inverse operations are being deployed. He could say something fancy like: In order to find the value of y in the equation I need to isolate the variable (or have y stand all by itself)...
I am all for requiring students to understand what they are doing but requiring them to write disquisitions on the level of deep-understanding math thinkers a la Liping Ma and David Klein is a bit much.
My first thought was, "Isolate the variable." Of course you're using inverse operations, but that seems so obvious since that's what was done in the "show your work" phase.
I understand the need for this at a certain point in learning, but the frustration is pretty great for kids who are developing fluency and have to stop and "go back" to the beginning.
I remember a similar thing happening to my son when the 5th grade testing was coming up. The gifted pullout kids had to be taught how to "go back" and draw out a chart for a problem when all of them could solve abstractly and mentally. I can't remember the problem exactly, but the chart was practiced faithfully (and rotely, I might add) for a few days so that they would answer it in the say the testers wanted to see it.
The kids were bored out of their minds drawing a huge chart that might have helped them 1 or 2 years earlier. The were past this phase of learning and knew how to problem solve in a more abstract manner, but there was nothing on the test that identifies more advanced approaches to a skill.
These kids literally spent a month pretending to have good 5th grade skills and thinking when they were all advanced beyond them.
I am all for requiring students to understand what they are doing but requiring them to write disquisitions
I absolutely see the value of having kids use words to identify steps in solving an equation or a problem. I assume this is in line with "formalism;" it certainly reinforces the concepts which at this point is becoming CRITICAL. Christopher's math knowledge is unbelievably, shockingly fragmented. He's had essentially nothing but fragmeneted, over-rapid procedural teaching for two school years running now. Ed and I parachute in every few days to try to make sense of the whole morass for him, but none of these activities adds up to a coherent curriculum with coherent teaching.
At this point I'm looking for "shortcuts" to learning & comprehension (not a royal road, just a SHORTCUT) and I think having a student write down each step of solving and equation along with a word or phrase next to it identifying the principle used is one that probably works.
The fact that the Russian Math book makes students do it is enough for me to go on.
What I object to here, as always, is the sloppiness.
Why have them create an "open-ended" response.
It's cr**.
There's no reason for it to be open.
Kids should have questions where they go through each step of the equation solving process and identify what principle has been used.
These kids literally spent a month pretending to have good 5th grade skills and thinking when they were all advanced beyond them.
We have the exact opposite problem.
The material on this test is supposed to be material Christopher & his class learned last year, since they're at least one year accelerated.
The fact that all of his knowledge of this stuff is so tenuous is just fricking horrifying.
AND GUESS WHAT!
TEST PREP BOOK IS 353 PAGES LONG WITH NO ANSWERS!
"VACATION" COMING UP NEXT WEEK!
HIGHEST PROPERTY TAXES IN THE COUNTRY!
NO ANSWERS!
ANSWERS ARE TOP SECRET!
ANSWERS BELONG TO TEACHERS, NOT PARENTS!
CERTAINLY NOT TO STUDENTS!
Watch out, she's got the caps out.
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