Which is why you’re suppose to plug your answer into the original equation(s) to check it. Trial and error may work fine for trivial problems such as the one in the OP, but when you have more unknowns you’re going to have to resort to proper equation solving methods.
I always thought there was something fundamentally wrong with the universe.
Yes–before division (or any other operation) is a procedure, it’s a concept. You do not increase or decrease your guess randomly, because you have already conceptually “done” the division sufficient to guide your guessing–you’ve applied the concept that by increasing one, the other must decrease.
What I’m saying is that whether you realize it or not–whether you apply the procedures mindlessly or not–you must engage in the concept of division to prevent the guessing from becoming theoretically without end. You aren’t really just trying out any old numbers, until the “check” stage says they’re good. You have an underlying concept of division guiding your guesses, and in that sense you’re using division.
So, yeah, the teacher might be saying to the students, “We’re not doing division for this,” but that’s just a way of saying they’re not applying division with the particular protocol they happen to know.
[nitpick]If we are going to allow comments on the grammar of the question, then let’s address the misplaced apostrophe in “CD’s”. There’s nothing possessive about it.[/nitpick]
Now, as to the statement that math is sometimes taught (or, “maths are” for our friends in the UK and environs) by showing the “hard way” and then they reveal the “easy way”, I truly wish someone had told me that was what was happening back when I was young. I found math to be extremely difficult, and never had the “easy way” revealed to me. As a teaching methodology, it did not sink in with me.
What’s up with all the guessing about “maybe they’re doing ‘hard’ division and revealing an easy way later” and “they’re showing a need for division before they teach it”. It seems pretty clear what they’re trying to teach. It’s right there in the section’s title-
Try, check, and revise.
When I was a kid, they called it “guess and check” but it’s the same concept. Are you guys forgetting that you learned that, too? It’s a valid method for solving a math problem and it’s useful even in adulthood.
Quick, what’s the square root of 5? Well, I know that sqrt(4) = 2, so it’s a little more than 2. 2.2? That’s 4.84. So it must be higher. 2.25? That’s 5.06, so it’s like 2.4.
See? I guessed and checked. And I’m a math-literate adult. Imagine I’m in the store with $23 in hand and I see that I can buy various amounts of…I dunno, Pepsi, where the price changes depending on how much bulk I buy. How would I figure out how to get the most Pepsi I can afford? Dividing $23 by some cost-per-volume equation? No. I’d just guess which of the three or four options I think is my best shot, figure out the cost via multiplication, and see if it suffices. If not, I’d revise my guess.
You can make up any scenario where your choices are discrete and finite and easy to compute, where you’re looking for a certain “golden” result. The easiest way to do that is not to construct and equation but just to Try-Check-Revise.
So THAT’S why your daughter is learning the process. It’s got nothing to do with division. It’s its own legitimate, independent, necessary tool in her math toolbox.
This may be unrelated, but many math problems also focus on estimation. The ability to get close to the right answer with some rough logic. On advantage of teaching the kids estimation skills is that it allows them to get a feel if their calculation actually came up with a reasonable answer. So if she estimates it’s about 16 each and then does the division and gets some wacky number, she can realize she made a mistake.
ETA: Or what the post above me said.
No, that’s just normal paranoia. Everyone has that.
This applies to higher grades as well. I remember a physics test in 12th grade where we were supposed to use a formula to calculate a current or some such.
I must have made some stupid mistake in the process and came up with a number that was wildly of. Because I was running out of time and couldn’t do the whole thing over, I estimated and wrote: “This number can’t be right, should be about 15 A.”
I received full credit for the question.
I agree- I was grading some upper level lab reports in which the students calculated that the dilution had about 10000 cells/ml but the concentrated sample had about 10 cells/ml. Really? Fewer cells in the concentrated sample? They had divided when they should have multiplied, but because they didn’t have a good estimate they were dramatically off. Your physics teacher was smart- often a good estimate can demonstrate more understanding that a small mistake that results in an answer that makes no sense.
Someone up above suggested using pennies to help solve this problem. That or M&Ms would work well without ANY division.
What do you know? You know
- The total must be 42 M&Ms
- One person has 4 more M&Ms than the other.
Start with the second requirement. Put them on a table and give your daughter 4 M&Ms. You have zero.
Add one to each pile. Show your daughter that by adding one to each pile, you still keep 4 difference. “See? You now have 5 and I have 1. Now you have 6 and I have 2. If we each get one more, we always stay 4 away from each other.”
Now deal them all out, one at a time.
Have her count them out when you’ve dealt 42 M&Ms. What does she have? 23. What do you have? 19.
Tada. Nary a division sign anywhere.
How do you solve the following problem without division? (Math education question)
"My 3rd-grade daughter had to do her math worksheet last night which contained problems such as the following:
“Carly and Dave have 42 CD’s. Carly has 4 more CD’s than Dave. How many CD’s does Carly and Dave have?”
Here is how I tell my 3rd grade students to solve this problem:
C + D = 42 ( Do this line first along with the par. in the next row)
(D+4) -4 ( Do the subtraction next)
____ (This is the equals line for the subtraction problem.)
19 + 19= 38 (Figure out which number plus itself equals the answer to the sub. problem)
D=19 (That number is the number of the letter which didn’t have par. under it)
C=19 + 4 which is 23
19 + 23 = 42
However, solving the equation (x+x=38) is equivalent to dividing 38 by 2, so you have to perform division one way or another, even if it’s by trial-and-error.
Congratuations! Now for extra credit, fill in the blanks to the following question:
“The daughter just d_____ed the M&Ms between you two.”
That’s like saying, in order to total up the price of goods in my shopping cart, I just have to…hand it to the cashier! Tada. Nary a plus sign anywhere.
The penny example you quoted teaches her the underlying concepts for division, when she learns the mathematical function called “division” it’s putting a name and a symbol to a process she understands already. That’s the idea.
I’m not understanding this analogy at all. The point wasn’t to add up a total without addition. That’s impossible. The point was to solve a math problem without using division but still using a guess and check system and getting her to understand the fundemental concepts behind some of the math equations. My suggestion does all three.
But you seem to be saying that my solution dumps the problem right back on someone else to figure out, which isn’t the case at all. She’s doing the bulk of the work there.
Thanks for all your help on this - I have a better understanding of what the point of this assignment is now.
We had her schools open house two nights ago and no less than three parents (myself not included) complained about this assignment for the same reason I stated in the OP. Before the Q&A session, the teacher mentioned that this section would not be covered in the upcoming test (which implies to me that my email about it wasn’t the only one), but apparently some still loathed it enough to bring it up again during the Q&A.
I think the point is that by starting with two piles of candies that MUST equal a certain amount, you are conceptually performing division, ipso facto. It’s about the concept, not the actual mechanism of the operation.