You and a lot of others in this thread seem to have had some really shitty teachers in elementary school… 
Then what’s the fucking point?
I realize you’re critiquing the educational system, not the idea of providing explanations, but if the educational system is set up poorly (and you are correct that it is often is, in many ways, although I don’t think this thread is an example of that), it is all the more imperative to add the value to it that would otherwise be missing.
If you want your second-grader to skip the understanding of their math problems, just go whole hog and let them skip the math problems altogether… Either do things for a purpose, or don’t do them at all.
Mirror image: 125+150=275~~275-150=125
A math palindrone… wherein the subtraction is solved in reverse of the addition.
Now that I think about it - you are right backwards is much better.
As far as the vocab goes - I don’t have kids, but I have a REALLY hard time believing that any kid can understand words like that. In general I don’t think you should ever have a word that is more complicated than what you are trying to teach. I never saw the point in using those part of speech words when teaching a primary language either. Most of those were way more complicated and just off putting. Reminds me of that joke about the kid and “Richard Stands” when it comes to the Pledge of Allegiance - they aren’t understanding - just repeating when you use words no one else does and that they never hear elsewhere.
I’d be curious to know if any of these work.
My daughter’s school also used the term “fact family” for that type of thing.
Also be prepared to explain to your child that “regrouping” is really borrowing and carrying over. Don’t know why they felt the need to rename this but they did and kids had trouble understanding the concept. Once we explained the “borrowing 10 from your neighbor” when subtracting multiple digits and “carrying the leftovers up to your neighbor” when adding them, they understood perfectly!
Why would “borrowing and carrying over” intrinsically be more intuitive terminology than “regrouping”? I suspect the efficacy of your explanation was not in the choice of jargon, but rather in the fact that you were likely simultaneously providing a detailed explanation of the reasoning.
(I also suspect that part of the reason “borrowing” was apparently abandoned is because it has weird connotations; if you borrow something, you have to eventually pay it back, right?)
FWIW I’ll throw out this strategy.
In an equation you can take any number on one side and move it to the other side as long as you make it the opposite, so you can keep doing that until you get to the combination 275 - 150 on the same side. That would take 1 step, moving the +150 to the other side and making it the opposite, -150. It’s backwards, but that’s what the ‘=’ means. Its the same thing both ways.
The rest might be advanced but you could play with this all day. Pick one number, move it, make it the opposite, check yourself.
125 + 150 = 275
I’ll pick left 150. Now we have
125 = 275 - 150
Now pick right 275–>
125 - 275 = -150
I pick right -150–>
125 - 275 + 150 = 0
I pick left -275–>
125 + 150 = 275
I pick left 125–>
150 = 275 - 125
and so on.
125 + 150 = 275 shows us that these three things have a relationship.
If we put these two things together, 125 and 150, we get the third thing, 275.
If we break 275 apart we can get 125 and 150.
These number will always have this realtionship.
Please don’t try to teach “moving” on the number line. Motion is a hard thing to imagine, especially for kids. It’s easier to see still picture. I recommend instead of teaching that points slide along the line, teach that there are bars/segments/blocks that stack up or lie together on the line.
To teach “7 + 4 = 10”, I’d teach the 7 as being a bar that stretches from the 0 to the 7 and the 4 as stretching from 7 to…what number? Yes, 10. By using the bar method, they can ‘see’ and be taught that:
- the addends are still present in the sum.
- they only “add” because they’re stacked/placed/lying next to each other.
- one bar can be removed without changing the size of the other bar.
- This works the same way even if you don’t start at zero.
These things are not possible with a moving point, as the child loses track of where he started and where he’s been.
Yes, this is an excellent method for teaching “fact families”. The different-color (or whatever property) is important because the student needs to see the separate addends within the sum.
Some day, your high schooler will ask you why (4+2)/2 isn’t just the same as 4+(2/2). And you’ll have to say “because that first one is like splitting the whole pile of 4 red marbles and 2 blue marbles into two new piles, while the second would be like just splitting the blue marbles only.”
So this stuff goes well beyond second grade.
You absolutely must start. Visual aides are crucial to translating numbers and operations into real-world, tangible scenarios. When Johnny’s money falls out of his pocket in a world problem, the student must see that as subtraction. When piles get split up among people, they must see that as division.
I think this is probably the issue. With some teachers it doesn’t matter if kids get the right answer, it has to be done a particular way with particular terms. I was trying to help someone learn how to multiply fractions, but the teacher insisted that they show their work using a particularly baroque method.
Heaven forbid you try and teach your kid “carry the ones”.
The teacher may not want your kid to “understand” it, they may just want him to parrot back a pat answer using the approved terminology. Posters have show that there are multiple ways to approach the problem. Some kids will learn better with paperclips, others with number llines, and others with the commutative property.
I’m not totally convinced that this is a good method of teaching addition…
Basic set completeness - addition and subtraction.
Q: If I have a hot chocolate with whipped cream, and I take away the whipped cream, what’s left?
A: the hot chocolate.
Q: If I have a hot chocolate with whipped cream, and I take away the hot chocolate, what’s left?
A: the whipped cream
Now do it with hot chocolate, whipped cream, and the cherry…
How many items? 3.
Take away 1 - the cherry. Now what’s left? whipped cream and hot chocolate. How many items is that? 2.
and so on.
Then give him hot chocolat with whipped cream and a cherry on top. That, he’ll understand…
Unless you are Nigel Tufnel.
“Wha? I was asking about parentheses, and now you’re going on about marbles. What gives?”
“Well, I was showing you the real world applications and what not.”
“Um… okay. Thanks? Anyway, what’s the answer to the question?”
“Because you do what’s inside the parentheses first.”
“Okay, got it, thanks.”
That would have been me, anyway. But I know not everyone is alike…
I like this explanation, not least because of the chocolate.
I would explain it as “pieces”. This piece plus that piece makes up this. If you take away one piece, that leaves the other piece.
125 is the first piece. 150 is the second piece. Put the pieces together, and you have 275.
Take away the second piece, and only the first piece is left. QED.
Regards,
Shodan
I did not have this kind of problem with my kids because I communicated with the teacher, ( had a few spirited discussions he he he ) so I was always aware of therminolgy and what that teacher wanted.
Those that taught to the test only are not really teachers but just government drones doing the ‘every child wins all the time and never fails and is never left behind’ thing.
You have to home teach to rescue your child from that teacher if you can’t get your kid moved.
Myself, back in the day had mean, cranky Nuns and I never was beat up with unusual words or that stuff.
Now was O nor did I let my child ever thin\k there was only one way to do something in math.
Wait untill they get older and get those teachers that say their way is the only way to write papers… Bawahahaha
If your kid understand the math, good, but if the teacher will only allow one special idea to be expressed as an answer, get the answer from the teacher and tell the kid to use it to please the teacher but the child is plenty old enough to understand what is wrong with what the teacher is doing.
Short answer, ‘get involved in your child’s education.’
Know their teachers. Especially the first 6-7 years of school.
YMMV
PS: All the above stuff is good ways to teach the kids but word problems need word answers & that seems to be what the teacher wants. the teacher should have already taught the reasoning the kids need to give the answer they want. If not, bad teacher, not a math problem, it is a communication problem or a teaching problem…
My educational career K1 through BA (English Lit & Political Science)
spanned the years 1955-1971. I was not an outstanding mathematician
(597 SATM), but I did pass two college-level math courses (B- Algebra, C- Probability).
This is the first time I have ever heard the terms addend, minu(t)end
and subtrahend. I also was taught the terms numerator and denominator
rather than dividend and divisor.
On the other hand I am quite sure the word “sum” was introduced to me
by the 2nd grade, and probably in the 1st grade.
The infusion and juggling of terminology makes we wonder what the hell
our schools of education have been up to in the 40 years. Also take a look
at this thread, including the links:
FL School Board Member Can’t Answer Any Math Questions on FCAT
As for the OP I would try to get across that adding a number to one side
of an equation is the same as subtracting the same number from the other side,
and if that does not sink in right away, hope it soon will.
Maybe I missed it, but I haven’t seen anyone here suggest the first thing that came to my mind.
You know that 125 + 150 is 275.
You’re asked what 275 - 150 is.
Since 125 + 150 is the same thing as 275, then you know that 275 - 150 is the same thing as 125 + 150 - 150.
Since 150 - 150 is nothing, then you know the answer is 125.
Isn’t that second-grade simple?
I don’t know of anybody who actually uses those words. (Well, except for “divisior,” as in “greatest common divisor” and contexts like that.) I think somebody just decided there had to be actual words for things like “the thing you’re subtracting from the other thing.”
Worse than that! If you look in old enough books, it was:
addend + augend = sum
This goes back to the days of certain mechanical adding machines, where the two numbers to be added had to be entered into the machine in different ways, so it was useful in the training manuals to have two different words for the operands.
Going back to the OP: The thing you gotta 'splain to your second grader is this:
Once your 2nd grader fully groks that, what could be simpler? :smack: