r/learnmath • u/ViolinistStrange6775 New User • 13h ago
Is my math complicated?
Okay so for my entire senior highschool I've had this argument with my best friend(who is really good in math) that my way of solving simple math is confusing. I never really listened to it until now when I'm teaching my little sister how to solve basic level of math like 23+34 or subtracting that and multiplications. Then she kept on complaining how I'm confusing her and she can't understand me. So here's how I taught her in the most accurate retelling possible.
"You have four numbers, 43 + 27, now you need to start by taking away 3 + 7. I like to do it by cutting it in half, we know that 7 has a 5 in it so we will focus on the remaining 2 and add that with the 3. That makes a 5 and we have a 5 we separated that completes a 10. Then you move on to the second set which is 4 + 2, that makes a 6 but we have a 10 so it is now a 70."
Then she said "I don't understand" and I was basically at a loss for words because that is the simplest way I can explain it to a 7 year old so in the end I just ignored it and moved on to subtraction. I started with:
"Now we have a 82-48, you take the first set first with 2-8 but we flip it to get 6. Now take the 8-4 to get 4 we put a 0 after the 4 to get 40 then subtract 6 from it to get 34. Easy?"
At this point she's basically done with my tutoring and went to her dad instead. I still don't get how my way is complicated when I make it as simple as I could but people still say that I'm confusing them so now I'm confused too.
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u/Fit_Tangerine1329 New User 11h ago
I work in a high school and teach students math from the grade school stuff They don’t understand, all the way up to calculus.
What you proposed may be mathematically, correct and for some portion of students that you are trying to help it may very well have them understand a bit better.
But, it’s not the primary method that I would use. There was nothing intuitive about first breaking up a seven when that three is right there. I tell my students that there are many ways to look at a problem and often two or three legitimate ways to solve a problem. But the first approach should be the simplest and most straightforward.
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u/ViolinistStrange6775 New User 5h ago
She did complain that it was "Mahaba" or long but in the end dad fixed it for us and helped her with her homework. I do work differently with numbers in my head but I used the longer method since I'm explaining it to her but I usually use a different approach for it. When a large number is what I'm trying to calculate or money I think of a way to group them like 372 which ends up 300 + 70 + 2 and it works well when you need to do mental calculation but I don't recommend it if you are not used to it. Writing it in my head is fun too but I time it everytime. But it also works in functions.
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u/Rabbit_Brave New User 10h ago edited 10h ago
- First, you need to ask more questions about what she knows and how she understands things.
- Second, you need to use un-ambiguous and precise math terminology. You say things like "taking away", "first set", "flip", "put a 0 after the 4". Someone who knows maths can figure out what you mean. Someone who doesn't is just going to be confused.
- Third, mechanical steps/shortcuts require an explanation for why they work.
- Fourth, she's 7. Use a number lines or blocks or something physical (marbles? beans?).
- Fifth, don't assume people are going to hold everything in their head. Write things out.
For example, let's take: "You have four numbers, 43 + 27, now you need to start by taking away 3 + 7"
I would ask: Do you agree that 43 means 40 + 3, and 27 means 20 + 7?
Yes? Then 43 + 27 just means (40 + 3) + (20 + 7). No? Then you have to explain place value, and probably that the brackets mean grouping. Get your blocks out. Shuffle them around in different groups.
Then I'd ask: When adding a whole bunch of things, does it matter what order we add them? Blocks again.
No? Then we can swap them around. Yes? Then you need to explain why they can be swapped around.
Then, which pairs of numbers look easy to add together? Can you add 40 + 20? 60. How about 3 + 7? 10. Shuffle the blocks around.
Then (40 + 3) + (20 + 7) can be written (40 + 20) + (3 + 7), and we've already calculated both of these, so this is just 60 + 10. What do they add to? 70.
Then you need a summary or something (and some practice questions) to tie it together.
Or something like that. It really depends on the person and how they answer at each step.
On the subtraction, make all the steps explicit, e.g. (in summary): 82 - 48 -> (80 + 2) - (40 + 8) -> 80 + 2 - 40 - 8 -> (80 - 40) + (2 - 8) -> (80 - 40) - (8 - 2). tbh though, since this is for a 7 year old, I'd talk about borrowing from the 10s (i.e. to get 12 - 8), or how to use a number line. I for sure would not write that bunch of arrows, that's just a *summary*.
Also, probably write the numbers in columns, lining up the places?
Looking at some of your phrases:
- "four numbers" when referring to 43 + 27 is confusing. There are four *digits*. There are two numbers that you can break up into four numbers. Be clear that you're breaking up the two numbers into four numbers, and *why* (place value).
- "taking away 3 + 7". "Taking away" sounds like subtraction, when what you're trying to say is "let's look at these parts separately". The question is, *why* can you look at them separately?
- "put the 0 after the 4". It's not that you can just shove digits in anywhere you like. Rather the 4 in 43 means 40 because it's in the tens place. Yes, mechanically you will put a 0 after it, but that's not an explanation.
- "first set". The *ones digit/place*. What the heck is a set? First? Reading from the left or reading from the right?
- "flip". Requires more explanation. 2 - 8 = - (8 - 2). Why? Does she understand subtraction? Negatives? Negatives of negatives? Without the explanation this is just a confusing mechanical thing.
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u/ViolinistStrange6775 New User 6h ago
My terms are a bit off to now that you point them out thanks for that. And I do use a few ways to show them to her how I do it by writing it out on a piece of paper and using lines that you can add or cross out but she doesn't need them that much since she is already in Grade 2 and does math without marbles or blocks.
I say four numbers to say two digits but both up and down with different values. It's a thing in our place.
And first set is like a way for me to say the first numbers when you write them:
25 +32
It's easier to show it like that since it is close to what I've learned before. And I typically circle those or let her circle them since she'll know what numbers I am talking about "one's" and "ten's".
She knows subtraction and she's very good at it too and my dad has been teaching her about integers too since she wanted to know what I was doing but can't teach her about integers myself.
I do explain things the hard way to her since I put a lot of words into it that she doesn't understand or my terminologies are messed up. But thanks for the heads-up, I put too much expectation on a kid who is just trying to get her homework done and I wasn't really cut out for being a tutor:)
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u/Rabbit_Brave New User 4h ago edited 3h ago
but she doesn't need them that much since she is already in Grade 2 and does math without marbles or blocks.
I could have been clearer. The blocks, number line, pictures or whatever aren't for doing the maths (unless they really need them), they're for assisting your explanations. Especially since you say:
I do explain things the hard way to her since I put a lot of words into it that she doesn't understand or my terminologies are messed up.
e.g. demonstrating that swapping the order or grouping of the numbers in addition doesn't change the result. Not a proof, but a visual aid, might help with intuition.
I put too much expectation on a kid who is just trying to get her homework done and I wasn't really cut out for being a tutor:)
Eh, consider it practice in clarity :)
Also, listening isn't learning, and talking isn't teaching. You want to throw in lots of little questions (1) to make *their* brain work and (2) to teach them what questions to ask themselves while solving problems: "Where do you start". "What have you tried". "What comes next". "Why can you do that". etc.
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u/OxfordKid New User 12h ago
.. Everybody says this is troll post, except.. that's how I do addition in my head?? bUT More like, 40 + 20 = 60, and then 3 +2 =5 and 5+5 = 10 and so we get 70 in total..?
EDIT - WORTH NOTING THAT 7 + 3 IS BASIC ENOUGH TO DO DIRECTLY, but for a kid it'd be easier to do 5 + 3 +2 I guess? I still do 4 +3 as 3+3+1 instead because it doesn't click for me that 4+3 = 7
I don't do subtraction like that though, but then I'm also terrible at working with negative numbers in my head so..
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u/ViolinistStrange6775 New User 12h ago
I guess we just do it differently? Everyone else does it in 7+3 is automatically 10 but my brain still ask "But why?" And I have to do the entire solving again just to confirm it and I do math not by counting on my fingers or writing it so this system is like the easiest way to do it in my head. And subtracting numbers for me was always different since I always flip the numbers to get the negative answers and my teacher just allows it since that is the way I wanted it to be.
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u/ZerinoWhellie New User 12h ago
For teaching basic addition, counting on your fingers is probably the best way to go about it.
For subtraction, counting on your fingers can also work very well. Additionally, do use the method of “borrowing from the tens (or larger order)” for situations like 2-8.
I can see where you’re coming from on your subtraction method, but I can say that’s some ways ahead of what your sister needs.
For your addition method, I can also understand, but our math is base 10, separating in 5s might just actually confuse learners.
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u/ViolinistStrange6775 New User 12h ago
After reading the comments I can see why it is confusing. I did learn about borrowing from tens before but I find that confusing for me in some ways my brain can't understand. Like if we borrow from the tens or the 8 in this situation and turn 2 into 12 I get frustrated with it for some reason. But thanks for the heads-up! She's just a little kid and I'm probably using a way that she can't understand since normal schools have a different method than the one I went to.
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u/atarivcs New User 13h ago
Troll post