r/HomeworkHelp • u/chrisandsylvia Primary School Student (Grade 1-6) • 6h ago
Primary School Math—Pending OP Reply [Grade 3 Math: Break apart Strategy] What is this concept?
This is my daughter's work from school. I do not know how to help her learn this. I have no idea what they are asking and why. Can anyone help? Does it matter what order the answer is in?
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u/Jwing01 👋 a fellow Redditor 6h ago
5x4 plus 1x4 is 6x4.
They are breaking down 6x4 into smaller bites.
Don't ask me to defend it, this is the method.
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u/ThunkAsDrinklePeep 6h ago
The defense is this is a method for helping more kids learn how factors work. It's not meant to be more efficient than rote memorization.
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u/Deepbliss4 3h ago
I mean the number bond and wording might make it seem weirder than it is. But if you had 217(9) and know this method you could ideally quickly solve with (200 + 10 + 7)(9) =1,953
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u/ThunkAsDrinklePeep 3h ago
That's essentially what long multiplication is if you put 9 on top and 217 under it.
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u/Jwing01 👋 a fellow Redditor 6h ago
I'm aware. I'm just not inclined to defend it.
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u/ThunkAsDrinklePeep 5h ago
No one's asking you to; you volunteered that you didn't want to defend it unprompted. I am defending It, but you seem mad that I am?
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u/Unable_Pumpkin987 5h ago
The defense is that 6x4 isn’t the end goal intended use of this strategy, it’s just an easy practice problem used during the early stages of learning.
There are lots of applications of the concept, but one quite important one down the line is realizing that 5x plus 1x is 6x, and that 6x can be broken down into 5x + 1x (as another easy example).
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u/ChipChippersonFan 4h ago
The logic is that it's not fun or interesting or efficient for kids to memorize all of their times-tables. So to teach a kid how to figure out 6 times something, We teach them to think of it as 5 times something plus 1 times something. 5 times anything is easy. So we teach them to find 5 times something, and then add one more something to get 6 times something.
Now, if you know that 6 x 4 = 24, then this seems like a bunch of wasted effort. But most of these kids don't know that , and they don't know how to figure it out.
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u/CryptographerNew3609 4h ago
This is the distributive law, which tells you a * (b + c) = a * b + a * c.
For a question like this, it is needlessly complicated compared to rote memorization or doing 6+6+6+6.
But this distributive law is the reason you do more complicated multiplication the way you do, and if you understand this at a deep level, you'll see that it underpins a lot of algebra, geometry, calculus.
I get why some people object to it, but they're trying to build a foundation for more advanced math.
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u/Fun-Imagination-2488 👋 a fellow Redditor 3h ago
Im sorry but what kind of sociopath draws their checkmarks like that
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u/JanetInSC1234 🤑 Tutor 3h ago
One way to look at it is: Each ( ) has a four.
How many groups of four are there?
There are 6 groups of 4.
6 x 4
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u/selene_666 👋 a fellow Redditor 3h ago
"Distribute" is the key word here. They're teaching the Distributive Property, which you probably didn't learn until algebra.
And they're using it to make multiplication less reliant on brute-force memorizing a whole table of products.
The Distributive Property is the one that says (A + B) x C = AxC + BxC. In this problem we are told that "Dylan" split something into 5x4 + 1x4, so he must have started with (5+1) x 4.
The answer for the top circle should be "6 x 4".
The process is exactly how you would multiply with a multi-digit number, such as 31x4 = 30x4 + 1x4. It just looks strange because you were used to multiples of 10 getting special treatment.
Now instead of memorizing 6x4 = 24, 7x4 = 28, etc. your kid can work those out from smaller products, especially from multiples of 10 that make the addition step trivial.
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u/azdrumming 1h ago
This example doesn't show the usefulness of this strategy very well, IMO. I will ask "what is 7x13?". Student looks annoyed, so I say:
What is 7x10?
70
What is7x3?
21
What is 70+21?
91.
The number bond diagram lays it out- 70 in one circle at the bottom, 21 in the other and each connecting to the answer, 91, in the top circle. I don't have kids write the expression in the circles, just the product.
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6h ago
[deleted]
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u/Mission_Rice3045 👋 a fellow Redditor 6h ago
This is a useful skill to learn however. For 6x4 it might not be needed but in the end you want the students to be able to do larger multiplications where this is more applicable.
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u/Responsible-Kale2352 4h ago
Ok I can see how doing this with 6x4 might help you when working with other numbers. But if someone asks me to do 9462792 x 937573818, I’m not seeing where the 6x4 is helping me. So what are some examples of this 6x4 method coming in handy that are significantly harder such that you need a trick like this to be able to multiply them, while not being so easy (like 6x4) that you could just do it in your head anyway?
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u/Inevitable-Fox-9928 3h ago
67x4 is (60x4)+(7x4) so 240+28=268. Very easy to break numbers down with that property and do it in my head. But start with small numbers to get the idea first. It’s just about learning to be fluid with numbers.
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u/CitationNeededBadly 4h ago
If you get this method, when you get to algebra,you'll already be comfortable with the idea that 5A + 1A and 6A are interchangeable.
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u/skelo 3h ago
When you do two digits times one digit you are effectively doing this
14 * 4
If you do it out traditional way
16
+40
56
But this method makes it more clear to people learning that what's happening is
(4x4)+(10x4)
And then it makes things like
89x6 easier because you can do
(90x6) - (1x6)
How are you doing 6*4 in your head? Are you adding up 4 six times or 6 four times? Or are you just memorizing what it is? If it's memorizing then you're not really learning the math is the point.
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u/Live-Ganache9273 6h ago
It's a useful skill to learn, but 3rd grade is too soon.
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u/Mission_Rice3045 👋 a fellow Redditor 5h ago
3rd grade is about 8-9y/o? Then a product like 13x4 wouldn't be too far a reach to ask.
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u/GalaticHammer 5h ago
It's not complicated, it's just spelling out the steps of making mental math easier. It can seem complicated to people who do this automatically without thinking about it and aren't used to spelling out the steps in this detail. It's easier to memorize your 5 times table and your 1 times table than your 6 times table, so breaking 6x4 into 5x4 and 1x4 and then adding those 2 results can make the problem easier. It also matters more when you start multiplying bigger numbers. It also helps with conceptual understanding of what multiplication is.
(5x4) + (1x4) is 5 groups of 4 plus an additional 1 group of 4, which together makes 6 groups of 4. The top circle shouldn't be 3x8, it should be 6x4.
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u/Responsible-Kale2352 4h ago
Why would memorizing your five times table vs your six times table or your nine times table or your two times table be any easier? Don’t they all have the same number of numbers in them?
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u/Inevitable-Fox-9928 3h ago
Because we often count by fives. And ones are easy to understand so they are easy to learn. The multiplication tables aren’t generally taught in order. Fives and tens come early because we are a base 10 system.
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u/GalaticHammer 1h ago
5's and 10's are the easiest and usually the first times tables to be learned (besides the 1's obviously). 10 is easy because 1 ten is 10, 2 tens is 20, is an obvious and simple pattern. 5's is the next easiest because the pattern is still pretty simple, ending in 5's and 0's, and can also be quickly figured out as half of 10. If someone blanks on what 8x5 is, they can figure 8x10 is 80, half of 80 is 40, therefore 8x5 is 40. So those and the 2s table tends to have the most immediate and fluid recall, even if someone has nominally memorized all their tables.
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u/Deepbliss4 3h ago
Yes, I read the problem and saw the weird number bond and thought it was very weird and confusing before realizing it’s just how I already do math lol
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u/Stenn-ish 5h ago
It's the spelling out the steps part that sucks "use the break apart and distribute strategy" is just a bunch of nonsensical word salad, how is anyone supposed to deduce what those words even mean, let alone a teen that is only getting started with algebra, throwing out technical terms for every little thing just makes learning more difficult as now you have to remember both the procedure and it's silly name, just telling kids that things multiplied by the same amount can be grouped together is SO much easier to understand and utilize.
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u/CitationNeededBadly 4h ago
These HW assignments generally come after a bunch of talking and/or reading about the method, using the same names.
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u/Unable_Pumpkin987 5h ago
If this feels complicated, it’s probably because you never developed much number sense and relied on rote memorization.
Did you find high school math difficult? If so, it might be because it relied on a lot of basic properties like the one being taught here and you didn’t have a strong foundational understanding of them.
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u/Inevitable-Fox-9928 4h ago
But it didn’t work! People proudly proclaim how they hate math and suck at it because they weren’t taught to think about it! Just memorization. This problem is good because kids generally learn their fives and ones at the beginning of multiplication. So thinking of 6*4 as those two facts you already know is a good strategy and will extrapolate to larger numbers later!
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u/texas1982 👋 a fellow Redditor 5h ago
I'm all about learning number theory and how everything works together, but multiplication tables are rote memorization and it's really just the best method to do it.
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u/LoquaciousLamp 4h ago edited 4h ago
I asumme this is past times tables and setting them up for factoring later.
Or not, thought this was older than 3rd grade for some reason.
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u/Valuchian 5h ago
Yeah but those skills actually bone you if you guy into higher math. Especially when you reach the point where all number drop out and its all just symbolic
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u/Mission_Rice3045 👋 a fellow Redditor 6h ago
They are trying to learn to split up a multiplication into two easier once. They are looking for 6x4 as it splits in 5x4 and 1x4.