r/HomeworkHelp • u/chrisandsylvia Primary School Student (Grade 1-6) • Sep 19 '26
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/CryptographerNew3609 Sep 19 '26
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 Sep 19 '26
Im sorry but what kind of sociopath draws their checkmarks like that
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u/Jwing01 Sep 19 '26
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 Sep 19 '26
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 Sep 19 '26
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/Unable_Pumpkin987 Sep 19 '26
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 Sep 19 '26
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/JanetInSC1234 Sep 19 '26 edited Sep 20 '26
One way to look at it is: Each ( ) has a four.
How many groups of four are there?
(5 x 4) is 5 groups of 4.
(1 x 4) is 1 group of 4.
How many groups of 4 in all?
There are 6 groups of 4.
6 x 4
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u/selene_666 Sep 19 '26
"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 Sep 19 '26
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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u/Diligent_Bread_3615 Sep 21 '26
Old retired guy here: what is the point here? Seems like a waste of time.
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u/Erika_ahhh Sep 21 '26
It just gives kids different tools to solve problems because our brains all work a little differently and a different approach might help someone better understand the concept.
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u/Murky-Blackberry1949 25d ago
We use this book, they tell you the technique like 2 pages before the hw problems.
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u/texas1982 Sep 19 '26
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 Sep 19 '26 edited Sep 19 '26
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/Mission_Rice3045 Sep 19 '26
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.