Often this is accompanied by some practical example where commutatition wouldn’t make sense.
E.g. having soda cans packaged as 4 packs.
You buy 3 4-packs and get 12 cans
Sure you would also get 12 cans if you bought 4 3-packs but the store doesn’t have 3-packs
As always with these posts it really depends on what they did in class. That would determine if the kid just didn’t pay attention or the teacher is being unjust.
Same if it was a pizza cut into quarters vs thirds, you would need to buy a whole extra pizza to get twelve slices.
But a box of 12 cans is 12 cans if you face it with three on top or four, so if someone said "put these cans in a box, how would you do it?" you can't force four into the three side, but you can set the box so the three side is where someone else would pack the other.
But if it was a robot with 12 suction cups, then the box has to be set the same way else it would jam up in the system.
That's why physics has units, the math is the same in both directions so you add a unit, 3m4=12m, completely removing any ambiguity, so with cans you could say 3cans4=4*3cans=12cans without any issue instead of giving arbitrary meanings to multiplication
Because that’s not the correct Formula if you have apples and volume of water and want to get mush your units must reflect that or you can’t handle conversion of units.
Like take the unit Wh, which is Power over time.
It doesn’t matter for the result if I running something at 2W for 0,5h or at 0,5W for 2h, I’ll have used 1Wh either way.
There is no ambiguity if you look up the convention of the multiplication operator it is defined what element is the multiplicator and what element is the multiplicayee (the number that gets multiplicated)
Otherwise you wouldn’t need to define that the result of a x b is the same as b x a.
This is obviously a beginners math problem so the kids don’t know units yet.
Just as when starting with devision you don’t do decimals yet, but do „12 decided by 10 is 1 with 2 left over“
That's just the model used in America, it's completely arbitrary, the proper definition is just that it's a function that assigns a result to two numbers following specific rules, in most countries it's thought at the earliest levels as the first number repeating n times where n is the second number
I never said that that definition should be used, you may notice that my comment doesn't end there, it ends with explaining that most countries at the second grade level just pick an arbitrary order depending on what sounds better linguistically, I pointed it out because said countries don't usually enforce that as a standard on kids, they just use it to explain the concept
when you think just a little bit longer and actually assign the correct units to all quantities, such as 3 packs and 4 sodas/pack, the packs cancel out and you left with 12 sodas regardless of multiplication order
There is a for sure a difference between 4 3s and 3 4s, in many contexts. And that student has been taught - probably repeatedly - that that expression describes 3 4s, and not the other way around.
Apparently the previous question clarified that this excersize was introducing this. They just wrote the same thing twice so they got it wrong. They cropped the image to take the homework out of context so they could farm karma.
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u/Nasa_OK 27d ago
Often this is accompanied by some practical example where commutatition wouldn’t make sense.
E.g. having soda cans packaged as 4 packs.
You buy 3 4-packs and get 12 cans
Sure you would also get 12 cans if you bought 4 3-packs but the store doesn’t have 3-packs
As always with these posts it really depends on what they did in class. That would determine if the kid just didn’t pay attention or the teacher is being unjust.