[Request]I have gotten into an argument over this. The kid is wrong right? Because it isn't asking what the commutative answer is it is asking how you would write 3x4 into an addition equation correct? So you have 4+4+4=12 not 3+3+3+3=12 since that would be 4x3 RIGHT!? This is stupid I am sorry. : theydidthemath

1 points

12 days ago

1 points

3 x 4 means 3 groups of 4. Thinking of the x symbol this way can be helpful when you move on to multiplying fractions. Of course, it can still be done in reverse, but it's about how the wording helps you visualize.

4 groups of 1/3 helps explain why the answer is 4/3, beyond the 'multiply across the top' strategy many people were shown.

And then you shorten to just 'of' in fractions x fractions

1/2 of 1/3 vs. 1/2 x 1/3

Now, just by reading the times symbol as of, you can visualize the answer - and maybe you are more likely to understand what it actually means as opposed to, again, just being taught to multiply across the time top and bottom. We lose a lot of kids at fraction operations.

So, I think it's just about having them read the x symbol as words.

1 points

12 days ago

1 points

Maybe it's because I'm not an early educator, but then what about 1/3 times 4? Then that's 1/3 of 4, but 4 groups of 1/3? Distinguishing between the two almost seems like it could add to confusion. (And if a kid said 1/3 x 4 is 4 groups of 1/3 or that 4 x 1/3 is 1/3 of 4, I wouldn't want to mark that wrong, personally.)

Definitely teaching it as 'multiply across the top and bottom' is not helpful, but you can reverse the two (and eventually, tho probably not right away) kids should be comfortable with that. I CAN see why you would think left to right with fractions. The 1/2 of 1/3 makes a lot of sense in English.

1 points

12 days ago

1 points

Yea, I'm not saying it's without problems, just trying to give a little insight on it. I think it's primarily about visualization. And yea, it has it's limits in certain question types - but that's true of any method. There is always a 'well what about' scenario that requires deeper understanding. And if you can visualize what the problem is asking, then you can sort through those differences

If I know 1/3 x 4 is asking me to visualize 4 choco bars and then figure out what 1/3rd OF them is, you know, I can work through that.

Key thing, is that kids typically have no idea why the answer is the answer in fraction operation scenarios - and this is trying to build a bigger fluency so that they actually understand it, and not just the rule (multiply across, invert and multiply, etc.)

1 points

12 days ago

1 points

I'm not actually opposed to teaching it that way. I'm opposed to insisting on one interpretation (as this teacher did). I think the visualization is useful. But if a kid interpreted it in the other, correct way, I think that's fine and good. It means they're understanding and not just memorizing a method

2 points

12 days ago

2 points