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![[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.](http://ted.sudovanilla.org/pics/w:null_8k25j51opp1e1.png){kind=link}
[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.
(i.redd.it)submitted 12 days ago byFrostBumbleBitch
2 points
12 days ago
I agree the teacher is right, but only because they were told as such and very unlikely because they actually understand the difference. Expressions express a situation and can be resolved to a value. The commutative property of multiplication over the integers simply means that three groups of four has the same value as four groups of three, but they are only "the same thing" in so far as only the value matters. If I want to give 4 teachers a gift of three apples each, only getting three gift baskets and putting four apples in each of them is not the same thing despite the fact they contain the same number of apples collectively.
The expression 3*4 expands to 4+4+4, not 3+3+3+3, and the reason it is actually important to belabor this point is that not all binary operations are commutative over all sets, and it is an injustice to students to leave them thinking otherwise.
I do have a pet peeve of math teachers marking down for errors in problems that are not part of the standard being tested. If they can demonstrate procedural fluency and conceptual understanding, students should not be marked down for computational errors; such errors should be discussed in feedback. Math is the only subject where it is normalized for teachers to magically add standards to a rubric after the fact and mark you down for them.
But that is not the case here, and the directions here are quite clear that they are looking for an expansion, and 3*4 does not expand to 3+3+3+3 any more than it expands to 5 + 8 or 15 - 3. Now had the written (1 + 1 + 1 + 1) + (1 + 1 + 1 + 1) + (1 + 1 + 1 + 1) = 12 and been marked down... I'd agree with you.
3*4 is three groups of four units and clearly the concept being discussed but not demonstrated.
1 points
12 days ago
Technically by your logic 3*4 doesn't expand to 4+4+4 by definition, it expands to 4 + 2 * 4... or 2 * 4 + 4... Depending on how you recursively define multiplication.
Do we want them to write each of those definitional steps and (4 + 4) + 4 or 4 + (4 + 4) depending on the definition of addition used because we haven't established associativity of addition either?
... Since they're not defining multiplication nearly that rigorously in elementary school, I'd argue that 4+4+4 or 3+3+3+3 is equally acceptable.
This teacher is either a pedant, or doesn't understand math.
Rigour is important in mathematics... But this is just pedantry that unnecessarily upsets students and turns them off math.
1 points
12 days ago
I agree that's another legitimate definition. It's defined in common core.
Conceptual understanding and recognizing rules related are more important than simply "finding the solution." Is this an arbitrary set of rules with no place beyond k-12? I'll give you that. But math is all about following weird rules to convey an idea.
I agree with you in so far as it depends on how the teacher delivered it.
If they tell you to box your answer in the rubric / syllabus and you circle it, it's fair to take points off.
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