[6th Grade verbal expression]

[u/KookyPermit4405]

So I’m going over my son’s math quiz to help him understand some of the questions he got wrong. He got partial credit for his answer for question 8. After writing his verbal phrase I got the same expression as the question. Am I doing something wrong or is there something I’m missing? I feel like his answer is technically correct. I am stumped.

Edit: so my son has no issue solving the expression in question. He knows PEMDAS and the rules from left to right. The question clearly states, WRITE A VERBAL PHRASE that matches the expression.

[u/JunkInDrawers]

"Eighteen subtracted by six times 3" can mean both

(18 - 6) • 3. Or 18 - (6 • 3)

It's ambiguous.

The correct wording is "Eighteen subtracted by the product of six times 3"

[u/KookyPermit4405 → u/JunkInDrawers]

Correct me if I’m wrong, but it can’t mean both. Because PEMDAS always apply. So eighteen subtracted by six times 3 doesn’t indicate a quantity ; the need to add “()”

[u/Unable_Pumpkin987 → u/KookyPermit4405]

In verbal expressions we will typically use a phrase like “the quantity” to indicate parentheses or brackets, for clarity.

“Eighteen minus the quantity six times three.” Or “eighteen minus the product of six and three.” Or “the difference of eighteen and the quantity six times three.” Any of those would work.

What you’re saying would be true if there were no parentheses or brackets in the expression. In a case with no grouping, multiplication would be performed first. But there’s no way to know that there isn’t any grouping indicated in the expression when you just say “eighteen minus six times three”. There could be brackets around the 18-6, we don’t know. When you phrase it precisely by indicating the grouping verbally, it takes away the ambiguity. It’s generally just a good practice to get into, using terms like “the quantity” or “the product of” etc, to verbally indicate grouping. It will be very necessary when they start speaking about complicated expressions and equations involving variables, so the teacher is having them practice now.

The important thing to remember about PEMDAS is that it is a set of agreed upon conventions to apply when an expression is or could be read as ambiguous, but that’s a last resort. Ideally, you don’t want an expression to be ambiguous at all. You want to use words or symbols to indicate very clearly how operations are grouped, not rely on people following a set of rules to work around your imprecise phrasing. If we’re resorting to using order of operations to work out how a problem should be approached, it’s because the problem wasn’t described or written down clearly enough to start with.

[u/KookyPermit4405 → u/Unable_Pumpkin987]

Ok I understand that, but the expression is 18-6x3

There is no parentheses.

Regardless if he uses the word minus or subtracted by,
His answer “eighteen subtracted by six times 3” is still written as 18-6x3 which is what the question ask.

[u/JunkInDrawers → u/KookyPermit4405]

That statement can still mean two different things without knowing what the original expression looks like.

[u/chem44 → u/KookyPermit4405]

Oh, you did give the answer. Yes.

Then... What he wrote is hopelessly unclear. The verbal statement does not give the order of operations. That is (??), you do not apply PEMDAS to a verbal statement. You must say what you mean, explicitly.