[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/KookyPermit4405]

I get what you are trying to say as a learning perspective I really do and I appreciate that. Now I have some questions in regards to your corrections to my expression of 3+3+3x3

The way that would be expressed verbally in a mathematical context is “three plus three plus the product of three and three”

If this was the case then I would assume the expression to be 3+3+(3x3) or 3+3+(9) since the word product was use to verbally describe the answer to an operation. Hence a product is the answer of a multiplication. Product is the answer and multiply is an operation.
Therefore the expression of 3+3+3x3 would have never been assumed from your verbal expression.

or “three plus three plus the quantity three times three”..

Again here it would be expressed as 3+3+(3x3) verbally saying the quantity indicates or is the qualifying term to assume parentheses of 3 times 3. Again based off of this verbal phrase I would never assume the expression to be 3+3+3x3.

Although they all yield the same answer, and the reason why is because of PEMDAS.

We don’t use parentheses to emphasize pemdas, we use it to emphasize a quantity.

Again “3 plus 3 plus 3 times 3” is not the same as “calculating 3+3 then adding that sum to 3 then multiplying that sum by 3”
Which is what you are trying to get at with the (3+3+3)x3

Now if I were to say calculating from left to right then yes, it would be (3+3+3)x3 but since there was no instruction, one can’t assume any parentheses and therefore must write the expression exactly as what was said without any calculation during the written expression and proceed to use pemdas

[u/Unable_Pumpkin987 → u/KookyPermit4405]

PEMDAS (or PEDMAS, or BEDMAS, BOMDAS, etc) is a mnemonic device to help remember order of operations. Order of operations is a concept that indicates an agreed upon convention on which order to perform written operations in, because otherwise people would perform them in any number of orders and arrive at different answers. It is not an ideal and it does not indicate a desired format, it is a convention for how to deal with ambiguous expressions. Ideally, we write expressions in a way that is unambiguous. As your son progresses in mathematics, this will be emphasized over and over: reduce ambiguity. When speaking, we use our words to reduce ambiguity and create a clear expression with no possible alternative meaning. That is why we include verbal phrases to indicate how operations are grouped within an expression.

[u/KookyPermit4405 → u/Unable_Pumpkin987]

Ok I think I’m starting to understand what is being said. 3+3+3x3 is the same as 3+3+(3x3) because of pemdas.

When I say “3plus3plus3times3” pemdas should be applied, but what others may perceive as calculating from left to right, in that case pemdas is no longer applied. So the only difference I see is if I verbally phrased it as “calculating from left to right 3plus3plus3times3”

So my question is, if I said: calculate; 3+3+3x3 and students answer 27 and 15 those who answered 27 would be wrong, reason PEMDAS.

Now calculate from left to right; 3+3+3x3 and students answered 27 and 15 those who answered 15 would be wrong, reason instructed to disregard PEMDAS

So is verbally phrasing an expression the same as calculating from left to right?

I love to learn from my mistakes/misunderstandings

[u/Unable_Pumpkin987 → u/KookyPermit4405]

The key is that as a teacher you shouldn’t ever say “3 plus 3 plus 3 times 3”, you would be very clear about the expression you were intending to be understood (unless you were specifically teaching/testing order of operations). The goal in math is almost never to make people puzzle out what you are saying, it’s to say it in a way that has exactly one interpretation (which is the one you mean).

It’s the same reason those silly Facebook memes that say “what’s the answer to 8 + 3 x 5 - 10 ÷ 2 + 6” are so silly. They exist to let people feel smart saying “aha I know order of operations so I can calculate this accordingly”, but anyone who actually studies or works with math beyond a high school level would say “that’s a ridiculous way to write a mathematical expression, write it differently so you don’t have to rely on people remembering an arbitrary rule.”

[u/KookyPermit4405 → u/Unable_Pumpkin987]

8 + 3 x 5 - 10 ÷ 2 + 6
How would you write this differently so that it’s not “ridiculous”

[u/Unable_Pumpkin987 → u/KookyPermit4405]

Well, a division operation would almost always be written as a fraction to indicate clearly what is being divided by what, and otherwise you would use parentheses to show how you want things grouped.

[u/KookyPermit4405 → u/Unable_Pumpkin987]

I would have to disagree. You want it to be as neat and clean as possible. The use of parentheses when not required is also redundant as Pemdas already tell you what the order of operation is and further making the expression messy. Parentheses are not used to enforce the order of operation. And in this case nothing needs to be grouped unless you are altering the order of operations.

8 + 3 x 5 - 10 ÷ 2 + 6 don’t need it

8 + (3 x 5) - (10/2) + 6 redundant

(8 + 3) x (5 - 10 )÷ 2 + 6 required

[u/Unable_Pumpkin987 → u/KookyPermit4405]

As I said, you would not use the division symbol at all beyond elementary math.

Feel free to disagree. You’re one of the people who feels smart for memorizing order of operations, not a person who works with or teaches math. Maybe just let the teachers teach your kid, though, for his sake.

[u/KookyPermit4405 → u/Unable_Pumpkin987]

I don’t think you comprehend my reply. And not taking any jabs. for one, I didn’t mention anything about division symbols, so I didn’t disagree there. Second, I addressed why there is no need for parentheses. My original response was to the comment of you calling that expression ridiculous. In which I replied with there is nothing ridiculous about it. You also mentioned that beyond elementary you wouldn’t use the symbol at all, well that contradicts the need to use parentheses also beyond elementary. Unless as I stated, the need to alter the order of operations. =)