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6.EE.2c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2.
I’m trying to figure out what the last clause modifies. Is it:
1) [Perform arithmetic operations, including those involving whole-number exponents, when there are no parentheses to specify a particular order (Order of Operations)] in the conventional order.
or
2) Perform arithmetic operations, including those involving whole-number exponents, [in the conventional order when there are no parentheses to specify a particular order (Order of Operations).]
The second one implies that there is a conventional order that is used for problems with no parentheses (i.e. EMDAS). When parentheses are present, that order doesn’t change, we just think of the things in parentheses all as one group. In 2(8+7), the conventional order of multiplication coming before addition is still true, it’s just that we multiply the whole group (8+7) times 2.
Basically, it seems like that last clause is unclear based on its location.
If I boil it down, I think 6th graders are supposed to be able to use whole-number exponents and parentheses, but not at the same time. Yes?
So the question is whether “when there are no parentheses to specify a particular order” as an adverbial clause modifying the verb “perform” or an adjectival clause modifying the noun “order”? Since that noun occurs in the adverbial phrase “in the conventional order,” the second interpretation is quite awkward. If that had been the intended meaning it would have been better to write “in the order that is conventional when there are no parentheses …”. And, as you point out, this interpretation suggests that there is a special convention for problems with no parentheses, which you quite correctly debunk. So all in all I think the first interpretation is the most natural. There does remain some ambiguity, however. Are the parentheses to be absent from the entire expression in order for the standard to apply, or merely absent from the part of the expression where the matter of order is at stake? I think the latter interpretation makes more sense. That is, the standard expects students to interpret 5 + 2(8+7) correctly.
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