1/26/17 Week 3 Thursday mindstretchers:
The vocabulary of expressions/
Order of operations/ Evaluating expressions
1) Eduardo said, “Order of operations is easy. All you do is follow PEMDAS in order:
parentheses, exponents, multiplication, division, addition, and finally subtraction.”
a. In what way is Eduardo on the right track?
b. Is there anything you’d change in his explanation?
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2)
[−12 −(23 −42 )] +1
16−6+10
=
(Try this one both by hand and with the calculator.)
3) Eleanor evaluated x  x2 for x = –3 on the calculator and got 12. Jacob did it by
hand and got –12. Unfortunately, both are incorrect. They need your help.
a. What do you get?
c. What did Eleanor probably do to get her answer?
b. Where did Jacob likely go wrong?
4) Pick whichever is most unfamiliar to you—order of operations or evaluating
expressions—and do a handful of traditional practice exercises on them.
There’s an online worksheet for both. There’s also a book option for evaluating
expressions. See the yellow assignment sheet.
D. Stark 1/10/2017
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1/26/17 Week 3 Thursday mindstretchers:
The vocabulary of expressions/
Order of operations/ Evaluating expressions
KEY
1) Eduardo said, “Order of operations is easy. All you do is follow PEMDAS in order:
parentheses, exponents, multiplication, division, addition, and finally subtraction.”
a. In what way is Eduardo on the right track?
Eduardo is right that PEMDAS helps you follow operations in the proper
order. And you do start with parentheses (at least those with stuff inside you
can do—not parentheses that mean multiplication or that just highlight a
negative number). Next, you do handle exponents (and roots.)
b. Is there anything you’d change in his explanation?
Yes, Eduardo fails to point out that multiplication and division have the same
priority status. The same is true for addition and subtraction. There are 4
levels, not six, in PEMDAS.
If the operations were boarding an airplane, parentheses with stuff inside
would board first, like parents with small children, such parents always
having extra stuff to do to get the kids settled. Then exponents, the elite first
class passengers, would board. Then the businessmen & businesswomen—
multiplication and division—would board. It’s not the men first and then the
women or vice versa. It’s whoever is first in line—the one furthest to the left—
who goes first. Finally, the economy class of addition and subtraction
boards. Again, within this priority class, it’s not addition who automatically
goes first. It’s whoever is first in line, that is, whoever is the furthest left.
D. Stark 1/10/2017
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2
2)
[−12 −(23 −42 )] +1
16−6+10
𝟐
[−𝟏𝟐 −(𝟖−𝟏𝟔)] +𝟏
𝟏𝟔−𝟔+𝟏𝟎
𝟐
[𝟕] +𝟏
𝟏𝟔−𝟔+𝟏𝟎
=
=
(Try this one both by hand and with the calculator.)
𝟐
=
[−𝟏𝟐 −(−𝟖)] +𝟏
𝟒𝟗+𝟏
𝟏𝟔−𝟔+𝟏𝟎
𝟏𝟔−𝟔+𝟏𝟎
𝟓𝟎
=
𝟏𝟔−𝟔+𝟏𝟎
=
=
[−𝟏−(−𝟖)]𝟐 +𝟏
𝟏𝟔−𝟔+𝟏𝟎
𝟓𝟎
𝟓
𝟏
𝟐𝟎
=
𝟐
or 𝟐
=
𝟐
You wouldn’t need to show all these steps. I’ve just shown them so you can see
each little move.
You’ll need to do the numerator and denominator separately on the calculator as
well as by hand. Generally speaking, you can do fractional order of operations
all at once on the calculator if you remember to put parentheses around the
denominator so you divide by the whole denominator and not just by the first
term. However, this one is too long, so the calculator chops off part of the
problem and can’t do it all at once.
3) Eleanor evaluated x  x2 for x = –3 on the calculator and got 12. Jacob did it by
hand and got 6. Unfortunately, both are incorrect. They need your help.
a. What do you get? x  x2
(3)  (3)2 [Use parentheses so the  doesn’t get lost.]
=39
= 6
b. What did Eleanor probably do to get her answer?
Eleanor probably plugged things into the calculator without remembering to use
parentheses around the 3.
 3  32 = 12
c. Where did Jacob likely go wrong?
Jacob likely forgot the negative in front since x is already a negative number.
3  (3)2 = 3  9 =  12
4) See the back of the book for book answers. For online handouts, see the
answer keys at the end of the online worksheets or check the printout in the
folder on the board.
D. Stark 1/10/2017
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