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Directed Learning Activity (DLA)
Order of Operations
M002.1
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Directed Learning Activity – Order of Operations
Description: In this Directed Learning Activity (DLA), you will discover how to simplify an
expression using order of operations.
Prior Knowledge: In order to complete this DLA, you will need to know how to perform operations
with integers.
Adding and Subtracting Integers
−𝟐 𝟑
−𝟓 − 𝟒
𝟕 − 𝟏𝟎
1
-9
-3
Multiplying and Dividing Integers
−𝟖
−𝟐(𝟑)
− 𝟓(−𝟐)
𝟒
-6
10
-2
−𝟏𝟖
𝟓 − (−𝟐)
−𝟔
5+2
-3
7
Directions: Please read the examples and answer the questions that follow carefully – and in order.
Please do not skip ahead. PEMDAS is not correct, and it should not be used. If you have a question,
please ask for help.
After reading the examples, spend some time thinking about what is being presented. When
you feel you understand the examples, try to answer the practice questions.
When you are finished, spend some time thinking about this activity and complete the
reflection section. Remember that this is a learning activity, and you are not being graded.
Part One: Understanding Order of Operations
Order of operations is the order in which mathematical operations must be performed to simplify
an expression. It is:
Order of operations
(
)
) [
] {
} |
| √
1. Symbols of Grouping: (
(
)
2. Exponents
3. Multiplication or Division, FROM LEFT TO RIGHT
4. Addition or Subtraction, FROM LEFT TO RIGHT
Here is an overview of how the order of operations is executed:
4  4  6  4  32  5 1) Symbol of Grouping
(
)
(
)
2
(
)
28  4  3  5
2) Exponents
28  4  9  5
795
63  5
68
9
3) Multiplication or Division, FROM LEFT TO RIGHT.
7
4) Multiplication or Division, FROM LEFT TO RIGHT.
63
5) Addition or Subtraction, FROM LEFT TO RIGHT
63+5
2
Before we attempt a long problem, let’s start at the bottom or last step: Addition and Subtraction.
Part Two: Adding and Subtracting, FROM LEFT TO RIGHT
Addition and subtraction must be performed FROM LEFT TO RIGHT as they appear.
Between each of our numbers, there is an operation; we perform each of the addition or subtraction
operations from left to right.
−
−
− (− )
− (− )
(We perform the operations one at a time, from left to right, so 3+5=8)
(The next two numbers, from left to right, are 8-11= -3)
− − (− )
(Then, from left to right, we have -3-(-4) =-3+4 =1)
(Finally, 1+7=8)
If you notice, the operations are performed:
i) proceeding one at a time,
ii) rewriting the expression after each operation is performed, and
iii) after performing the operations, the work resembles an upside down triangle.
Simplifying the problem in this fashion helps us to stay organized and allows us to determine the
next operation to be perform.
Simplify: −
− (− )
Answer: 12
Part Three: Multiplying or Dividing, FROM LEFT TO RIGHT
Multiplication and division must be performed FROM LEFT TO RIGHT as they appear.
Between each of our numbers, there is an operation; we perform each of the multiplication or division
operations from left to right.
Example 1:
, so
Example 2:
( )
( )
( )
( )
, so
( )
8
Simplify:
( )
Answer: 9
3
Part Four: Working With Exponents
Exponents tell us how many times to multiply the base by itself.
Example 1:
An exponent of 5 tells us to multiply the base by itself 5 times.
32
Here are four examples of other types of exponent problems:
Example 2:
Example 3:
The negative is inside parentheses, so it
The negative is not inside parentheses, so
it is not included in the multiplication.
(− )
must be included in the calculation.
(− )(− )
−
−
−
Example 4:
Example 5:
If the base is not zero and has an
exponent of zero, then the answer is 1.
−
−
1
Simplify: ) (− )
The negative is not inside parentheses, so
it is not included in the multiplication.
)−
Answers: a) 16
b) -16
Part Five: Putting It All Together
So far we have taken a look at:
2. Exponents
3. Multiplication or Division, FROM LEFT TO RIGHT.
4. Addition or Subtraction, FROM LEFT TO RIGHT.
Here we have an example with exponents, division, multiplication, subtraction, and addition.
−
(− ) − (− )
−
(− ) − (− ) first with this
Exponents go
(− ) − (− )
−
− (− )
−
−
−
− (− )
problem.
−
−
−
Multiplication or
Division from left to
right is next.
(− )
−
Then,
Addition or
Subtraction from left
to right is last.
− −
−
Then −
−
− (− )
−
−
Simplify: (− ) −
Answer: 0
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Part Six: Understanding Symbols of Grouping – Basics
Symbols of grouping are used to group numbers and operations together.
(
)
) [
] {
} |
| √
They include (
(
)
Symbols of Grouping are the first step in order of operations.
The order of operations
) [
] {
}|
1. Symbols of Grouping: (
|
√
(
)
(
)
2. Exponents
3. Multiplication or Division, FROM LEFT TO RIGHT.
4. Addition or Subtraction, FROM LEFT TO RIGHT.
Example:
(
−
)
The symbols of grouping, parentheses in this case, create a little
order of operations problem.
( )
−
2. Exponents
−
3. Multiply or divide from left to right
−
Simplify:
(
4. Add or subtract from left to right
) −
Answer: 47
Part Seven: Understanding Symbols of Grouping – Fractions
Here is another type of grouping symbol, fractions:
(
)
(
)
The numerator and denominator have assumed parentheses, making
them groupings.
(𝟗 𝟑)
𝟗 𝟑
𝒓𝒆𝒂𝒍𝒍𝒚
𝒍𝒐𝒐𝒌𝒔
𝒍𝒊𝒌𝒆
𝒕𝒉𝒊𝒔
(𝟐𝟑 − 𝟓)
𝟐𝟑 − 𝟓
Example:
−
We simplify the numerator and denominator separately.
Top
Bottom
3
−
4
−
3
Simplify:
−
Answer: -2
5
Part Eight: Understanding Symbols of Grouping – Radicals and Absolute Values
Here are two other types of grouping symbols, absolute values and radicals: |
Example 1:
− |− − |
− |− |
−
The symbols of grouping –
absolute values, in this case –
group the information inside
the absolute value.
−𝟒 − 𝟓
Example 2:
− √
− √
−
|
√
The symbols of grouping –
radicals, in this case –
group the information inside
the radical.
𝟗 𝟏𝟔
−
−
−
−
Simplify: a) |
| − |−
|
b) − − √
−
Answers: a) -11
b) -11
Part Nine: Reflection
a) Why did you (or your instructor) decide that completing this activity was a valuable learning
experience?
b) Name one thing that you understand better about the order of operations as a result of
completing this activity.
c) Name one thing that you still do not understand about the order of operations.
d) What are the order of operations?
STOP. Please go over your work with a tutor at this time.
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M002.1 – Order of Operations
__________________________________________________
PRINT STUDENT NAME
_______________________
STUDENT #
Tutor Feedback:
________The student completed the entire activity.
________The student attempted to answer every question.
________The student demonstrated an understanding of the order of operations during the discussion
of his/her work.
Additional Comments:
____________________________________________________________________________________
____________________________________________________________________________________
____________________________________________________________________________________
____________________________________________________________________________________
___________________________________________________
PRINT INSTRUCTOR/TUTOR NAME
___________________
DATE
INSTRUCTOR/TUTOR SIGNATURE
STUDENT – DO NOT FORGET TO TURN THIS SHEET IN
AT THE FRONT DESK!
You may not get credit for completing this DLA if you fail
to leave this sheet with the front desk receptionist.
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