Teaching Notes 1.5: Simplifying Expressions with
Grouping Symbols and Exponents
Expressions that involve exponents, parentheses, or several operations are often confusing to
students. To ensure that your students become proficient in simplifying such expressions,
reinforcement of the order of operations is essential.- Explain that some expressions contain exponents. Depending on the abilities of your
students, you might find it helpful to review 1.4: ‘‘Using Positive Exponents and Bases
Correctly.’’ - Explain to your students that the order of operations may become confusing when they must
compute using multiple operations. Suggest that students use the acronym ‘‘Please excuse
my dear Aunt Sally’’ to help them remember the order of operations for expressions with
grouping symbols and exponents:- P stands for parentheses (or grouping symbols).
- E stands for exponents.
- M stands for multiplication.
- D stands for division.
- A stands for addition.
- S stands for subtraction.
Note that although multiplication precedes division in the acronym, these operations must
be completed in order from left to right. Therefore, there will be times students will divide
before multiplying. Similarly, addition precedes subtraction in the acronym, and these oper-
ations must also be completed in order from left to right. There will be times students will
subtract before adding.- Review the steps for using the order of operations and the examples on the worksheet with
your students.
EXTRA HELP:
Suggest that students rewrite each problem after they have completed an operation. This will help
them organize their work and avoid mistakes.ANSWER KEY:
(1) 13 (2) 112 (3) 43 (4) 19 (5) 46 (6) 26 (7) 3 (8) 3
------------------------------------------------------------------------------------------
(Challenge) 7
------------------------------------------------------------------------------------------10 THE ALGEBRA TEACHER’S GUIDE