Teaching Notes 1.3: Simplifying Expressions with Nested
Grouping Symbols
If an expression has nested grouping symbols—one or more sets of grouping symbols inside
another—some students ignore the innermost symbols. They then go on to simplify the
expression incorrectly.- Explain that grouping symbols help to indicate what operations to do first when solving
expressions. - Explain that when a grouping symbol is set within another, the expression within the
innermost grouping symbol must be simplified first. Provide the following example:
12 −(5+(3×2)). Explain that there are two sets of parentheses in this problem. Oper-
ations in the inner set of parentheses must be completed first and then work is completed
outward. Demonstrate this by first solving 3×2 and replacing the answer, 6, in the new
problem: 12−(5+6). The correct answer is 1. - Emphasize that students should always work outward from the nested grouping symbol,
following the order of operations. Depending on your students, you may want to review the
order of operations:- Multiply and divide from left to right.
- Add and subtract from left to right.
- Review the steps for simplifying and the examples on the worksheet with your students. Note
the use of grouping symbols and particularly the innermost grouping symbols.
EXTRA HELP:
Parentheses, brackets, and fraction bars are examples of grouping symbols.ANSWER KEY:
(1) 24 (2) 22 (3) 120 (4) 80 (5) 91 (6) 220 (7) 4 (8) 3
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(Challenge) 4
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