The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Teaching Notes 1.8: Writing Expressions Involving

Grouping Symbols

Some expressions describe operations as a sum, difference, product, or quotient. To write

expressions like these, students may have to include grouping symbols. Ignoring necessary

grouping symbols is a common error.

1. Discuss basic examples of expressions:
   
   
   • 3 times a number plus 2 can be written as 3n+2.
   
   
   • 3 times the sum of a number and 2 can be written as 3(n+2).
   
   
   
   


2. Explain that in the first example the number is multiplied by 3, then 2 is added. In the
   second example, the sum of the number and 2 is multiplied by 3.n+2 must be written in
   parentheses.


3. Emphasize that these two expressions have different values. For example, ifn=4, 3n+ 2 =
   14 and 3(n+2)=18.


4. Encourage your students to consider whether an expression refers to a quantity or only one
   number. Remind them that the words ‘‘sum,’’ ‘‘difference,’’ ‘‘product,’’ and ‘‘quotient’’ often
   signify that grouping symbols are needed.


5. Review the examples on the worksheet with your students.

EXTRA HELP:

Quantities must be written in grouping symbols.

ANSWER KEY:

(1)

n+ 12

5

(2)n+

12

5

(3)(4n)^3 (4) 4 n^3 (5)2(n−10) (6) 2 n− 10 (7)(4+n)^2 (8) 4 +n^2

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(Challenge)

x+y

2

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16 THE ALGEBRA TEACHER’S GUIDE