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Evaluating Expressions with Parentheses and Brackets

written by: Donna Ventura • edited by: Carly Stockwell • updated: 5/28/2014

Students will evaluate numerical expressions with parentheses and brackets.

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    Lesson Objective: The lesson is aligned to the Common Core State Standards for Mathematics –5.OA.1–Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

    Materials Required: Calculator

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    Lesson Procedure:

    Using Order of Operations to evaluate numerical expressions with parentheses and brackets.

    The four basic operations in mathematics are add, subtract, multiply, and divide.

    To evaluate an expression with just one operation, we start at the left and go to the right. For example, to find the value of the numerical expression 3 x 6, start with the number 3 and multiply 3 with 6. The value of the numerical expression 3 x 6 is 18.

    When numerical expressions have more than one operation, mathematicians have agreed to follow the rules of Order of Operations.

    Parentheses - Do the operation in the parentheses first.

    3 x (5 - 1) Subtract 5 - 1 first.

    3 x 4 Therefore, 3 x (5 - 1) = 12

    Exponents - Do the power.

    3 + 22 Square 2 first.

    3 + 4 Therefore, 3 + 22 = 7

    Multiply or Divide - After the operations in the parentheses and the exponents, start from the left and go to the right and multiply or divide the numbers.

    3 + 5 x 2 Multiply 5 x 2 first.

    3 + 10 Therefore, 3 + 5 x 2 = 13

    Add or Subtract - After the operations in the parentheses, the exponents, multiply and divide, start from the left and go to the right and add or subtract the numbers.

    You can remember this by using this phrase…

    Please Excuse My Dear Aunt Sally.

    Find the value of each numerical expression.

    1. 5 + (3 x 7)

    2. 6 + 42

    3. 8 + 3 x 42

    Answers:

    1. 5 + (3 x 7) = 5 + 21 = 26

    2. 6 + 42 = 6 + 16 = 22

    3. 8 + 3 x 42 = 8 + 3 x 16 = 8 + 48 = 56

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    Individual or Group Work:

    Find the value of each numerical expression. Remember to use the rules of Order of Operation.

    1. 8 / 4 + 3 x 2

    2. 6 x 7 - 15 / 3 + 9

    3. 4 + (3 x 5) - 6

    4. 28 - (3 + 42)

    5. (15 - 3) / (3 x 2)

    Answers:

    1. 8 / 4 + 3 x 2 = 2 + 6 = 8

    2. 6 x 7 - 15 / 3 + 9 = 42 - 5 + 9 = 37 + 9 = 46

    3. 4 + (3 x 5) - 6 = 4 + 15 - 6 = 13

    4. 28 - (3 + 42) = 28 - (3 + 16) = 28 - 19 = 9

    5. (15 - 3) / (3 x 2) = 12 / (3 x 2) = 12 / 6 = 2

5th Grade Math Lessons on Pythagorean Theorem

Give your students a concrete understanding of the order of operations. Lessons are aligned to the Common Core State Standards for Mathematics 5.OA.1, 2 and 3.
  1. Evaluating Expressions with Parentheses and Brackets
  2. Writing Simple Expressions with Numbers and Parentheses
  3. Generating Two Numerical Patterns: 5th Grade Lesson
  4. Assessment on the Pythagorean Theorem