Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

Students are able to… 

  • Solve word problems and expressions that require the use of order of operations, including parenthesis.
  • Understand that, when evaluating expressions with different grouping symbols, such as parentheses, the operation(s) inside the grouping symbols should be solved first.
  • Translate word problems into expressions and expressions into word problems.
  • Explain their thinking as they use order of operations to solve different examples.

Students are able to…because teachers:

  • Provide opportunities for students to make connections between numerical expressions and problem solving scenarios.
  • Use problem solving scenarios that model why multiplication and division are completed before addition and subtraction.
  • Provide opportunities for the students to evaluate expressions that include grouping symbols with up to 4 operations and explain how to apply order of operations.

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Questions to ask students:

  • Ask students to explain the order of operations.
  • Point to or write an expression that includes division before multiplication or subtraction before addition (Example: 24 ÷ 6 × 2) and ask students to explain how to use order of operations to solve.
    • Sample answer that indicates understanding: multiplication and division are interchangeable (because division is the opposite of multiplication) in order of operations, so we work left to right. In this example we should first divide 24 ÷ 6 = 4, then multiply 4 × 2 =8. (Or should have used parentheses!)
    • Sample answer that indicates an incomplete understanding or a misconception: multiplication has to be done before division, (often students memorize the acronym PEMDAS or “My Dear Aunt Sally) so 6 × 2 = 12, then 24 ÷ 12 = 2.

FOR CLARIFICATION ON THE TOPIC ABOVE, WATCH THIS VIDEO AND SCROLL AHEAD TO THE 7:40 MARK.

  • Ask students how changing the placement of parenthesis in an expression, will change the order in which the operations are solved.
    • Sample answer that indicates understanding: The operation that is in the parenthesis will always be solved first.
  • Point to an expression and ask students to think of a word problem that represents the expression.

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FSA Notes

Cognitive Complexity Level: 1 – Recall

Achievement Level Descriptors:

Level 2: evaluates a simple numerical expression with whole numbers, using parentheses, brackets, or braces, with two procedural operations

Level 3: evaluates a numerical expression that contains a fraction, using parentheses, brackets, or braces, with three or more procedural operations

Level 4: analyzes an error in the evaluation of a numerical expression that contains parentheses, brackets, or braces

Level 5: inserts parentheses, brackets, or braces in numerical expressions to make a statement true or to equal a specified value

Assessment Limits:

  • Expressions may contain whole numbers or fractions with a denominator of 10 or less.
  • Expressions may not include nested parentheses.
  • Multiplication cross symbol is the only acceptable symbol for multiplication. The multiplication dot may not be used.
  • When grouping symbols are part of the expression, the associative property or distributive property must be found in the expression.

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Additional Resources:

Additional in depth content knowledge:

 

Video: Order of Operations

Blog Post: A World Without Order (of operations)

 

Sample Formative Assessment Task: