ACOS Objective 2


Use order of operations to evaluate numerical expressions.
  • Computing absolute values
  • Finding square roots of perfect squares through 225.
  • Evaluating powers
  • Applying properties of operations to computer with integers, fractions, and decimals

ARMT Possible Points = 4 (MC, GR)
  • More than one set of parentheses may be used.
  • The four basic operations (addition, subtraction, multiplication, and division) will be required.
  • Only integers may be used.
  • Either the division symbol (รท) or the fractional form may be used for division.
  • Parentheses or the multiplication symbol (*) will be used for multiplication.
  • The multiplication symbol (x) will not be used.
  • Brackets ({}) may be used for grouping.
  • No word problems/real-life situations will be used.

Sample problems from Item Specs

Prerequisites from Curriculum Guide


Objective 7.2.1: Demonstrate the commutative, associative, and identity properties of addition and multiplication of whole numbers.
Objective 7.2.2: Apply the distributive property to evaluate numerical expressions.

Additional content to be taught:
  • Computing absolute values
  • Finding square roots of perfect squares through 225
  • Evaluating powers
  • Applying properties of operations to compute with integers, fractions, and decimals


No discussion of the order of operations would be complete without "Please Excuse My Dear Aunt Sally!"
What else can help our students learn this important idea?

Interwrite Lesson
Evaluate Expressions
Students will evaluate expressions using order of operations and add parentheses to get certain outcomes.

TI-73 Lessons burst_new2.gif
The Right Combination
In this activity, students use the order of operations and number properties to create a unique expression from a set of numbers that must equal a given number. They will also determine how to correct an expression that does not equal that number. Students also explore the placement of parentheses to ensure number sentences evaluate correctly. Finally, students identify if the Commutative or Associative Properties of Addition and Multiplication are used in different scenarios.Students also explore the placement of parentheses to ensure number sentences evaluate correctly. Finally, students identify if the Commutative or Associative Properties of Addition and Multiplication are used in different scenarios.
I have taught this lesson with 7th graders, and it went really well! The students were engaged and seemed to enjoy solving the problems in the lesson. These problems would also work well as bellringers.

Squares - Perfect or Not
In this activity, students explore the relationship between a number and its square roots. Students estimate square roots by finding the next closest perfect square. Then, students look at the use of square roots in different situations, including finding the perimeter of a square, given the area.



Understanding the Properties of Arithmetic: A Prerequisite for Succes in Algebra
Mathematics Teaching in the Middle School, Aug. 2006, pp. 23-25.