Order of Operations with Grouping Symbols

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SWBAT evaluate numerical expressions involving whole-number exponents and grouping symbols following the Order of Operations

Big Idea

When evaluating expressions, mathematicians all over the world use the same order of operations to get to the answer.

Think About It

5 minutes

Students work in pairs on the Think About It problem.  After three minutes of work time, I bring the class back together.  First, I have them vote for the teacher they think is correct.  This gives me a quick read on performance on this problem. 

I ask for a volunteer to read his/her written response.  I give in-the-moment feedback on the response, addressing strengths and ways to make the answer better.  I do this for 2-3 oral responses.  

I then ask students why it is important to follow the conventional order of operations, as a way to reinforce the learning in the previous lesson.  

I frame the lesson by letting students know that we're going to continue our work with order of operations, and we'll add some work with grouping symbols (in this lesson, grouping symbols only are parentheses).

Intro to New Material

15 minutes

To start the Intro to New Material section, I evaluate the first example.  The visual anchor for this lesson is the steps along with my work for the first example.  I leave this displayed on the document camera as students work later in the lesson.

Students had practice in the previous lesson with following the order of operation and organizing their work.  The new piece in this lesson is to evaluate inside of the grouping symbols first.

For examples 2 and 3, I release the thinking and work to the students.  I cold call on students, and ask 'what do we do now?'  Students guide me through the steps for each example.

Finally, students complete one problem on their own.  After students independently evaluate the expression, I display the work of one student on the document camera for the class.

Partner Practice

15 minutes

Students work in pairs on the Partner Practice problem set.  As students work, I circulate around the classroom.  I am looking for:

  • Are students accurately following the order of operations?
  • Are students organizing their work correctly by writing new expressions after each operation is performed?

I am asking:

  • How did you know where to begin calculating your response?
  • What would happen if you started calculating out of order?
  • When do you subtract before you add? Divide before you multiply?
  • What is the base?  What does it indicate?  What is the exponent?  What does it indicate?
  • What would happen if there were no grouping symbols? How would they change the expression and how you simplify it?


After 10 minutes of work time, students complete the Check for Understanding problem independently.  I ask students to whisper their final answer on the count of three.  I then pull a popsicle stick as a way to pick a student sample to display on the document camera.  Students give positive and constructive feedback on the displayed work.

Independent Practice

15 minutes

Students work on the Independent Practice problem set.  This problem set is pretty straight-forward.  The goal of this lesson is to have students internalizing the order of operations.

As students work, I am making sure that they are organizing their work, and annotating each step of the problem.  I also scan their work to be sure that they are correctly evaluating the exponents in the problems that have them (particularly in problem 6, which has a fraction base, and problem 9, which has 4 different exponent pieces).

Closing and Exit Ticket

10 minutes

After independent work time, I bring the class together for a conversation about Problem 11.  This problem has an exponent, a grouping symbol, a decimal, and a fraction.  I cold call on students to identify each step and create an exemplar response with their help.

Students then work independently on the Exit Ticket to end the lesson.