Learning About the Orders of Operations

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SWBAT to use the orders of operations to solve numerical expressions

Big Idea

8 ÷ 4 x 2 is the answer 4 or 1? Students find out!


15 minutes

I chose this problem because it can be solved without using exponents.  Students can draw a diagram or use a table to solve.  I’m going to have students work independently on this problem, at first.  While students are working on the problem, I’m going to walk around to see how they are solving it.  If students are not using exponents, then I’m going to ask them if they notice anything about what is happening in their table or diagram.  Is there a method that might work that would be easier? (SMP 2)  When students have finished working on the problem, I’m going to have them share at their tables using a Round robin share. (SMP 3)

Explaining the orders of operations

15 minutes

I have two vocabulary words and a table to help explain what the orders of operations are.  I begin by asking the students what the word “orders” means?  I take a few responses.  When we have established that order can mean step by step or maintaining peace, I like to ask them “what if our society didn’t have order”.  Again, they say things like it would be chaotic or out of control.  I explain that this is what happens when we have numerical expressions that don’t get solved using the orders of operations.  We have chaos!  I go through the steps with them.  Be sure to emphasize that Multiplication and Division (step 3) and Addition and Subtraction (step 4) should be solved left to right.  I like to say, “it’s like reading a story.”  What you see first (step 3 or step 4) is what you solve first.

What comes first?

15 minutes

I chose to identify the first step to help students establish a starting point (SMP 1). I’ve included several examples that have different steps to begin the problem.  The hardest part for the students is to remember that step 3 and step 4 use left to right to solve.  (keep reminding them of this).

Using the orders of operations

15 minutes

Now we will apply all of the steps to several problems.  Again, I’ve chosen several problems that have a different first step.  When I teach the students about orders of operations, I tell them that we do one step, one line. (SMP 6). The reason we do this is because we won’t get all mixed up within the problem.  Our problem will be easy to follow and neat.  We can go back at anytime and fix our errors if we continue to re-write the problem after each step. 

White board problems

15 minutes

At this point, I want to check for understanding.  I like to use the white boards because it allows me to assess a large group at once.  I’ve chosen four problems for them to work out independently.  As students are working out the problems, I will be walking around the room.  I will be looking for the first step to be correct, proper execution of the exponents, and the solution.  (SMP 1,2,3,6).  When students have finished working out their problem, have them turn their white boards over (this will signal who is done). Once all students are done, have them all raise their boards when you say “white boards up”.  If there are any incorrect answers, call a student to the board (with a correct answer) to explain their solution. 


10 minutes

The students will be writing about their learning for the day.  They will be explaining the how, why, when to use orders of operations.  The format for their writing will be to an absent student.  If time permits, have students partner share their reflections. (SMP 3)