True/False Equations: Working with the Order of Operations + Show what you know

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SWBAT: • Use OOO to simplify numerical expressions • Show what they know about OOO

Big Idea

Does 15 + 2^3 = 15 + 2 x 3? Students work with equations that get to many common misconceptions that involve the order of operations. Students also take a short assessment.

Do Now

5 minutes

See my Do Now in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day.  Here, I am introducing the activity students will work on with partners.  I want students to use what they know about order of operations to create their own arguments.  Students engage with MP3: Construct viable arguments and critique the reasoning of others.

Students may need a reminder that 3 (4 + 5) is the same as 3 x (4 + 5).  Although this example demonstrates the distributive property, I am not going to take time to talk about it here.  We will address that in a later lesson.  For number one I tell students that since the equation is true, we can say that the expression on the left side of the = sign is equivalent (or equal) to the expression on the right.

More True/False Equations

20 minutes


  • Before the lesson, I print and cut out sets of the True False Equations Cards.  I like to print them on card stock and label the sets and place them in envelopes.  For example, for set 1 I put #1 on the back of each card and label the envelope #1.  That way when (inevitably) a card falls on the floor, it can easily be returned to the proper envelope.
  • If you have experienced particular student misconceptions that are not covered in the cards, by all means create new ones!  I would love for you to write me a comment with your ideas!
  • I use the data from the tickets to go in the Order of Operations lesson to Create Homogeneous Groups for this part of the lesson.

I tell students that today they will work on more true/false equations as well as take a short quiz on the order of operations.  I demonstrate that students will work with a partner to categorize the cards into two groups: True Equations and False Equations.  We go through a card together as an example.  I stress to students that it is important that they show their work so that other people can understand why they put a card in a particular category.  I also talk about what it means to be a good partner.  Good partners work together and ask each other questions.  They do not announce answers before other people are finished, or simply accept someone’s answer without first trying it themselves.  I want students to be engaging in discourse about their work.  They will be using MP3: Construct viable arguments and critique the reasoning of others and MP7: Look for and make use of structure.

I show students their groups for the activity and pass out the materials.  I walk around and monitor student progress.

If students struggle with the task, here are some questions I may ask:

  • What is similar about the expressions on either side of the equal sign?
  • What is different about the expressions on either side of the equal sign?
  • How do we know if the equation is true?
  • What do you get when you simplify the left side?  The right side?  Are they equal?
  • What is the order of operations?  What should you do first on this side? Why?
  • If students struggle with basic math facts, I will give them a simple operation calculator.  They still have to apply the order of operations correctly, but a simple math mistake will not hold them back.

If students successfully categorize the cards, they can take turns creating equations and having their partner categorize them as true or false and explain why.

This activity is meant to introduce the skill of identifying equivalent expressions.  Students will use some of these same skills with more difficult problems in the next lessons (Equivalent Numerical Expressions)


10 minutes

I have students get out card F and H.  I ask students to show by raising their hands if they think each equation is true or false.  Then I will declare that I think they are both true.  I go through example F, showing that each side is equivalent to 35.  And H has the same numbers and operations, so it must be true also.  I want students to raise their hands energetically to argue with me.  I am looking for students to articulate that the expression on the right side of H has parentheses around 12 + 15, therefore you have to simplify the parentheses first.  That means the right side of the equation will result in 32 – 27, which is 5.  I want students to explain why then H is false.

If I have time, I ask for volunteers to show and explain their thinking about card D.  I want students to make the connection that 5 (10 + 2) is the same as 5 (12).  If we split 12 into (10 + 2), then 5 (10 + 2) is the same as 5 x 10 + 5 x 2.  I want students to be engaging with MP7: Look for and make use of structure. 

Show what you know + Homework

25 minutes

I review the Quiz expectations.  I have students complete the quiz independently.  If students do not finish in the allotted time, they set up a time (preferably that day) to come in and complete it.  I use this data to inform my instruction.   If students struggle with a concept, I will spiral it into do nows and homework assignments.  I may also add a few problems on that topic to the next quiz. 

I pass out the Homework at the end of class.  Explain to students that they may not know how to do everything on this assignment, but that is okay because they will be working on a similar task in class.  The important thing is that they try their best and explain their thinking.  This homework is a formative assessment for the Equivalent Numerical Expressions lessons.  I want to have time to collect and analyze this assignment before teaching the Equivalent Numerical Expressions lessons.   This is taken from the “Laws of Arithmetic” lesson  that is part of the Mathematics Assessment Project.