Identifying Equivalent Expressions

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SWBAT identify when two expressions are equivalent

Big Idea

Properties of operations allow mathematicians to rewrite expressions with equivalent expressions and recognize multiple representations of an expression.

Think About It

7 minutes

Students work with their partners on the Think About It problems.  After 3 minutes of work time, I have students share out their responses.  I am looking for students to say that the expressions are equivalent because the answers are the same.  The difference is that the factors are in a different order.

I'll frame the lesson by telling students that in this lesson they will prove that two expressions do or do not have the same value using number properties and evidence through providing examples.   

Intro to New Material

10 minutes

To start the Intro to New Material section, I have students turn and talk to their partners about the first problem.  I then articulate the key points myself:  The expressions are equivalent.  The commutative property tells us that the order doesn’t matter.  This property only works for addition and multiplication.

We then look at the second example.  Again, I have students turn and talk about whether or not the expressions are equivalent.  Here, I also articulate the key points: The expressions are equivalent.  The Associative Property tells us that no matter how you group the numbers the result will always be the same.  The Associative Property can only be applied to addition and multiplication.

For both properties, I have students help me come up with equivalent expressions (numerical and algebraic).

My expectations for student work throughout this lesson is that students will identify and define the appropriate property for each problem, when asked to write/explain.  The more practice students get with identifying and defining the properties, the more quickly they will internalize each of them.

In this lesson, I have students independently complete some quick practice problems, before we move into partner practice.  This gives me a chance to check for student understanding and also make sure students are doing the appropriate amount of writing for each problem.

As a resource, there is a reference sheet attached.  I don't yet give this to students - I choose to provide it as a resource after our lessons on the distributive and the identity properties.  I've provided it here so that you can use it as you see fit.


Partner Practice

15 minutes

Students work in pairs on the Partner Practice problem set.  As students work, I circulate around the room and check in with each pair.  I am looking for:

  • Are students correctly identifying an equivalent expression?
  • Are students correctly identifying the math property related to the equation?
  • Are students correctly applying a math property to create an equivalent expression?
  • Are students correctly explaining the math property they used and why it applies?


I'm asking:

  • How did you know that the expressions were equivalent?
  • How can you prove that two expressions are in fact equal?
  • How can you determine which math property to use to help you create an equivalent expression?


If groups finish quickly, I have them work with their partner to create equivalent expressions using each property.  You can challenge students by asking them to create a pair of equivalent expressions using both the associative and commutative properties.


Independent Practice

20 minutes

Students work on the Independent Practice problem set. 

Problem 7 is one that I like - options A, B, and C are all equivalent, but only one of them applies the associative property.  This question requires students to apply what they know about the properties.  

Problem 10 asks 'which student solved correctly?' - both students did!  This question gives students the chance to really write a robust response, using definitions and examples in their writing.

Closing and Exit Ticket

8 minutes

After independent work time, I have students come back together for a conversation about Problem 9.  First, I ask students to vote with their thumbs about whether or not they think James is correct (I expect to see a few people vote that James is correct).  I'll then have students share the examples they used in their writing with their partners.  Finally, I'll ask the class who thinks their partner has a strong example that proves James' thinking is incorrect, and allow that student to share.  

Students then independently complete the Exit Ticket to close the lesson.