Applying the Properties

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SWBAT apply the properties of operation to generate equivalent expressions

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 in pairs on the Think About It problem.  Students are likely to come up with 3(2 + x) and 6 + 2x.  After 2-3 minutes of work time, I have students share out the expressions they wrote. I'll ask how they know the expressions are equivalent, and will ask which number property they applied (if the student doesn't name in his/her explanation).

I tell students that in this lesson they'll be able to apply the number properties we've learned to more mathematical and real world problems.

Intro to New Material

10 minutes

To start the Intro to New Material section, students complete the review of properties section with their partners by filling in numerical and algebraic examples. I have students share out as a class and have students identify whether or not he examples that students provide are in fact correct. 

I then have students help me with Example 1.  First, I want students to articulate that we'll need to add up all of the sides to find the perimeter.  Students will create the expression 3x + 2 + 3x + 2 + 8, and then I'll ask students how we can simplify.  Finally, I want students to articulate that they were able to apply the commutative property of addition to combine like terms using addition to get to 6x + 12. 

I'll then ask students if we can come up with another way to find the perimeter of this isosceles triangle.  What I'm looking for here is that we can multiply the side with a length of 3x + 2 by two,and then add 8.  Students will write 2(3x + 2) + 8.  I'll have students turn and talk with their partners about how to simplify this expression.

Together, as a class, we'll construct an exemplar response for the question.  Our response might look something like: I found the perimeter by using the commutative property of addition and combining like terms.  I added all of the sides together, and then added terms together that were the same.  

For Example 2, I'll first have students spend a moment looking at the expressions and deciding whether or not they think they're equivalent.  I'll have students vote up/down with their thumbs.  I'll ask for volunteers to explain how they can apply the properties of numbers to prove that the expressions are equivalent.  

One student might say they applied the commutative property to combine like terms in y + 2y - 3 t get 3y - 3 and then used the distributive property to factor out the 3, leaving us with 3(y -1).

Partner Practice

15 minutes

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

  • Are students correctly identifying the number properties present in the problem?
  • Are students accurately rewriting the expression in application of the given property?
  • Are students correctly recognizing that some properties are unique to certain operations?


I'm asking:

  • Which property(ies) did you apply to create your expression(s)?
  • 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?


After 10 minutes of partner practice time, students work independently on the Check for Understanding problem.  I'll circulate around the room and check papers as students work.

Independent Practice

15 minutes

Students work on the Independent Practice problem set. 

For this lesson, I will have hard copies of this reference sheet available for some students to use as a support.  I don't supply it to all of my students, as they can go back and use their packets from previous lessons as they work.  You can certainly give this reference sheet to all students, if that works better for your classroom organization system.

Closing and Exit Ticket

10 minutes

After independent work time, I'll bring the class together to share out answers for Problem 9.  There are multiple possible expressions, and I'll allow students to share out as long as there are unique answers left.  Expressions that students may share:

4.5x + 2.5 + 4.5x + 2.5 + 4.5x + 2.5 + 4.5x + 2.5

4(4.5x + 2.5)

18x + 10

2(9x + 5)

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