Equivalent Expressions Using Mathematical Properties

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Students will be able to use mathematical properties to identify and create equivalent expressions

Big Idea

The Properties of Equivalency! Using math properties to prove equivalency.

Curriculum Reinforcer

10 minutes

The curriculum reinforcer, is a daily practice piece that is incorporated into almost every lesson to help my students to retain skills and conceptual understanding from earlier lessons. My strategy is to use Spiraled Review to help my students retain what they learned during the earlier part of the year. This will help me to keep mathematical concepts fresh in the students mind so that the knowledge of these concepts become a part of students' long term memories.



10 minutes

In today's opening, I will have my students engage in a vocabulary and mathematical property review activity. To do this, I will randomly choose one of my students using popsicle sticks. That student will choose a card that has a vocabulary word or a mathematical property on it. The student will need to explain the meaning of the vocabulary word or mathematical property to the class.

I will continue this process until all the cards have been selected and presented.

The cards will contain the following vocabulary words and properties:

  • Coefficient
  • Constant
  • Variable
  • Term
  • Operation
  • Exponent
  • Base
  • Evaluate
  • Expression
  • Equation
  • Distributive Property
  • Associative Property
  • Identity Property
  • Commutative Property 
  • Zero Property

Instruction & Teacher Modeling

10 minutes

During this lesson I will instruct my students on how to use the different mathematical properties to determine when two or more expressions are equivalent. The properties that I will address are as follows:

  • Identity Property
  • Commutative Property
  • Associative Property
  • Distributive Property


Furthermore, I will introduce the concept of combining like terms. To introduce this topic, I will start off by presenting my students with the number 3. I will present the students with the following:

3 + 3 + 3 + 3 + 3

The above numerical expression above can be rewritten as 5(3) because I am adding the number three 5 times.

For this reason the following is true:

3 + 3 + 3 + 3 + 3 = 5(3)


If I replace the three with a variable. In this case, I will use the variable a. It would look like the following algebraic expression:

a + a + a + a + a

This algebraic expression can be rewritten as 5(a) or 5a because I am adding the unknown quantity 5 times. Therefore, no matter what number a represents, I would be able to evaluate this expression, if given the value of a, using either expression.

For this reason, the following is true:

a + a + a + a + a = 5a


Also, during this instruction piece, I will give my students an example of both equivalent numerical expressions and equivalent algebraic expressions. I will break down each expression using different mathematical properties and in doing so, I will generate several equivalent expressions.

Try It Out

5 minutes

For today's guided practice, I will present my students with 3 sets of equivalent expressions. They will have to write down what property or properties makes each set equivalent.

Please see the attached PowerPoint for the 3 sets of equivalent expressions.

Independent Exploration

20 minutes

To practice the concepts taught during this lesson, the students will participate in an activity where they will be required to identify equivalent algebraic expressions and determine which of the mathematical properties prove that the expressions are, in fact, equivalent.


Students will be put in partnerships based upon ability level. A higher achieving student will be partnered with a lower achieving student. Those student who are considered, "bubble" students, meaning their achievement levels are somewhere in the middle will be paired with other "bubble" students. The reason for this is to allow for understanding to develop from peer interaction.

While with their partner, I will provide my with a set of cards that they will have to sort into equivalent expressions. There are 10 pairs of expressions that are equivalent.

After the students find all pairs of equivalent expressions, they will then need to write what math properties prove that the expressions are equivalent.

Attached to this section of this lesson are the cards and the sheet upon which the students will record their answers.

***Please Note: There are two sets of cards provided as well as two record sheets. The reason for this is for level of difficulty.

One of the documents containing the cards separates the cards into two sets... One set is numbered and the other set is lettered. With this set, students know that one of the numbered expressions match up to one of the lettered expressions. This provides those students who are lower achieving with a little bit of help with this activity. This set of cards has a matching record sheet that lists the numbered expressions and only require the students to write matching lettered expressions across from the numbered expressions.

The other document containing the cards contains expressions that aren't lettered or numbered. For this reason, it will take a bit longer for students to match up the cards as they will have to eliminate more options. This set of cards is for the higher achieving group of students. This set of cards also has a matching record sheet which has nothing listed in the boxes. The student will be required to provide everything the belongs in the boxes.

Closing Summary

15 minutes

To close out today's lesson, I will have 2 pairs of students from the lower achieving group, come up to present their answers. The reason I am choosing this group of students is because their record sheets are numbered and provide a specific expression for each number. The higher achieving group does not therefore, their 1 through 10, will more than likely not match everybody else's 1 through 10.

So, one pair, of the two chosen pairs of lower achieving students, will present their responses to 1 through 5 on their record sheet. The other pair will present their responses to numbers 6 through 10.

From this point, I will facilitate a discussion about accuracy of what was presented and the process by which students determined equivalency. All students are expected to participate in the discussion, providing comments, questions, and/or critique.