Mathematical Properties in Action

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SWBAT demonstrate their understanding of mathematical properties and how they help to make math easier to interpret and manipulate.

Big Idea

No Trespassing! Understanding that mathematics has boundaries, rules called properties that make mathematics predictable.

Curriculum Reinforcer

5 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.


5 minutes

To open up the lesson for today, I will start off using the "Before the lesson" section of the Conjectures About Properties task which, my students will complete during the independent practice portion of this lesson.

The section labeled “Before the Lesson” states the following:

Post the following expressions and questions on the board.

36 + 45 = 45 + 36

Ask students: Is it true or false?

123 + 24 = 24 + 123

Is it true or false?

4 + 6 = 6 + 4

Is it true or false?

Next, analyze and discuss using the following guiding questions:

Looking at these three number sentences, what do you notice?

Do you think this is true for all numbers?

Can you state this idea without using numbers?

By using variables we can make a number sentence that shows your observation that “order does not matter when we add numbers.”

      • a + b = b + a

Do you think this is also true for subtraction?

Do you think it is true for multiplication?

Do you think it is true for division?


These questions are designed to facilitate a deeper discussion about the meaning behind mathematical properties. 

Instruction & Teacher Modeling

10 minutes

During today's instructional piece, I will introduce students to each type of mathematical property presented in this unit. I will also provide examples of each property. During this time, my students should be taking notes. They will use these notes at a later date to review the mathematical properties using a graphic organizer.

The properties that I will present today are as follows:

  • Identity property of Addition
  • Identity Property of Subtraction
  • Identity Property of Multiplication
  • Identity Property of Division
  • Zero Property of Multiplication
  • Distributive Property
  • Commutative Property
  • Associative Property
  • What it means to be undefined


I will present each property one by one and provide an example of each. During this time, my students will be taking notes using the document attached to this section of this lesson.

Try It Out

10 minutes

During this section of the lesson, I will present my students with five equations. My students will be required to determine which property is represented by each equation. To do this, I will display the PowerPoint attached to this section of this lesson and I will go through each slide one by one, asking my students to write their answers on the whiteboard paddle that I will pass out to each students. They will raise their answers in the air so that I can see them. I will use the information that I see to determine those math properties that I may need to review. 

After my students raise their answers, I will take note of any incorrect responses. Then, I will click the PowerPoint to reveal the correct response. From this point, discussion will commence depending upon what I saw when the whiteboard paddles were raised in the air.

Independent Exploration

20 minutes

For the Independent Practice portion of this lesson, I will have my students complete the “Conjectures about properties” task which requires that the students make observations about what they see when presented with specify types of equations.

This is a wonderful task for getting students to think about mathematical rules and those mathematical elements that are always the same no matter what. It si also a great task for teh development of mathematical practice standard eight (MP8).

To compete this task, I will break my class up into groups of no more than three. Each group will be given three of the sets of equations presented in the task to write about and present. The students will follow the directions as outlined by the task.

Closing Summary

20 minutes

My students will close out this lesson by presenting what they have learned about their assigned portion of the "Conjectures about Properties." Each group of three students will come up to the front of the classroom and thoroughly present, using precise mathematical language what they have observed and learned about the sets of equations that they were assigned to. The group(s) that were assigned the same set(s) of equations will present side by side, comparing and contrasting their observations and learning experience.

The students who are not presenting will ask questions and critique those students who are presenting. These students will also be taking notes of those sets of equations that their group did not work with so that they will have a complete picture of the task and its significance.