Multiplication Using The Commutative Property

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SWBAT model and explain how the order of factors in multiplication does not change the product, but the array looks differently.

Big Idea

Understanding the commutative property of multiplication helps students master math facts.

Warm Up

5 minutes

During the warm up of this lesson, students are practicing modeling multiplication with groups and items within a group.  Using whiteboards, I give the students a multiplication sentence such as: 

3 x 7 = ______ 

4 x ____ = 12 

_____ x 3 = 18 

These types of sentences give students the opportunity to find the missing variable in a multiplication sentence by drawing a model.  This is a fast paced review, because the students have been practicing multiplication for several lessons.  Many of the students were able to work through these quickly, and needed more challenge which is why I chose to include missing variables. Some of my students needed more support, so I gave them multiplication only requiring them to find the products.  The focus remained on drawing a model of multiplication. 

Mini Lesson

10 minutes

Reviewing the difference between rows and columns is the focus of this mini lesson.  This structure is used in building the arrays with the tiles, and then transferring them to grid paper.  Using the sentence structure to create arrays for rows x columns = product helps students visualize how an array changes based on the structure of the number sentence.  This provides a visual model of the abstract aspect of the Commutative Property of Multiplication.

In the Common Core standards, it is not necessary for the students to use this terminology in third grade.  However, applying it until they "know it" is crucial for their understanding of multiplication and mastering math facts.

It is important for students to also understand the difference between rows and columns. To make the vocabulary of row and column "sticky", I make a real world connection. I remind students of a movie theater, of seats in a row where you sit shoulder to shoulder.  Children sit in a row with their families and friends, rather than in columns.

Using dice, students create their arrays using tiles and grid paper.  

Try It On Your Own

20 minutes

Students using randomly chosen numbers generating by rolling dice, to create multiplication facts modeled by arrays (MP4). The students use tiles and grid paper to create the arrays.  As students create arrays with the tiles, I want to see how they rotate the array and demonstrate how the number sentence changes with rows and columns.  The goal of students will be to fill their grid as quickly as possible with all arrays touching.  


5 minutes

To close the lesson the students write in their journals how arrays and multiplication sentences change as they are rotated or ordered to explain the commutative property.  I provide students with models of arrays to use as the examples for their journals. I also ask them to explain what happens when multiplying doubles.