## Lesson: Using Arrays to Show Multiplication Concepts Developing the Concept

In this lesson, students will apply their understanding of arrays to the Commutative Property of Multiplication.

Materials: square grid transparency, erasable markers, and an overhead projector for demonstration; square grid paper and crayons for each student

Preparation: none

Prerequisite Skills and Background: Students should know how to use arrays to multiply.

• Say: Draw an array with 8 rows of 2 squares.
You may need to remind students that rows go across.
• Ask: What is the total number of squares in the array?
Students will probably skip count by 2 to find the answer, 16.
• Ask: What multiplication sentence describes the array?
Have a volunteer write the multiplication sentence on the board and label the numbers.
• Say: The numbers in multiplication sentences have special names. The numbers that are multiplied are called factors. The answer is called the product.
• Have a volunteer label the factors and product and read them aloud with the class.
• Say: Turn the array on its side.
You may want to demonstrate this for the class.
• Ask: Now how many equal rows are in the array?
Students should realize that there are 2 equal rows in the array.
• Ask: How many squares are in each row?
Students should realize that there are 8 squares in each row.
• Ask: What is the total number of squares in the array?
Some students may start to count the squares. Remind them that the array was turned on its side, so the number of squares is still 16.
• Ask: What multiplication sentence describes the array?
Have a volunteer write 2 x 8 = 16 on the board, underneath the first multiplication sentence.
• Ask: What happened to the factors in the second multiplication sentence?
Students should observe that the order changed.
• Ask: Did the product change?
Students should realize that the product stayed the same.
• Say: Changing the order of the factors in any multiplication sentence does not change the product. This is called the Commutative Property of Multiplication.
• Ask: With what other operation have you used the Commutative Property?