Math Background

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.
    two columns of eight squares
  • 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.
    multiplication sentence
  • 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.
    multiplication sentence
  • Say: Turn the array on its side.
    You may want to demonstrate this for the class.
    two rows of eight squares
  • 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.
    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?
    Students should recall addition.
  • Ask: Who can tell me how the Commutative Property of Addition works?
    Most students should remember that changing the order of the addends does not change the sum.
  • Have students model more examples of the Commutative Property on their grid paper. Prompt students with questions similar to those above.

Wrap-Up and Assessment Hints
Have students explain the relationship between the arrays they made and the corresponding multiplication sentences. Encourage them to use mathematical language in their explanations. Then have them use arrays to model the Commutative Property of Multiplication.


Houghton Mifflin Math Grade 3