Math Background

Lesson: Relating Multiplication and Division
Introducing the Concept

Students have already used arrays to model multiplication. Use this first lesson for a quick review of arrays and multiplication before introducing students to arrays and division.

Materials: 16 counters for each student or pair of students

Preparation: Distribute counters to students.

Prerequisite Skills and Background: Students should understand the concept of multiplication.

  • Say: Show 4 rows of 3 counters.
    four rows of three counters
  • Ask: What is an arrangement of objects in equal rows and columns called?
    Students should answer “array.“
  • Ask: How can we find the total number of counters in the 4 x 3 array?
    Some students may say to skip count by 4 or 3. Most students may say to multiply the number of rows by the number of counters in each row.
  • Ask: What is the total number of counters in the array? (12)
  • Ask: What multiplication sentence describes the array? (4 x 3 = 12)
    Have a volunteer write the multiplication sentence on the board.
  • Ask: What are the factors in the multiplication sentence? (4, 3) What is the product? (12)
    Have a volunteer label the multiplication sentence.
    factor factor product
    4 x 3 = 12
  • Say: Use your 12 counters to show a different array.
    When students finish, have volunteers describe their arrays by answering the following questions.
  • Ask: How many equal rows of counters are in your array? How many counters are in each row?
    Possible answers include 3 rows of 4 counters, 2 rows of 6 counters, 6 rows of 2 counters, 12 rows of 1 counter, and 1 row of 12 counters. If no one makes an array with 12 rows of 1 counter or 1 row of 12 counters, point out that an array can be formed by just 1 row or 1 column.
  • Ask: What multiplication sentence describes your array?
    Have volunteers write the multiplication sentences on the board.
    (3 x 4 = 12, 2 x 6 = 12, 6 x 2 = 12, 12 x 1 = 12, 1 x 12 = 12)
  • Repeat the steps above for 16 counters.
    (1 x 16 = 16, 16 x 1 = 16, 2 x 8 = 16, 8 x 2 = 16, 4 x 4 = 16)

Houghton Mifflin Math Grade 3