Math Background

Lesson: Using Arrays to Show Multiplication Concepts
Introducing the Concept

Students used equal groups to multiply in the first lesson on multiplication in their math books. Now they will use this experience to explore how to use arrays to multiply.

Materials: 15 counters and an overhead projector for demonstration, one sheet of paper and 15 counters for each student or pair of students

Preparation: Distribute paper and counters to students after you demonstrate the concept.

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

  • Place 2 groups of 4 counters on the overhead projector.
two groups of four dots
  • Ask: How many equal groups of counters are there?
    Students should recognize that there are 2 equal groups.
  • Ask: How many counters are in each group?
    Students should recognize that there are 4 counters in each group.
  • Ask: What is the total number of counters?
    Students will probably add 4 and 4 or skip count by 4 to find the answer, 8.
  • Ask: What multiplication sentence describes the model?
    Have a volunteer write the multiplication sentence on the board and label the numbers.
multiplication sentence
  • Rearrange the counters in 2 rows of 4.
two rows of four dots
  • Ask: How many equal rows of counters are there?
    You may need to tell students that rows go across, not down. Then they will know there are 2 equal rows.
  • Ask: How many counters are in each row?
    Students should say there are 4 counters are in each row.
  • Ask: What is the total number of counters?
    Students should say that the same number of counters was used, so the answer is 8.
  • Ask: What multiplication sentence describes the model?
    Have a volunteer write the multiplication sentence on the board and label the numbers.
multiplication sentence
  • Say: Arrangements of objects in rows and columns are called arrays.
  • Write “array” on the board.
  • Ask: What objects in our classroom are arranged in arrays?
    Elicit responses from students such as papers on a bulletin board, groups of desks in the room, and so on.
  • Ask: What objects in your home or other places you go are arranged in arrays?
    Encourage students to think about games, hobbies, and sports they participate in. Some possible answers are seats in an auditorium, spaces on game boards, pictures in a photo album, and so on.
  • Distribute one sheet of paper and 15 counters to each student or pair of students.
  • Say: Show 3 groups of 5 counters.
  • Ask: What is the total number of counters?
    Students will probably skip count by 5 to find the answer, 15.
  • Ask: What multiplication sentence describes the model?
    Have a volunteer write the multiplication sentence on the board: 3 x 5 = 15.
  • Say: Rearrange the counters in a 3 by 5 array.
  • Ask: How many equal rows are in the array?
    Students should say there are 3 equal rows.
  • Ask: How many counters are in each row?
    Students should say there are 5 counters in each row.
  • Ask: What is the total number of counters in the array?
    Students should realize that they used the same counters to make the array that they used to make equal groups, so the answer is 15.
  • Ask: What multiplication sentence describes the array?
    Have a volunteer write the multiplication sentence on the board: 3 x 5 = 15.
  • Have students model more arrays with counters and write corresponding multiplication sentences.
Houghton Mifflin Math Grade 3