Math Background

Using Arrays to Show Multiplication Concepts: Tips and Tricks

  • Show students an arrangement of 6 counters with unequal rows.
    six dots

    Discuss with students why multiplication could not be used to find the total number of counters. Have a volunteer rearrange the counters in equal rows and write the corresponding multiplication sentence.

    two columns of three dots - three times two equals six
  • As students leave the classroom for lunch or recess, have them line up in arrays. For example, ask one group of 8 students to line up in a 2 by 4 array; have another group of 9 students line up in a 3 by 3 array, and so on.
  • Have students write story problems that describe an array. For example, “There are 6 rows of cars in the parking lot. Five cars are in each row. How many cars are in the parking lot?” Students switch problems with another student who models the array with counters and writes the multiplication sentence to solve the problem.
  • Write a number on the board such as 12. Have students draw all the arrays they can for the number.
  • Students can work in pairs to do this activity. One student rolls a number cube labeled 1-6 for the number of rows in an array. The other student rolls the number cube for the number of objects in each row. The first student uses counters to model the array. The second student finds the product and records the multiplication sentence.
  • Do this quick warm-up activity to reinforce the Commutative Property of Multiplication. Say a multiplication fact such as 3 x 4 = 12. The first student to raise his or her hand and say the related multiplication fact, 4 x 3 = 12, becomes the leader and continues the activity by saying a new multiplication fact.
  • Have students work in pairs for this activity. One student models an array using counters and then writes the corresponding multiplication sentence. The other student changes the order of the factors to write a new multiplication sentence, then models the new array.

Houghton Mifflin Math Grade 3