Lesson Plans

Multiplication & Division with Arrays

Written by:

Graphics, Editing, and Formatting by:

Dr. Beth McCulloch Vinson

I. Preparing (to plan for instruction)

Materials:

Alabama Course of Study: Mathematics, Pages 29 & 30, numbers 8, 11, & 28, children’s literature: The Doorbell Rang, bags of buttons, pegboard and golf tees, bags of teacher made cookies, chalk board and chalk, number cubes, graph paper, colored pencils, overhead projector and one transparency with an array and fact family, cookie sheet with teacher made cookies attached with Velcro, and toy trucks

Objectives: The students will:

(Application) work with the fact families using the commutative property.

Example of a Fact Family:

2 x 3 = 6

3 x 2 = 6

6 ¸ 3 = 2

6 ¸ 2 = 3

(Synthesis) arrange arrays with manipulative.

(Application) multiply and divide symbolically with numbers.

Grade Level: third

II. Orienting (to establish purpose, build background, sustain motivation, and provide directions

· Anticipatory Set: The teacher will read the book The Doorbell Rang by Pat Hutchins. The teacher will inform the students that they are about to learn a new way to multiply and divide.

· Purpose: The teacher will say, “The purpose of this lesson is to add another quick and easy way to multiply and divide to the ways you have already learned. After this lesson, you will be able to tell how many desks are in a classroom without counting them one-by-one.”

· Connection to previous learning/Build background knowledge: The teacher will say, “We have already learned how to multiply by using repeated addition. I also know that we can multiply and divide by using equivalent sets. Today, we are going to rearrange those equivalent sets to form rows and columns.

III. Presenting (to use sequential direct instruction)

· Teaching Procedures:

· The teacher will say, “An array shows objects in rows and columns. The teacher will show an example of a row and column using cookies on a cookie sheet. (2 x 6 = 12)

· The teacher will use toy trucks to form equal groups in an equivalent set. The teacher will then model how to change the groups into an array.

· The teacher will use the overhead projector and the array transparency to explain how the students can create their fact family using arrays.

· The teacher will use the cookies on the cookie sheet to model several arrays, turning the cookie sheet 90º to demonstrate the commutative property.

· The teacher will remind the students of the commutative property making the creation of the fact families easier.

IV. Practicing and Summarizing (to reinforce and extend ideas)

Review:

Using pegboards and golf tees, the teacher will ask the students to create an array and hold it up in the air when completed. (3 x 2 = 6)

The teacher will ask for volunteers to tell four number sentences for their array.

Using the peg board and tees the teacher will ask the students to create a group of tees at the top and an array of tees at the bottom of the peg board.

The teacher will ask for volunteers to explain the commutative property.

Guided practice:

The teacher will ask the students to get out their bag of cookies. She will write a number sentence on the board. Using a pegboard and tees, she will model how to construct the array.

The teacher will then give four number sentences for the array.

The teacher will instruct the students to get out their bag of buttons, using different number sentences on the board the teacher models the arrays on the peg board while the students work with their buttons. (3 x 6 = 18)

Independent Practice:

The teacher will pass out small number cubes, graph paper, and colored pencils.

Using large number cubes so the students can see, the teacher will instruct the students to roll the cubes ten times. Each time the cubes are rolled, they will multiply the numbers.

Using the number sentence, the students will create an array on the graph paper with the colored pencils.

The teacher will instruct the students to write four number sentences for each array drawn on the graph paper.

4 x 3 = 12

3 x 4 = 12

12 ¸ 4 = 3

12 ¸ 3 = 4

Summarizing:

The teacher will say, ”Today we learned a new and fun way to multiply and divide by using arrays. We also learned about the commutative property and the fact families. I think we all had fun. When you go home today, notice in the parking lots that cars are sometimes parked in rows and columns. In addition, notice the egg cartons in your refrigerator are divided in rows and columns. Tomorrow we will share with each other some of our observations of arrays at home.”

V. Assessment: (to check for attainment of objectives)

The teacher will assess the guided practice by observing the students as they hold up their pegboards. The teacher will place a check mark beside each child’s name if he or she creates the arrays correctly. For enrichment, those students will be instructed to create larger arrays and peer tutor the students who need remediation. For remediation, those students will receive peer tutoring and will continue to create arrays using their buttons and cookies (concrete, manipulative objects).

These things are attached to this lesson plan: (a) multiplication and division journal article, (b) sample multiplication and division student textbook page, (c) pages of the Alabama Course of Study for Mathematics with highlighted multiplication and division objectives.

Also, see the Multiplication and Division PowerPoint Slides Shows at:

http://www.athens.edu/pt3/vinson/multiplication.ppt

http://www.athens.edu/pt3/vinson/measure.ppt

http://www.athens.edu/pt3/vinson/partitive.ppt