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Multiplication & Division with Arrays

PEPE Lesson Plan Format

(Alabama Professional Education Personnel Evaluation Program)

written by: Lanier Pearce (Spring, 2001)

graphics, editing, & 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:  Amanda Bean’s Amazing Dream, bags of pennies (15 in each bag), dry-erase boards, magnet counters, overhead projector, pictures of rows and columns, transparencies (2 arrays on each)

• Objectives:  The students will:

• (Application) work with the commutative property,

• (Synthesis) create and manipulate arrays, and,

• (Application) multiply and divide numbers.

• Grade Level:  third

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

• Anticipatory Set:  The teacher will read the book Amanda Bean’s Amazing Dream.  The teacher will express to the students that they will be learning a new way to multiply and divide.  The teacher will say, “This new way can make multiplication and division very easy.”
• Purpose:  The teacher will say, “The purpose of this lesson is to give all of you another way to multiply and divide.  After today’s lesson, you will be able to stand in a room full of desks and tell how many there are without counting them all.”
• Connection to previous learning/Build background knowledge:  The teacher will say, “I know all of you can multiply and divide using equivalent sets.  Today, we will simply manipulate our groups in the set to form rows and columns.”

III.  Presenting  (to use sequential direct instruction)

• Teaching Procedures:

• The teacher will define "array."  The teacher will say, “Arrays are simply arrangements of objects in rows and columns.”  The teacher will show various pictures of rows and columns.

• The teacher will say, “My garden has an array of plants in it.”

• The teacher will say, “We are now going to look at some equivalent sets and see if we can rearrange our groups in the set to form an array.”

• The teacher will use 6 magnet counters to group equivalent sets on the board and model how to construct an array form that set.  There will be 2 rows and 3 columns.

• The teacher will show on of the transparencies to explain how to get four algorithms from one array.

• The teacher will count the rows and columns on the transparency to create a number sentence.  One will be created for multiplication, and one will be created for division.

• The teacher will turn the transparency one-quarter turn to the right.

• The teacher will count the rows and columns of the “new” array.  He or she will then create the other two number sentences.

• The teacher will explain, and remind from addition, that the commutative property allows us to know that two factors can be reversed and we will still arrive at the same product.

• The teacher will relate the content to other subjects by giving examples of how to use arrays.  The teacher will say, “When you see your spelling words, you can multiply the rows and columns to know how many there are.”

• The teacher will relate the content to other subjects by giving examples of how to use arrays.  The teacher will say, “When you see your spelling words, you can multiply the rows and columns to know how many there are.”

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

• Review:

• (Application) The teacher will call on volunteers to use the word “array” in a sentence.

• (Analysis) The teacher will call on volunteers to tell us the difference between a “group” and an “array.”

• (Comprehension) The teacher will call on volunteers to tell us in their own words, what the commutative property is.  In addition, the teacher will ask a volunteer to come to the board and show us how the commutative property works.

• Guided Practice:

• The teacher will ask everyone to get out his or her bag of pennies.  The teacher will use magnetic counters on the board so that everyone can see.  

• The teacher will construct one array and then give the four algorithms.  

• The teacher will ask volunteers to suggest different number sentences to model with the magnets. 

• The teacher will model and guide each number sentence that is suggested while the students participate using their pennies.

• Independent Practice:

• The teacher will ask everyone to get out his or her dry-erase boards and markers.  The students will get into groups of two.

• The teacher will instruct the students to draw arrays and get their partner to give the four number sentences.  After their partner draws, the other student will draw arrays.  The students will simply take turns doing this.  They must draw four arrays each.  

• Summarizing:

• The teacher will say, “Today, we learned what an array is, how the commutative property is used through arrays, and how to create our own arrays.  I want everybody to go home and try to make at least two different arrays with items from your house.  I think all of you will find that multiplication and division are easier when you use arrays.”

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

          The teacher will use a checklist to assess the guided practice and independent practice activities.  The checklist will have the objectives listed as column headings.  Checks and minuses will be used to determine attainment.  For enrichment, those students will be instructed to use arrays larger than 20 total when they construct them.  For remediation, those students will stay on the concrete level by using their pennies to construct the arrays instead of drawing the arrays or writing the number sentences.

• 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

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