Arrays and Commutative Property for Mulitplication

Objectives:

• Students will be able to identify arrays in their classroom environment.
• Students will discover the commutative property for multiplication by building arrays.
• In partnerships, students will be able to outline two corresponding arrays (for example, 8 x 4 and 4 x 8) on graph paper and give the final product for each array. 
• Students will be able to investigate multiplication equations on the computer that are equivalent to each other using their new knowledge of arrays.

NCTM Standard: Numbers & Operations

·         4.N.6: Understand, use, and explain the commutative and associate property of multiplication

·         4.N.16 Understand various meanings of multiplication

Anticipatory Set:

Teacher will hold up an egg carton and explain that it is an array (items in a number of equal-sized rows).  I will ask students if they have ever seen an array before.  The teacher will then challenge students to identify other arrays in the room.  As students identify the arrays, the teacher will record findings on large chart paper. 

Teaching: Input

 The teacher will use one of the concrete examples in the room to show students how to find the total when something is in an array (length x width). 

Teaching: Modeling

The teacher will then hold up an index card with a multiplication fact written on it.  Using large graph paper, the teacher will model how to draw an array using the given fact (8 x 4). 

Teaching: Checking for Understanding

·         Holding up the modeled array, the teacher should ask students “Does it matter how I hold my array?  Will I have 32 squares when the array is both vertical and horizontal?  How do you know?”

·         Ask, “If I was handed an index card that read 4 x 8, would my array look the same?  How do you know?”

Guided Practice:

Partnerships will be handed an envelope with a flashcard inside, graph paper, and a marker. Students will be asked to outline and cut out the array that corresponds with their given flashcard. The sample will be hung up on the board.  When students are finished, they will hang their arrays on the front board so that the work can be shared with the class. 

Closure:

Students will come together as a class to make observations about the arrays.  Teacher will point out several arrays and repeat the Check for Understanding questions as found in the beginning of the lesson. 

Independent Practice:

Students will work independently on computers using the website:

http://illuminations.nctm.org/ActivityDetail.aspx?id=26

Students will be asked to manipulate the Pan Balance using what they learned about the commutative property of multiplication.  The students who are ready will be asked to jump further to explore the associative property (multiplying three or more numbers).

Materials:

·         Empty egg carton

·         Chart paper

·         Graph paper

·         Scissors

·         Markers

·         Envelope

·         Index cards labeled with multiplication facts

·         Computers

Duration: 45 Minutes