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Grade 3
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Developing The Concept

Properties of Multiplication

It is important to allow time for children to develop and understand the properties of multiplication. Simply telling students a mathematical rule rarely assures comprehension of the idea. Provide students with many opportunities to reinforce their understanding of these concepts.

Materials: poster board; string and manipulatives such as counters or cubes for each student

Preparation: Arrange students in pairs. Each pair should have 50 or more counters or cubes and twenty 12-inch strings. Construct on poster paper an example of each of the properties. Post them on a bulletin board. An example of each is shown below.

Commutative Property of Multiplication: Construct 3 groups of 4 and 4 groups of 3.

 x 
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3 x 4 = 12 4 x 3 = 12
3 x 4 = 4 x 3
Associative Property of Multiplication: Construct 2 groups of (3 groups of 5) and 5 groups of (2 groups of 3). 2 x (3 x 5) = (2 x 3) x 5
    Multi-digit by one-digit:

    Properties of Multiplication:
. . .

 

Identity Property of Multiplication: Construct 5 groups of 1 and 1 group of 5.

 

Property of Zero for Multiplication: Construct 3 groups with 0 objects in each group.

You can talk to your students about 0 x 3 = 0 which is 0, or no groups with 3 in each group. If you have 0 groups, then there would be nothing to count.

  • Say: We have learned four different properties for multiplication: the commutative property, associative property, identity property, and the zero property.

  • Use your counters and strings to model an example of each of the properties. Use different numbers than the ones I have used in my examples on the bulletin board. When you complete each model, have your partner check to make sure you correctly used each property.

Wrap-Up and Assessment Hints You can assess student progress by having students explain and justify their answers. For example:

  • Ask: If 12 x 9 = 108, does 9 x 12 = 108? If you answered yes, does this work for any two numbers. Explain how you know that is true. If you answered no, explain why this does not work.

  • Ask: Is the product of 1 and any number always 1? Explain why or why not. What is the product of 0 and another number? How do you know?
    Student explanations will give you excellent insight to their understanding of the properties.

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