## 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  x  x  x x  x  x  x x  x  x  x
 x  x  x x  x  x x  x  x x  x  x
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.