Properties of Multiplication
As soon as students begin multiplying numbers, they start to unknowingly test different mathematical properties and concepts. When introducing multiplication properties such as the commutative property, associative property, identity property, and zero property, it is important to provide several effective examples of each new property as well as adequate time for students to learn how to identify these properties. In this lesson, the commutative property of multiplication is introduced.
Materials: Overhead projector, string, manipulatives such as counters or cubes for students
Preparation: Arrange students in pairs. Each pair should have 50 or more counters or cubes and twenty 12-inch strings.
- On the overhead projector, arrange counters in 3 groups with 4 objects in one group, 5 objects in another group, and 6 objects in another group. Use an overhead marker to draw a ring around each group.
- Ask: How many groups do I have? How many objects are in each group? Can we use multiplication to find the total number of counters? Why or why not?
Students should recognize that there are 3 groups with 4 objects in one group, 5 objects in another group, and 6 objects in another group. They should also be able to explain that multiplication cannot be used to find the total number of counters, because of the different number of counters in each group.
- Now arrange the counters in 3 groups with 5 objects in each group. Draw a ring around each group.
- Ask: How many groups do I have? How many objects are in each group? Can we use multiplication to find the total number of counters in these groups? How?
Students should be able to explain that multiplication can be used to find the total number of counters, because the number of counters in each group is equal.
It is also important that students recognize that 3 groups of 5 is 3 x 5 and not 5 x 3, because 5 x 3 stands for 5 groups of 3.
- Say: In your pairs, use your objects and string to make 3 groups of 5.
Walk around the room monitoring progress and helping students that need extra assistance.
- Say: Now use additional objects and string to make 5 groups of 3.
Don't touch your construction of 3 groups of 5.
- Ask: How many objects are in 3 groups of 5? How many objects are in 5 groups of 3?
Students should say 15 objects in each.
- Ask: If 3 groups of 5 can be written as 3 x 5, how can you write 5 groups of 3?
Make sure that students recognize that 5 groups of 3 is 5 x 3.
- Ask: What do 3 groups of 5 and 5 groups of 3 have in common?
Both have a product of 15.
- Repeat the activity with several additional examples.
Multi-digit by one-digit:
Properties of Multiplication: