6 Multiplication Concepts

Multiplication concepts are built on addition and skip-counting principles. Often we refer to multiplication as “repeated addition.” However, multiplication is more than this simple phrase implies.

Learners need to understand that multiplication is combining (like in addition) “groups of equal size numbers.” Multiplication is an act of composing a number from factors. One factor refers to the number of groups, and the other factor represents the size of each group.

EXPLORING MULTIPLICATION CONCEPTS

1. Have learners practice skip counting by 2, 3, and 4.
2. Ask what strategy they use to skip count quickly using the Nudget.
3. Guide learners in skip counting while keeping track of the number of skips they make. Learners should slide equal numbers of checkers as they count.
4. Introduce learners to the concept of “set” or “groups” of equal size.

Skip count to 20 by 2. Use tally marks to keep track.

Count, 1 “skip” or “group.”                           

Count, 2 “groups.”                                      

Count, “3 groups.”                                     

Count, “groups 4 and 5.”                       

Group a ten.                                             

Count, “groups 6, 7, 8, and 9.               

Count, “group 10.”                                 

Group a ten.                                         

Write:   20 = 10 x 2

The number 20 can be counted as “10 groups of 2 checkers.”

Learners should recognize that each slide is a group and the number of checkers moved represents the size of the group. Provide opportunity for learners to develop fluency in counting groups of equal numbers of checkers to ensure this concept is fully developed.

BASIC MULTIPLICATION FACTS

1. Have learners count groups of 3, write the number of groups counted, and the result.
2. Guide learners in recognizing and writing the fact family in multiplication.

Start with 0 and skip count by 3. Counting 1 group of 3 results in 3.  Write:    3 x 1 = 3

Counting 2 groups of 3 results in 6.  Write:    3 x 2 = 6

Counting 3 groups of 3 results in 9.  Write:    3 x 3 = 9

Count the one checker. Two more checkers are needed to complete the group of size 3.

Group a ten and reset.

Continue counting the group, “2, and 3.”

4 groups of 3 results in 12.  Write:    3 x 4 = 12

The multiplication fact family of 3:

Provide learners opportunity to master fact families through 12. Facilitate learners in connecting the groups of a size is a product principle with skip counting. Encourage learners to develop “quick” strategies for counting. It is important that fluency of multiplication facts is developed.

COMMUTATIVE PROPERTY OF MULTIPLICATION

1.  Have learners count 3 groups of equal size, writing the size of the groups counted, and the result.

2.   Guide learners to recognize that the number of groups can be interchanged with the size of each group to find the same result.

Count 3 groups of 2 checkers.

The result is 6.

Write:   3 x 2 = 6

Reset.

Count 3 groups of 4 checkers. Slide 1 group of 4.

Slide another group of 4 and count, “2.”

Slide 2 checkers. Two more checkers are needed to count group 3. Group a ten and reset.

Continue counting the group.  3 groups of 4 results in 12.

Write:  3 x 4 = 12

Reset.  Count 3 groups of 3 checkers.  The result is 9.

Write:   3 x 3 = 9

The multiplication fact family of 3:

Ensure learners develop fluency in combining groups of a size. Learners should recognize and articulate the commutative property of multiplication.