Developing Fluency with Multiplication Facts

Developing fluency with multiplication facts is important for supporting flexible number sense, problem solving and understanding of more complex concepts. But fluency, or having a way to get the answer that is "fast and accurate," is not the same thing as memorization. Because it is difficult to remember and retrieve all the multiplication facts, developing strategies that are based on understanding of the operation and number relationships is critical.

Understanding the meaning of the operation and properties of multiplication makes learning the facts much easier. For example, understanding the commutative property reduces the number of single digit facts to be learned from 100 to 55. Understanding the identity property of multiplication helps to illustrate multiplication by one (1 x a = a or a x 1 = a). The remaining 45 facts can be derived from known facts, visualizing open area models, and understanding of the distributive and associative properties of multiplication. Multiplication facts involving 2, 5, and 10 are easier for students to remember because they involve patterns. Array models can help students develop skip counting and additive strategies.

For the harder facts, the open area model can be used to help students build from facts that they know and can recall easily. Below are two examples of how the open area model can be used to derive the fact 6 x8 from easier facts.

Targeted Math Fact Practice

Using a set of 55 flashcards to represent the unique facts from 1-9, show the child one card at a time and sort the cards into 3 piles as they give an answer:

1. Knows automatically (within 3 seconds)
2. Fluent (derives within 3-5 seconds)
3. Does not know

Here is an example of how you might record this information: The facts the student knows automatically are crossed out, the fluent facts are circled, and the ones the student does not yet know are left blank. Targeted math fact practice should focus on helping the student develop strategies for the facts he or she does not know so that they can be moved into the fluent pile for practice. Students can create flashcards for these facts with a "clue" to derive the fact, such as the one shown below.

Action Item

• Conduct Math Fact Interviews with your students and document the facts to work on for fluency and automaticity on the Learning Your Multiplication Facts Recording Sheet.
• Have the child create flash cards for the facts they need to work on (limit to about 10 cards at a time). Have students practice their personal set of facts with a partner during centers or free time. 
• Send Learning Your Multiplication Facts and flashcards home so students can practice at home with a parent or caregiver.