3.OA.C.7
Standard:
Fluently multiply and divide within 100, using strategies such as the relationship between
multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or
properties of operations. By the end of Grade 3, know from memory all products of two
one-digit numbers.
*Because of the fluency element of this standard, the “task” component may not be as
helpful in developing fluency. In place of the “task” is a resource of various activities
that might be helpful in attaining math fact mastery.
Commutative Property:
It is imperative that students completely understand the commutative property.
This can be visualized by using arrays. For example, a 2 x 8 array can be described
as 2 rows of 8 or 8 rows of 2. In both cases, the answer is 16. Understanding the
commutative property cuts the basic facts to be memorized in half (Van de Walle,
2012).
A virtual site that to connect arrays to multiplication facts is:
www.haelmedia.com/OnlineActivities_txh/mc_txh3_002.html
Doubles:
Facts that have 2 as a factor are equivalent to the addition doubles and should
already be known by students. Help students realize that 2 x 7 is the same as double
7, but so is 7 x 2. Try word problems in which 2 is the number of sets. Later, use
problems in which 2 is the size of sets (Van de Walle, 2012).
Fives:
This group consists of all facts with 5 as the first or second factor.




Practice skip counting by fives to at least 45
Connect by fives with arrays that have rows of 5
Use number lines to practice skip counting by fives
Create models with manipulatives in groups of five, and count groups of 5
Activity Clock Facts (Van de Walle, 2012):
Focus on the minute hand of the clock. When it points to a number, how many
minutes after the hour is it? Connect this idea to multiplication facts to 5. Hold up a
flash card, and then point to the number on the clock corresponding to the other
factor. In this way, the fives facts become the “clock facts.”
Zeros and Ones:
Thirty-six facts have at least one factor that is 0 or 1. These facts, though apparently
easy on a procedural level, tend to get confused with “rules” that some students
learned for addition. The fact that 6 + 0 stays the same, but 6 x 0 is always zero. The
1 + n fact is the next counting number, but 1 x n is the same. The concepts behind
these facts can be developed best through story problems. Alternatively, ask
students to put words to the equations. Avoid rules that aren’t conceptually based,
such as “Any number multiplied by zero is zero” (Van de Walle, 2012).
Example:
5 x 0= 0 (five groups with zero items in them)
“There are 5 grocery sacks with no groceries in them.”
0 x 5= 0 (there are five in the group, but no groups)
“I worked zero hours at raking leaves at $5 an hour.”
Nines:
Facts with a factor of 9 include the largest products but can be among the easiest to
learn because of the various reasoning strategies and patterns.
One strategy is for students to derive that 6 x 9 is the same as 6 x 10, minus one set
of 6, or 60-6. This is an effective approach for many students can often easily
multiply 6 x 10 and subtract from a decade value.
A table of nine facts includes some interesting patterns that lead to finding products.
 The tens digit of the product is always one less than the “other” factor (the
one other than the 9)
 The sum of the two digits in the product is always 9
 They can use fingers to determine the product
* Encourage students to list each fact for nine, discover the patterns, and reason
about why these strategies work.
Using Known Facts to Derive Other Facts:
The following chart shows the remaining 25 multiplication facts. It is worth pointing
out to students that there are actually only 15 remaining facts to master because 20
of them consist of 10 pairs of turnarounds (e.g., 6 x 3 is the same as 3 x 6) (Van de
Walle, 2012).
These 25 facts can be learned by relating each to an already known fact. Because
arrays are such a powerful thinking tool for these strategies, provide students with
copies of 10 x 10 dot array paper (below). The lines in the array make counting the
dots easier and often suggest the use of the easer five facts as helpers (Van de Walle,
2012).
Division Facts:
Mastery of multiplication facts and connections between multiplication and division
are key elements of division fact mastery. For example, to solve 36 ÷ 9, we tend to
think, “Nine times what is thirty-six?” reasoning facts for division are to (1) think
multiplication and then (2) apply a multiplication reasoning fact, as needed (Van de
Walle, 2012).