Multiplication Facts - Strategies for Thinking
Strategy
Foundation Facts
x2
x 10
x5
x1
x0
Building on the Foundation
x3
x4
x6
x9
x8
x7
Description
Examples
Students have lots of experience skipcounting by 2s and grouping in pairs and
have developed an understanding of
doubling. This set of facts is a natural place
to begin exploring multiplication facts.
The understanding of 10 is foundational in
our number system. Students have
experience skip-counting by 10, grouping in
tens, and working with models of 10, such
as ten-frames and base-10 blocks.
Students have experience skip-counting by
5. They recognize connections with money
concepts (nickels). Previous exploration
with x10 facts leads to the insight that
multiplying by 5 can be thought of as half of
multiplying by 10.
2x8=?
Think: 2 times 8 is the same as doubling 8, and
I know that 8 + 8 = 16.
Although x1 and x0 facts are simple to
memorize, beginning with these facts can
be confusing. Giving students opportunities
to explore groups of 2, 5, & 10 first provides
a stronger foundation for understanding
multiplication facts.
Multiplying by 3 can be thought of as
multiplying by 2 and then adding 1 more
group, or as tripling a number.
Multiplying by 4 can be thought of as
doubling, and then doubling again (2 x 2).
Students that have mastered their x2 facts
can quickly double x2 facts to find x4 facts.
Multiplying by 6 can be thought of as
doubling a multiple of 3: 6x4=(3 x 4)+(3 x 4).
Multiplying by 6 can also be thought of as
multiplying by 5 and then adding one more
group: 6 x 4 = (5 x 4) + (1 x 4).
Building on knowledge of x10 facts, the
product of a x9 fact is one group less than
the product of the same x10 fact. Multiply
by 10 and subtract the number.
Multiplying by 8 results in a product that is
double that of multiplying by 4 (2 x 4), or
doubling a number three times (2 x 2 x 2).
Multiplying by 7 may be the most difficult
for students. It can be seen as multiplying
by 5, and then multiplying by 2 (or adding
the double).
4 x 10 = ?
Think: I know that 4 times 10 means 4 groups
of ten. I know that if I have 4 tens that equals
40.
5x6=?
Think: 5, 10, 15, 20, 25, 30. That's six 5s so the
answer is 30.
5x6=?
Think: I know that 5 is half of 10, and 10 groups
of 6 = 60. If I take half of 60, that equals 30, so
5 x 6 = 30.
1x9=?
Think: I know that 1 x 9 means 1 group with 9
in it, so 1 x 9 = 9.
4x0=?
Think: I know that when multiplying by 0, there
are 0 groups, or nothing/0 in a group, so the
answer is 0.
3x6=?
Think: 2 groups of 6 is 6 + 6 = 12, and another
group of 6 is 12 + 6 = 18. Or 6 + 6 + 6 = 18.
4x7=?
Think: Double 7 is 14 and double 14 is 28, so 4
x 7 = 28. Or double 7 is 14, so 14 + 14 = 28.
6x7=?
Think: 3 x 7 is 21, if I double 21 I get 42. Or 5 x
7 is 35, add another 7 and that equals 42.
9x7=?
Think: 10 groups of 7 is 70, and if I subtract
one group of 7, that equals 63.
8x6=?
Think: 2 x 6 is 12, 2 x 12 is 24, and 2 x 24 is 48.
7x8=?
Think: 5 x 8 is 40, 2 x 8 is 16, 40 + 16 is 56. Or
5 x 8 = 40, and double 8 is 16, and 40 + 16 = 56.
Adapted from: Mastering the Basic Math Facts in Multiplication and Division, 2011, Susan O’Connell and John SanGiovanni