Multiplication
Facts Using
Strategies
David McKillop
Making Math Matter, Inc.
Why should students
learn the number facts?
They are the basis of all mental math
strategies, and mental math is the
most widely used form of computation
in everyday life
 Knowing facts is empowering
 Facilitates the development of other
math concepts
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How is fact learning
different from when I
learned facts?
1. Facts are clustered in groups that can be
retrieved by the same strategy.
2. Students can remember 6 to 8 strategies
rather than 100 discrete facts.
3. Students achieve mastery of a group of
facts employing one strategy before
moving on to another group.
General Approach
For each cluster of facts that you are going to introduce, start
by showing students one of the facts and ask them to put up
their hands when they have the answer. Then ask some
student(s) to explain how they did it. This can lead to a
discussion of a variety of strategies from which you can
extract the one you will highlight. Students should understand
that they can use whatever strategy makes sense to them and
enables them to get an answer in a reasonable time frame.
You will be highlighting a specific strategy for each cluster but
students may use other ones. Therefore, during the
reinforcement activities when you ask students to explain their
strategy, you should be open to, and welcome, any strategy
that is reasonable. You don’t want to lose sight of the mission
to have students be flexible in their thinking. As well, you will
have students who know facts automatically without using a
strategy, so you should be open to “I just knew it.” when you
ask to explain how they did it. In fact, our long-term goal would
be automaticity of the facts for all students.
General Approach
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Introduce a strategy using association,
patterning, contexts, concrete materials,
pictures – whatever it takes so students
understand the logic of the strategy
Practice the facts that relate to this strategy,
reducing wait time until a time of 3 seconds,
or less, is achieved. Constantly discuss
answers and strategies.
Integrate these facts with others learned by
other strategies.
IT WILL TAKE TIME!
Facts with 2s:
2 x ? and ? X 2
Highlighted Strategy: Connect to
Doubles in Addition
 Start with 2 x ?
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Relate ? X 2 to 2 x ?
Practice the Facts
Webs
 Dice games
 Card games
 Flash cards
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Facts with 9s:
? X 9 and 9 x ?
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Highlighted
Strategy: Nifty
Nines Strategy:
Two Patterns Decade of answer
is one less than the
number of 9s and
the two digits of the
answer sum to 9
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9 x 9 = 81
8 x 9 = 72
7 x 9 = 63
6 x 9 = 54
5 x 9 = 45
4 x 9 = 36
3 x 9 = 27
Practice the Facts
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Calculator
Facts with 5s
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The Clock
Strategy: The
number of 5s is like
the minute hand on
the clock – it points
to the answer. For
example, for 4 x 5,
the minute hand on
4 means 20
minutes; therefore,
4 x 5 = 20.
Practice Strategy
Selection
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Which facts can
use The Clock
Strategy?
Which facts can
use the Nifty Nines
Strategy?
Which facts can
use the Doubles
Strategy?
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3x5
5x9
8x2
9x7
9x2
2x5
7x5
6x9
Facts with 0s
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Highlighted
Strategy: The
Tricky Zeros: All
facts with a zero
factor have a zero
product.
(Often confused with
addition facts with
0s)
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If you have 6 plates
with 0 cookies on
each plate, how
many cookies do
you have?
Facts with 1s
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Highlighted
Strategy: The No
Change Facts:
Facts with 1 as a
factor have a
product equal to the
other factor.
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If you have 3 plates
with 1 cookie on each
plate OR 1 plate with 3
cookies on it, you have
3 cookies.
Facts with 3s
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Highlighted
Strategy: The
Double and One
More Set Strategy.
For example, for 3 x
6, think: 2 x 6 is 12
plus one more 6 is
18.
Facts with 4s
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Highlighted
Strategy: The
Double-Double
Strategy.
For example, for
4 x 6, think: double
6 is 12 and double
12 is 24.
The Last Nine Facts
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6x6
6 x 7 and 7 x 6
6 x 8 and 8 x 6
7x7
7 x 8 and 8 x 7
8x8
Have students
suggest strategies
for these.
Possible Strategy:
Using helping facts:
6x6=5x6+6
7x6=5x6+2x6
6x8=5x8+8
7x8=5x8+2x8
8x8=4x8x2
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Some know 8 x 8 is
64 because of a
chess board
What about 7 x 7?
Practice the Facts
Flash cards
 Bingo
 Dice Games
 Card Games
 Fact Bee
 Calculators
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