Fact Learning – Multiplication
In grade 4, the expectation is that most students will have mastered the
multiplication facts with products to 81 by the end of the year. In our
provincial math curriculum, we want students to be directly taught
specific strategies that will help them learn their facts. With a strategic
approach to fact mastery, the 100 multiplication facts are clustered and
taught according to similarities that certain strategies work for.
The following are the strategies to be introduced by the teacher, in sequence,
starting at grade 3 and continuing through grade 6 for those students who
need them. An understanding of the commutative or “turnaround” property
in multiplication greatly reduces the number of facts to be mastered.
• x2 Facts (with turnarounds): 2x2, 2x3, 2x4, 2x5, 2x6, 2x7, 2x8, 2x9
These are directly related to the addition doubles and teachers need to
make this connection clear. For example, 3 + 3 is double 3 (6); 3 x 2 and
2 x 3 are also
double 3
• Nifty Nines (with turnarounds): 6x9, 7x9, 8x9, 9x9
There are two patterns in the nine-times table that
students should discover:
1. When you multiply a number by 9, the digit in the tens place in the
product is one less than the number being multiplied. For example
in 6 x 9, the digit in the tens place of the product will be 5
2. The two digits in the product must add up to 9. So in this example,
the number that goes with 5 to make nine is 4. The answer, then, is
54.
Some students might also figure out their 9-times facts by multiplying first
by 10, and then subtracting. For example, for 7 x 9 or 9 x 7, you could think
“7 tens is 70, so 7 nines is 70 - 7, or 63.
• Fives Facts (with turnarounds): 5x3, 5x4, 5x5, 5x6, 5x7
For example, if the minute hand is on the 6 and students know that means
30 minutes after the hour, then the connection to 6 × 5 = 30 can be made.
This is why you may see the Five Facts referred to as the “clock facts.”
This would be the best strategy for students who know how to tell time on
an analog clock, a specific outcome from the grade 3 curriculum. You
should also introduce the two patterns that result when numbers are
multiplied by 5:
1. For even numbers multiplied by 5, the answer always ends in
zero, and the digit in the tens place is half the other number. So,
for 8 x 5, the product ends in 0 and half of 8 is 4.
Therefore, 5 x 8 = 40.
2. For odd numbers multiplied by 5, the product always ends in 5,
and the digit in the tens place is half of the number that comes
before the other number. So, for 5 x 9, the product ends in 5 and
half of the number that comes before 9 (8) is 4, so 5 x 9 = 45.
• Ones Facts (with turnarounds): 1x1, 1x2, 1x3, 1x4, 1x5, 1x6, 1x7, 1x8, 1x9
While the ones facts are the “no change” facts, it is important that
students understand why there is no change. Many students get these
facts confused with the addition facts involving 1. For example 6 × 1
means six groups of 1 or 1 + 1 + 1 + 1 + 1 + 1 and 1 × 6 means one
group of 6. It is important to avoid teaching arbitrary rules such as “any
number multiplied by one is that number”. Students will come to this rule
on their own given opportunities to develop understanding.
• The Tricky Zeros Facts
As with the one's facts, students need to understand why these facts all
result in zero because they are easily confused with the addition facts
involving zero. Teachers must help students understand the meaning of
the number sentence.
For example:
6 × 0 means “six 0’s or “six sets of nothing.” This could be shown by
drawing six boxes with nothing in each box. 0 × 6 means “zero sets of
6.” Ask students to use counters or blocks to build two sets of 6, then 1
set of 6 and finally zero sets of 6 where they don’t use any counters or
blocks. They will quickly realize why zero is the product. Similar to the
previous strategy for teaching one's facts, it is important not to teach
a rule such as “any number multiplied by zero is zero”. Students will
come to this rule on their own, given opportunities to develop
understanding.
• Threes Facts (with turnarounds): 3x3, 3x4, 3x6, 3x 7, 3x8, 3x9
The strategy here is for students to think “times 2, plus another group”.
So for 7 x 3 or 3 x 7, the student should think “7 times 2 is 14, plus 7
more is 21".
• Fours Facts (with turnarounds): 4x4, 4x6, 4x7, 4x8, 4x9
One strategy that works for any number multiplied by 4 is
“double-double”. For example, for 6 x 4, you would double the 6 (12)
and then double again (24). Another strategy that works any time one
(or both) of the factors is even, is to divide the even number in half, then
multiply, and then double your answer. So, for 7 x 4, you could multiply
7 x 2 (14) and then double that to get 28. For 16 x 9, think 8 x 9 (72)
and 72 + 72 = 70 + 70 (140) plus 4 = 144.
• The Last Six Facts
After students have worked on the above seven strategies for learning
the multiplication facts, there are only six facts left to be learned and
their turnarounds: 6 × 6, 6 × 7, 6 × 8, 7 × 7; 7 × 8 and 8 × 8. At this
point, the students themselves can probably suggest strategies that will
help with quick recall of these facts. You should put each fact before
them and ask for their suggestions.
