Strategies for Basic Multiplication Facts
First, some fundamental concepts kids need to understand. They are
worth teaching/reviewing with older kids:
1. Multiplication is repeated addition
7x6=6+6+6+6+6+6 +6
Knowing the 6 x 7 fact lets you figure this out a LOT faster!
2. The multiplication symbol means “groups of” (or “sets of” or
piles of or whatever.
7 x 6 means 7 groups of 6
7 x 6 means 6, seven times
3. The order doesn’t matter. (Commutative property – kids don’t
need to know
this word).
7 x 6 is the same as 6 x 7.
4. Any fact can be modeled with an array, a.k.a. area model.
7x6
7
6
5. Practice doubling. Practice halving.
On to the strategies….
X 0 = “groups of nothing”
4 x 0 means 4 groups of nothing.
0 x 4 means no groups of 4
X 1 = the other number. “1” is like a mirror, reflecting the other number.
1 x 4 means “one group of 4”.
X 2 = double
X 2 = the other factor added to itself
8x2=8+8
X 4 = double, double.
Four goes to Tim Horton’s and orders a double, double, Double the other
number, then double again.
6x4=
Double 6 = 12
Double 12 = 24
X 8 = double, double, double
Eight is twice as much as four. Double the other factor three times.
7x8=
Double 7 = 14
Double 14 = 28
Double 28 = 56
(see where lots of doubling comes in handy? Kids
need practice doubling two digit numbers. )
X 10 = “tack on a zero”
(Never say “add a zero to the end”. We aren’t adding it, we’re tacking it on,
sticking it on, annexing it, etc. Choose your favourite; just don’t say “add”.)
X 5 = skip count by fives.
Students have learned to skip count by fives in primary grades. This
should come easily.
X 5 = double and half.
Double 5 = 10; cut the other number in half.
6 x 5 = 3 x 10 = 30
12 x 5 = 6 x 10 = 60
(This works great when the other factor is even. When it’s odd, it works if
kids are comfortable halving odd numbers. 7 x 5 = 3.5 x 10 = 35)
X 5 = 0,5,0,5 pattern in the ones’ place.
This visual/rhythmic pattern helps some kids remember.
Even number factors end in zero; odds end in 5.
X 5 = use the five minute intervals on a clock.
7 x 5 = 7 on the clock face – 35 minutes after the hour.
X3 = skip count by threes
Okay, not the greatest strategy, but it works for some kids. For other kids,
some of the x 3 facts remain ones that just need to be memorized.
X 3 = double and add one more set
3 x 6 = 2 x 6 = 12 plus one more set of 6 = 18
x 6 = use the closest x 5 and count on one more set
7 x 6 = 7 x 5 = 35 plus 7
8 x 6 = (8x5) 40 + 8
3 x 6 = (3 x 5) 15 + 3
X 9 = look at the patterns in the products.
* the digits in the products always add to 9
* you’re counting up in the tens’ place, and down in the ones’ place
* the tens’ place digit is one less than the factor
6 x 9 = one less than 6 is 5
5 will be the tens place. What adds with 5 to make 9? 4!
54
X 9 = the fingers trick!
Use your hands by putting both hands out in front of you.
Bend the finger of the number you want to multiply. Then count the number of
fingers on both sides of the bent finger to get the answer.
For 3 × 9, bend Finger 3.
For 7 × 9, bend Finger 7.
3 × 9 = 27
7 × 9 = 63
0
9
1
8
2
7
3
6
4
5
5
4
6
3
7
2
8
1
9
0
Some general ideas:
Use songs or raps.
 Look for the CD called Multiplication Unplugged
 Check out the youtube video here:
http://www.youtube.com/watch?v=CP0zm4rYZBA
(Mrs. D’s Multiplication Rap Remix)
The Rap-ability ones are cute, too!
Have the songs/raps playing when kids are
coming in to class every day, ad nauseum!
 Have kids write, perform, and record/video raps for
a time tables themselves!!
Whittle them down!
On an overhead or the Smart Board, look at a
times table and have kids talk about
strategies they already know. Cross off the
facts that kids can do readily, such as the x2
row (and because order doesn’t matter, the x
2
column too!). By the time you cross out the
x0, x1, x2, x5, and x10 rows, there’s not much left. (These are
shaded out on the table to the right.) You can then eliminate any
repeats. For example, you can leave 6 x 7, but you can cross off 7 x
6! Once you know one, you know the other one automatically!
(They’re shown with X’s on this chart.)
This will leave a very small number of “Tough Facts” or “Challengers”
or whatever nickname you want to give them. Have kids make their
own Challenger flash cards for practicing at home. Ask one to each
kid on the way in to class each day, or have being able to answer one
at the end of class their ticket out!
Among the Challengers are some “doubles” facts – 3 x 3, 4x4, 6x6,
etc. For many kids, these seem to stick in their heads easily and can
be crossed off. Also among these tough facts are some x4 (double,
double), some x 8 (double, double, double) and some x9 (fingers
tricks). With these strategies, even the touch facts can be easily
solved.
It’s very satisfying for kids to go through this process for themselves
on their own paper copy, crossing out or colouring in the facts they
already know automatically, and leaving only their own personal
tough facts. Kids should be working on memorizing their own
personal lists or sets of facts, rather than the long lists for all fact
families.
For late grade 4 and beyond, kids should be practicing the inverse of
these facts, the related division facts. Learning 4 x 6 = 24 means they
know 6 x 4, and they also know 24 ÷ 6 = 4, and 24 ÷ 4 = 6! But they
need LOTS of practice at this!