How do you build speed with multiplication,
teach place value, build confidence, reinforce
the joy of being challenged, and listen to a
fourth grader giggle?
Welcome to math tutoring!
Multiplication facts, times tables, whatever
you want to call them, you need to know them.
Well, okay, you can not know them, and I guess
the world wouldn't end, but your ability to enjoy
the beauty of more complex math would be stunted.
And if you don't care about that, well, all that repeated
addition is going to get old.
Our math curriculum, the one that my local school system
uses, which is part of the Common Core system,
doesn't subscribe to multiplication memorization.
Memorization doesn't denote deep understanding,
which is the goal of Common Core math, so the time
isn't set aside for refining that convention.
But, as much as arrays and unit blocks might create a
visual for 4x6 which can be expanded to other subjects,
my students are not absorbing the quick answer of 24.
My fourth grade students, all 5 of them, retreat to
calculation for their multiplication facts.
Some of them want to draw the array, some use the
mental prompts (like 4 tables are double/double),
and while having emergency fall back methods
are awesome, having to recompute constantly slows
down the fun of math. We don't want to recreate the
wheel every day, we want to explore on our hot rims.
As an alternative to doing sheets of timed multiplication
facts (gag me!), we've been doing a series of multiplication
games. My current favorite is a simple dice game using
10 sided dice.
The set up for this game requires trust, because I'm asking
the students to go quickly and to not worry about making
mistakes. "I want you to go as fast as you can, and to just
call out the first number that comes to mind." is a
surprisingly difficult thing to ask. (I think it's easy to forget
how vulnerable it leaves us to move quickly in uncertain
I start with a pair of ten sided dice. (For those who don't
game, dice come in a range of sizes and shapes, including,
but not limited to 4, 6, 8, 10, 12 20, and (the rare) 30
sided die. You can also find a 100 sided dice, but they are
very grumpy to use.)
I roll the dice, and say the two numbers aloud. They shout
out the product. I encourage speed. I don't want them to
have time to recalculate. If they are mistaken with their
product, I gently correct. If the product they call out is
the answer to another, nearby product,I give the the
correct factors. If they say, "I don't know", I encourage
them to guess. I don't push. I never scold. This has to feel
When they relax and I can see them starting to get the
groove (or grow bored), I swap out one of the ten siders
for a ten/ten sider (Okay, I made that word up. It's a ten
sided dice that has 10, 20, 30, etc on it, not 1, 2, 3).
Now they are multiplying 30x4. If they balk, I remind
them that they know 3x4. Now they are combining a
factor of 10, or adding a zero to the end of their product.
When that gets easy, I switch out the ten/ten for a 100/ten
dice (100, 200, etc). I also have a 1000/ten dice
(1000, 2000, etc). If they are having a good time, I will
mix up the dice and have numbers like 400x7000. And then
it's "Hey, you just created 2,800,000, and that's pretty
damn cool." (For the higher numbers, I let them use a piece
of paper to track the place values created by the added
zeros. This can slow down the multiplication facts, but
now we're concentrating on other things, and the
multiplication facts are coming fairly naturally.)
(For clarity, all of my students have already done
multiplication work in 3rd grade. They have "learned" their
math facts, but aren't fully fluent in their recall. Much of
what they need is confidence and refinement.)