Common Core standard 4.NBT.5 reads as follows:
“Multiply a whole number of up to four digits by a one-digit
whole number, and multiply two two-digit numbers, using strategies based on
place value and the properties of operations. Illustrate and explain the
calculation by using equations, rectangular arrays, and/or area models.”
Many of us are quick to jump right into the traditional
algorithm that we learned as 4th grade students. It is an efficient
strategy. The problem, however, is that our students end up memorizing
efficient steps instead of understanding the “whys” behind “what” they’re
doing. Essentially, we’ve been teaching
multiplication backwards.
Students need time with other methods of multiplication
before we introduce the “shortcut” algorithm we know and use. They need lots
and lots of hands on time! Research says that students could need as much as
two years of conceptual practice with multiplication before we introduce the
algorithm. This might be why the words “standard algorithm” for multiplication
isn’t mentioned in the CCSS until 5th grade (5.NBT.5 Fluently
multiply multi-digit whole numbers using the standard
Algorithm).
So how do teachers teach multiplication if we aren’t using
the algorithm?
Let’s start the way any good lesson might begin- with the
use of manipulatives. Most students have used the base ten blocks in the early
grades, so it’s a nice way explore multiplication. Let’s take the example of 24 x 6.
To use base ten blocks, we’ll multiply 20 x 6 and 4 x 6. The
partial products will be listed as base ten blocks.
From here, students should add the partial products together
to find the total product, 144. I like this method because I can visually see
and touch the product.
This method transitions well into my next suggestion. Once
we get the idea of how to use an area model of multiplication, we can replace
the base ten blocks with numbers.
I like this method because it’s a nice reference to the area
of a rectangle too. When we add up the area of the smaller rectangle and add it
together, we find the area of the larger rectangle.
I’d also like to suggest that you try teaching
multiplication based on partial products and place value. Place value is again
one of those topics that the early grades really emphasize, so it seems natural
to use their understanding of place value to multiply.
Let’s use 245 x 6.
245
x 6
30 6 x 5
+ 240 6 x 40
1200 6 x 200
1470
The great thing about this method is that students really
begin to see that they’re multiplying 6 times each place value- the hundreds,
tens, and ones. As a matter of fact, they can multiply ANY place value first
and get the same product!
Students need a lot of time to explore multiplication
through various representations before they’ll understand the standard
algorithm. Yes, they might be able to memorize the steps, but wouldn’t you want
their understanding of multiplication to go a bit farther? You don’t have to teach every alternative
algorithm out there. Students don’t need to master every alternative algorithm
either. You know your students and their learning styles, so focus on
strategies that best fit your students. Allow them to find a few methods that
they enjoy and go from there.
Looking for a few resources on the area model of multiplication? Check out my Multiplication Round-Ups!
These cowboy themed seat scoots focus on multiplying a 2 digit number by a 1 digit number and 3 digit by 1 digit using the area model method. Students will find partial products and add them together to find the product of various multiplication problems. But watch out! Some cards have missing factors as well!
