Multiplying using Partial-Products Strategy
Using the partial-products strategy will help students gain a deeper
understanding of how multiplication works with larger numbers.
24 is 2 tens and 4 ones.
38 is 3 tens and 8 ones. 345 is 3 hundreds, 4 tens, and 5 ones.
Understanding this will help students see how and why
multiplication strategies work, and using partial-products will
give them this understanding.
Array/Box method:
To multiply 14 x 6
We remember 14 = 10 + 4
So, we break apart the 14 into 10 + 4
We begin learning and understanding this strategy
using the array as a visual.
(10 x 6 = 60) and (4 x 6 = 24) then we add (60 + 24 = 84)
So… 14 x 6 = 84
We then move onto 2-digit by 2-digit
13 x 16
Remember 10 + 3 = 13 and 10 + 6 = 16
So we create a 13 by 16 array and break apart the tens and
ones for both numbers.
(10 x 10 = 100) (10 X 3 = 30) (6 X 10 = 60) (6 X 3 = 18)
Next, add the products of each: 100 + 30 + 60 + 18 =208
Now we know---13 x 16 = 208
Using the visual aid will help students gain a
deeper understanding of how multi-digit
multiplication works.
Box model (very similar to array model, just not to
scale)
24 x 36
30
6
20 600 120
4 120 24
Remember
In 37, the value of the 3 is 30
and the value of the 7 is 7
In 42, the value of the 4 is 40
and the value of the 2 is 2.
Now we add 600 + 120 + 120 + 24 = 864
And now we know 24 x 36 = 864
Partial Product without visual aid
42
X 37
14
280
60
1200
7 x 2 = 14
7 x 40 = 280
30 x 2 = 60
30 x 40 = 1200
14 + 280 + 60 + 1,200 = 1,554
42 x 37 = 1,554
If you look again at the box method below, you will see are just taking
the numbers out of the box and multiplying them without the visual of
the box
40
30
7
2
Another example without color
63
X 45
15
5 x 3 = 15
300
5 x 60 = 300
120
40 x 3 = 120
+ 2,400
40 x 60 = 2,400
2,835
One more with 3-digits
357
X 59
63
450
2,700
350
2,500
+ 15,000
21,063
9 x 7 = 63
9 x 50 = 450
9 x 300 = 2700
50 x 7 = 350
50 x 50 = 2,500
50 x 300 = 15,000