The Standard Multiplication Algorithm
This is a complete lesson with explanations and exercises about the standard algorithm of multiplication (multiplying in columns), meant for fourth grade. First, the lesson explains (stepbystep) how to multiply a twodigit number by a singledigit number, then has exercises on that. Next, the lesson shows how to multiply how to multiply a three or fourdigit number, and has lots of exercises on that. there are also many word problems to solve.
The standard algorithm of multiplication is based on the
principle that you already know: multiplying in parts
(partial products): simply multiply ones and tens
separately, and add.
However, in the standard way the adding
is done at the same time as multiplying. The calculation looks more compact
and takes less space than the “easy way to multiply” you have learned. 
The standard way to multiply 
"The easy way" 
1
6 3
× 4
2 

1
6 3
× 4
2 5 2 

Multiply the ones: 4 × 3 = 12
Place 2 in the ones place,
but write the tens digit (1)
above the tens column as
a little memory note.
You are regrouping
(or carrying).


Then multiply the tens,
adding the 1 ten
that regrouped.
4 × 6 + 1 = 25
Write 25 in front of the 2.
Note that 25 tens means 250!



6 3
× 4
1 2
+ 2 4 0
2 5 2 
In the "easy way," we multiply in parts, and the adding is done separately. 

The standard way to multiply 
"The easy way" 
3
7 5
× 7
5 

3
7 5
× 7
5 2 5 

Multiply the ones:
7 × 5 = 35
Regroup the 3 tens.


Multiply & add the tens:
7 × 7 + 3 = 52



7 5
× 7
3 5
+ 4 9 0
5 2 5 

1. Multiply using both
methods: the standard one and the easy one.
2. Multiply using both
methods: the standard one and the easy one.
3. Multiply. Be careful with the
regrouping.
a. 


b. 


c. 


d. 


e. 


f. 


g. 


h. 


i. 


j. 


k. 


l. 


4. Solve.
Also, write number sentences (additions, subtractions, multiplications) on the
empty lines.
a. What
is the cost of buying three chairs for $48 each?
_________________________________________________
And the cost for six chairs?
____________________________ 
b. You
earn $77 a day. How many days do you need to work
in order to have $600 or more? Guess and check.
_________________________________________________
_________________________________________________ 
With a 3 or 4digit number you have to
regroup many times. 
3 2 3
8
×
4
2 


1
3
2 3 8 ×
4
5 2 


1
3
2 3 8 ×
4
9 5 2 

Multiply the ones first.
4 × 8 = 32
Write 2 in the ones
place and regroup
the 3 tens to the
tens column. 

Then multiply the tens,
adding the 3 regrouped tens.
4 × 3 + 3 = 15
Write 5 in the tens place
and regroup the 1 hundred.


Then multiply the hundreds,
adding the regrouped hundred.
4 × 2 + 1 = 9
Write 9 in the hundreds place. 

1
7 6 5
2
×
5
0 


2
1
7 6
5 2 ×
5
6
0 


3
2
1
7
6 5
2 ×
5
2
6 0 


3
2
1
7
6 5 2 ×
5
3 8 2 6 0 

Multiply the ones:
5 × 2 = 10
Write 0 in the ones place and regroup
the 1 ten. 

Then the tens. Add
the regrouped ten:
5 × 5 +
1 = 26
Write 6 in the tens
place and regroup
the 2 hundreds.


Multiply the hundreds.
5 × 6 +
2 = 32
Write 2 in the
hundreds place,
and regroup the
3 thousands. 

Multiply the thousands:
5 × 7 +
3 = 38
Write 38 in front of
the 260. 

5. Multiply using both
methods: the standard one and the easy one.
6. Multiply using the standard method.
a. 


b. 


c. 


d. 


e. 


f. 


g. 


h. 


i. 


j. 


k. 


l. 


7. Solve the word problems.
Also, write number sentences (additions, subtractions,
multiplications) to show what you calculate.
a. The school has 304 students. To go to
the museum, they hired buses which can
each seat 43 passengers. How many buses
did they need?
Hint: Guess and check.

b. The school also has 24 teachers. How many
seats were left
empty in those buses when all
the students and all the teachers joined the trip?

This old video of mine below also also explains how to teach the multiplication algorithm. At first, the video goes through the partial products algorithm (multiplying in parts), and then explains the standard multiplication algorith (as in the lesson on this page).
This lesson is taken from Maria Miller's book Math Mammoth Multiplication 2, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Maria Miller.