The ideas in this lesson are taken from Multiplication Division 3 ebook. Only a few examples of each problem type are shown; you should make more problems of each kind for the student.
Multiplying in columns by a 2digit number
Free lesson plan from HomeschoolMath.net
Multiplying a 2digit number by a 2digit number is again based on distributive property. Let's look at 25 × 34. To take 25 times a number we can find 20 times the number and 5 times the number, and then add those two, just like 25 times a carrot would be the same as 20 times a carrot AND 5 times a carrot. So 25 × 34 = 20 × 34 + 5 × 34. You know how to find 5 × 34  multiply in columns. Since 20 is 2 × 10, we find that 20 × 34 can be broken
down as 10 × 2 × 34. Below is a simplified method for
finding 25 × 34.

Alternatively you can find 20 × 34 this way:
First put down that extra zero that goes to the end. 

Then multiply as if you were doing 2 × 34 (go 2 × 4, then 2 × 3). The digits just get scooted one place because the zero is already there. 


Another example: 30 × 58. 

First put down that extra zero that goes to the end. 

Then multiply as if you were doing 3 × 58 (go 3 × 8, carry, then 3 × 5 + 2). 

Study more examples. Note you have three separate calculations to do.
34 × 16

The traditional form of the algorithm The way presented above takes three separate calculations on paper. In the usual, traditional way all three calculations appear together. 67 × 54

Study these examples, too. Note the extra zero placed at the end of the second line!

Example problems
1. Multiply.
53

11

38

25

17

44

43

22 
62 
2. Word problems. Write a mathematical sentence for each one.
a. How many eggs is 15 dozen eggs?

b. The school has 455 pupils. They all were going to a zoo
by buses, and one bus could
seat 39 passengers. Was 11 buses enough to take them all? (Use
multiplication!)

g. Andrew saves of his earnings 15 dollars each month. How
much does he have saved
at the end of the year?

h. If he wants to by a radio that costs 78 dollars, how many
months does he have to save
for that?

3. Times eleven! Eleven is 10 + 1. So using distributive property, anything times eleven is easy.



4. Try if you can multiply these in your head (mentally).
a. 45 × 11 =  d. 35 × 11 = 
e. 20 × 45 =  h. 20 × 33 = 
5. What is the missing factor? Be careful with the zeros.
7 × __ = 560 40 × __ = 200 40 × __ = 2000 30 × __ = 360 30 × __ = 3600 
40 × __ = 320
10 × __ = 560 100 × __ = 5000 8 × __ = 160 200 × __ = 1600 
Multiplying a twodigit number by a twodigit number can be broken down into four parts using distributive property: 26 × 89 is first of all 6 × 89 and 20 × 89. 6 × 89 is 6 × 80 and 6 × 9. 20 × 89 is 20 × 80 and 20 × 9. So all total, 26 × 89 is... 20 × 80 and 20 × 9 and 6 × 80 and 6 × 9  four parts. The area of a rectangle is side times side. Where are those four parts represented in this picture? Can you explain why?
