Unit 7, Lesson 2
The Area Model for Multiplication
“What do you mean, it’s the wrong kind of right?”
Quick Practice
• Goal: Practice multiplying with tens,
hundreds, and thousands.
• 60 x 30 =
6 x 3,000 =
• 60 x 300 =
600 x 300 =
• 6x3=
60 x 3 =
Introducing Rectangle Sections
67 x 43 = ?
67
43
How would we find the area of this rectangle?
How can we use this information to
solve 67 x 43?
• When you multiply larger numbers, you often
need to break the problem into smaller parts
60
+
7
40
60 x 40
40 x 7
+
3
60 x 3
7x3
Multiply Them & Add ‘Em Up….
• 60 x 40 = 2,400
2,400
• 60 x 3 = 180
180
• 40 x 7 = 280
280
• 7 x 3 = 21
+ 21
2,881
Questions to Ponder
• How are the numbers 63 and 67 expressed?
Why?
• They are expressed as tens and ones to make the
multiplication easier.
• How can we use what we know about zeros
patterns in products to find the partial
products in the smaller rectangles?
• We know that 40 x 60 has 2 zeros, 40 x 7 has 1 zero,
and 3 x 60 has 1 zero
Questions to Ponder
• Does it matter in what order we multiply to get the
partial products?
• No
• What do we do with all of the partial products to get
the total product?
• Add them.
• Does it matter in what order we add the partial
products?
• No
• So, how are the Rectangle Sections used to solve the
multiplication?
• The area of each of the 4 smaller rectangles is found. Then the 4
areas are added to find the total area.
Let’s Try One More…
39 x 54
39
54
39 x 54
50
30
+
4
30 x 50
30 x 4
9 x 50
4x9
+
9
39 x 54
• 30 x 50 = 1,500
• 9 x 50 = 450
• 30 x 4 = 120
• 9 x 4 = 36
Add ‘Em up….
1,500
450
120
+ 36
2,106
Solve with Expanded Notation
43 x 67
• Write 43 and 67 using expanded notation
– 43 = 40 + 3
– 67 = 60 +7
• 40 x 60 = 2,400
40 x 7 = 280
• 3 x 60 = 180
3 x 7 = 21
• Add ‘Em Up …2,400 + 280 + 180 + 21 = 2,881
On Your Own…
•Turn to page 266 in your hard
math book (volume 2)
•Solve problems 5 and 6 using
either Rectangle Sections or
Expanded Notation
Homework…
•Homework &
Remembering page
163 (odd)