1. Area Model Multiplication
4.NBT.5 – We can use and explain the area model for multiplying large numbers

2. We know that the area of a rectangle measures the space on the inside.x
A 3 by 3 square has 9 square units of space on the inside,
or 3 x 3 = 9 un2

3. Area Model Multiplication uses the formula for finding area:
Area = Length x Width x 5 15 3

4. Try these 8 5 x ? A B ? x 10 2 ? C x 7 ? D x 6 9
Area = L x W

5. How did you do? 5 x 10 x 7 x B 20 40 A 2 49 C 7 8 x 9 54 D 6
Area = L x W

6. ? 18 x 5 Can we use area to multiply larger numbers like 5 x 18?
Turn and talk about what you would do. 18 x 5 ?
Area = L x W

7. To multiply larger numbers, decompose the numbers using place value.
5 x 18 = ? 18 x
5 x 10 =
5 x 8 = 50 + 40
= 90 5
Area = L x W

8. To multiply larger numbers, decompose the numbers using place value.
6 x 39 = ? 39 x
6 x 30 =
6 x 9 =
180 + 54
= 234 6
1 hundred
13 tens
4 ones
Area = L x W
It can be messy to add the area!

9. To multiply larger numbers, decompose the numbers using place value.
6 x 39 = ? x 6
It can be easier to add the area together if you turn the rectangle.
6 x 30 = 39 +1
180
6 x 9 = + 54
= 234

10. To multiply larger numbers, decompose the numbers using place value.
8 x 214 = ? x 8
Remember to line up the area for easy adding! +1
1,600
200+
214 80 + 32
= 1,712

11. Now you try one!
5 x 39 = ? 39 x 5 ?
Area = L x W

12. How did you do?
5 x 39 = ? x
150 45
=195 5
Area = L x W

13. Give it a go! 3 x
3 x 423 = ? ?
Remember: Small number goes on the small side, large number on the large side.
423

14. How did it go? 3 x
3 x 423 = ?
400 + 20 + 3
1,200
Remember: Small number goes on the small side, large number on the large side. 60 9
1,269

15. What if you want to multiply a 2-digit number by a 2-digit number?
Turn and talk about how you would solve this using an area model.
14 x 72 = ?

16. 10 + 4 x 70+ 2 14 x 72 = ? Multiplying a 2-digit number by a x
Step 1:
Draw square
70+ 2
Step 2:
Decompose numbers

17. Multiplying a 2-digit number by a
14 x
72 = ?
Step 3:
Multiply each top number by 70 then add. x
700
280
= 980
70+ 2
Step 4:
Multiply each top number by 2 then add. 20 8
= 28

18. Multiplying a 2-digit number by a
14 x
72 = ? x +1
700
280
980
70+ 2
Step 5:
Find the total area by adding. 20 8
+ 28
1,0 8

19. Now you try!
21 x
15 = ? x

20. How did you do?
21 x
15 = ? x
200 10
210
10+ 5
100 5 +
105
315