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

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

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

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

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

? 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

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

To multiply larger numbers, decompose the numbers using place value. 6 x 39 = ? 30 + 9 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!

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 = 30 + 9 39 +1 180 6 x 9 = + 54 = 234

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+ 10 + 4 214 80 + 32 = 1,712

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

How did you do? 5 x 39 = ? 30 + 9 x 150 45 =195 5 Area = L x W

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

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

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 = ?

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

Multiplying a 2-digit number by a 14 x 72 = ? Step 3: Multiply each top number by 70 then add. 10 + 4 x 700 280 = 980 70+ 2 Step 4: Multiply each top number by 2 then add. 20 8 = 28

Multiplying a 2-digit number by a 14 x 72 = ? 10 + 4 x +1 700 280 980 70+ 2 Step 5: Find the total area by adding. 20 8 + 28 1,0 8

Now you try! 21 x 15 = ? x

How did you do? 21 x 15 = ? 20 + 1 x 200 10 210 10+ 5 100 5 + 105 315