Download Area Model for Showing Multiplication

Area Model and Expanded Model Double Digit Multiplication
Area Model for Showing Multiplication
1-digit by 1-digit Multiplication
12 square units
Area model for 4 x 3
3
4
2-digit by 1-digit Multiplication
Area model for 12 x 3 using only unit cubes:
12
36 square units
Note that the above area model could also be expressed as two arrays (10 x 3) and (2 x 3)
30 square
units
22
10
6 square
units
3
3
By breaking the 12 up into 10 + 2, the product 36 is easier to visualize and
easier to build using the Base Ten Blocks.
2-digit by 2-digit Multiplication
When representing a 2 digit by 2 digit product using the area model, the same
idea of decomposing numbers into multiples of 1 and 10 is used to make the
total number of square units in the arrays easier to visualize.
Going back to the clown problem, we need to multiply 23 x 18.
To model this as an area, we need an array that is 23 units on one side and 18 units on the
adjacent side.
We can decompose 23 to make 20 + 3
We can decompose 18 to make 10 + 8
By doing this, four rectangles are formed, each with easy to compute areas. (See next page.)
Area Model and Expanded Model Double Digit Multiplication
23
20
3
20 x 10 = 200
10
3 x 10 = 30
18
20 x 8 = 160
8
3 x 8 = 24
To find 23 x 18, we can add the areas of the four arrays
200 + 160 + 30 + 24
360 + 54
414
You do not need a grid for the problem.
.
20
10
8
10 x 20 = 200
8 x 20 = 160
3
3 x 10
= 30
3x8=
24
Area Model and Expanded Model Double Digit Multiplication
EXPANDED MODEL
•
•
•
Take numbers and use “Expanded Notation” to decompose them
Multiple each set of numbers individually
Add all the products
1. Write the problem vertically, meaning one number on top of the other
2. Break apart both numbers based on place value (ones, tens) example: 28 = 20 (tens) + 8
(ones)
3. Multiply the ONES PLACE on the BOTTOM number by both the TENS AND ONES of
the TOP number, write the expression under the vertical problem
4. Multiply the TENS PLACE on the BOTTOM number by both the TENS AND ONES of
the TOP number, write the expression under the vertical problem
5. Solve all four multiplication problems
6. Add the products (or the answers), MAKE SURE YOUR PLACE VALUE IS LINED UP
7. The SUM is the answer to the multiplication problem, rewrite
EXPANDED MODEL EXAMPLE:
Original: 24x16
STEP ONE:
24
x16
STEP 2:
24 = 20 + 4
x 16 = 10 + 6
STEP 3:
24 = 20 + 4
x 16 = 10 + 6
6x4=
6 x 20 =
STEP 4:
24 = 20 + 4
x 16 = 10 + 6
6x4=
6 x 20 =
10 x 4 =
10 x 20 =
STEP 5:
24 = 20 + 4
X 16 = 10 + 6
20 x 10 = 200
20 x 6 = 120
10 x 4 = 40
4 x 6 = 24
STEP 6:
24 = 20 + 4
X 16 = 10 + 6
20 x 10 = 200
20 x 6 = 120
10 x 4 = 40
4 x 6 = 24
384
STEP 7:
24 x 16 = 384