Let's take a look at the area model below.
We complete this area model by finding the areas of each small rectangle and writing these values on the diagram:
Let's first look at the blue rectangle (the one on the top left). Its length is and its width is Therefore, the area of this rectangle must be Let's add this to our model:
Now, let's look at the pink rectangle (the one on the top right). Its length is and its width is Therefore, the area of this rectangle must be Let's add this value to our model:
Filling the other two missing values in the same way, we get the following:
And we're done!
From left to right, find the missing numbers in the area model below.
We need to look at the blue and pink rectangles:
Let's first look at the blue rectangle on the top left. Its length is and its width is Therefore, the area of this rectangle must be Let's add this to our model:
Now, let's look at the pink rectangle (the one on the top right). Its length is and its width is Therefore, the area of this rectangle must be Let's add this to our model:
Therefore, from left to right, the missing numbers are and
Find the missing number in the area model above.
|
a
|
$110$ |
|
b
|
$900$ |
|
c
|
$1,800$ |
|
d
|
$180$ |
|
e
|
$1,500$ |
From left to right, find the missing numbers in the area model above.
|
a
|
$40$ and $350$ |
|
b
|
$35$ and $270$ |
|
c
|
$20$ and $350$ |
|
d
|
$40$ and $270$ |
|
e
|
$20$ and $270$ |
We can use area models to represent two-digit by two-digit multiplication problems.
For example, let's consider the following area model:
Now, let's look at the big rectangle:
its length is
its width is
its area is
Therefore, this area model can be used to represent the following multiplication problem:
The area model above can be used to represent the following multiplication problem:
What is the missing number?
Let's look at the big rectangle:
its length is
its width is
its area is
Hence, this area model can be used to represent the following multiplication problem:
Therefore, the missing number is
The area model above can be used to represent the following multiplication problem:
\[ 29 \times \fbox{$\phantom{00}$} = 2,407. \]
What is the missing number?
|
a
|
$77$ |
|
b
|
$38$ |
|
c
|
$29$ |
|
d
|
$83$ |
|
e
|
$803$ |
The area model above can be used to represent the following multiplication problem:
\[ \fbox{$\phantom{00}$} \times 54 =1,566. \]
What is the missing number?
|
a
|
$29$ |
|
b
|
$19$ |
|
c
|
$34$ |
|
d
|
$24$ |
|
e
|
$39$ |
Using the area model below, find the value of
First, we compute the missing values. This gives the following picture:
Now, notice the following regarding the big rectangle:
its length is
its width is
its area is
Therefore, this area model can be used to represent the following multiplication problem:
Using the area model above, find the value of $32 \times 26.$
|
a
|
$792$ |
|
b
|
$902$ |
|
c
|
$832$ |
|
d
|
$612$ |
|
e
|
$652$ |
Using the area model above, find the value of $65 \times 27.$
|
a
|
$1,345$ |
|
b
|
$1,755$ |
|
c
|
$1,545$ |
|
d
|
$1,845$ |
|
e
|
$1,575$ |
Using the area model below, find the value of
First, we set up the model. The numbers and can be expressed in expanded form as and So, we place and above the rectangles and and to the left of the rectangles.
Next, we compute the missing values. This gives the following picture:
Now, notice the following regarding the big rectangle:
its length is
its width is
its area is
Therefore, this area model can be used to represent the following multiplication problem:
Using the area model above, find the value of $17 \times 14.$
|
a
|
$238$ |
|
b
|
$278$ |
|
c
|
$198$ |
|
d
|
$268$ |
|
e
|
$228$ |
The area model below represents the multiplication problem $42 \times 56.$ Insert the missing numbers.
|
a
|
|
|
b
|
|
|
c
|
|
|
d
|
|
|
e
|
