Let's consider the following area model.
To determine the missing length, we consider the area of the blue rectangle (the one on the right-hand side).
The area of the blue rectangle is and its width is Therefore, the length of this rectangle must be Let's add this length to our area model.
And we're done! Let's see another example.
From left to right, find the missing numbers in the area model above.
We need to look at the blue and pink rectangles:
Let's first look at the blue rectangle (the one on the left-hand side). Its area is and its width is Therefore, the length of this rectangle must be Let's add this to our model:
Now, let's look at the pink rectangle (the one on the right-hand side). Its area is and its width is Therefore, the length 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
|
$1$ |
|
b
|
$5$ |
|
c
|
$6$ |
|
d
|
$7$ |
|
e
|
$4$ |
From left to right, find the missing numbers in the area model above.
|
a
|
$10$ and $2$ |
|
b
|
$10$ and $4$ |
|
c
|
$8$ and $3$ |
|
d
|
$8$ and $2$ |
|
e
|
$10$ and $3$ |
Area models can be used to represent division problems.
For example, let's take a look at the following area model.
Now, let's look at the big rectangle:
its length is
its width is
its area is
Since the area of the big rectangle equals its length multiplied by its width, this model represents the following multiplication problem:
Writing this as a division problem, we get
Note: When using area models to represent division problems, the divisor ( in this case) is the number on the left-hand side of our model.
The area model above can be used to represent the following division problem:
What is the missing number?
Let's look at the big rectangle:
its length is
its width is
its area
Therefore, this area model can be used to represent the following multiplication problem:
Writing this as a division problem, we get
Therefore, the missing number is
The area model above can be used to represent the following division problem:
\[ 77 \div \fbox{$\phantom{00} $} = 11 \]
What is the missing number?
|
a
|
$6$ |
|
b
|
$8$ |
|
c
|
$18$ |
|
d
|
$7$ |
|
e
|
$9$ |
The area model above can be used to represent the following division problem:
\[ \fbox{$\phantom{00} $} \div 4 = 14 \]
What is the missing number?
|
a
|
$56$ |
|
b
|
$40$ |
|
c
|
$60$ |
|
d
|
$16$ |
|
e
|
$10$ |
Using the area model above, find the value of
First, we find the missing values. This gives the following:
Now, notice the following regarding the big rectangle:
its length is
its width is
its area
Therefore, this area model can be used to represent the following multiplication problem:
Writing this as a division problem, we get
Using the area model above, find the value of $84\div 7.$
|
a
|
$12$ |
|
b
|
$13$ |
|
c
|
$16$ |
|
d
|
$11$ |
|
e
|
$14$ |
Using the area model above, find the value of $90\div 6.$
|
a
|
$18$ |
|
b
|
$14$ |
|
c
|
$12$ |
|
d
|
$16$ |
|
e
|
$15$ |
