MACC.4.MD.3
Example: A plan for a house includes a
rectangular dining room with an area
of 60 square meters and a perimeter
of 32 meters. What is the length and
the width of the dining room if the
width is longer than the length?
What is being asked?
A plan for a house
includes a rectangular
dining room with an area
of 60 square meters and
a perimeter of 32 meters.
What is the length and
the width of the dining
room if the width is
longer than the length?
First we look to see what is
being asked of us.
What is the length and the
width of the dining room?
Solving the problem…
This problem seems easy at first but it is rather
complex. The student needs to understand the
difference between perimeter and area. They
should begin by listing the factors of 60 knowing
that they will have to multiply 2 sides of the
rectangle together to get the area.
Step 1:
Find the factors of 60:
Students can make a
list or chart of the
factors and check to
see if each set
works.
60:
1 x 60
2 x 30
3 x 20
4 x 15
5 x 12
6 x 10
Guess and Check ✔
Next the student may use the guess and check method.
Draw a rectangle and label each side with the factors
60m
1m
1m
60m
The factors 1 and 60 do not work because when you add the
sides of the rectangle together to find the perimeter, you get
122. We are looking to find a perimeter of 32m. We move to the
next set of factors.
30m
2m
2m
30m
The factors 2 and 30 do not work. When
you add the sides of the rectangle
together to find the perimeter, you get 64.
Again, we are looking for 32m. We move to
the next set of factors.
Guess & Check
We try the next set of factors: 2, 30
Check the next factors…
The factors 3 and 20 do not work.
When you add the 4 sides of the
rectangle together to find the
perimeter, you get 46. Again, we are
looking for a perimeter of 32m so
this is incorrect. We continue trying
the other factors.
20m
3m
3m
20m
The factors 4 and 15 do not
work. When you add the 4 sides
of the rectangle together to find
the perimeter, you get 38. Again,
we are looking for a perimeter of
32m so this is incorrect.
15m
4m
4m
15m
More factors
The factors 5 and 12 do not work. When you add
the 4 sides of the rectangle together to find the
perimeter, you get 34. Again, we are looking for
a perimeter of 32m so this is incorrect.
12m
5m
5m
12m
It works!!
The final factors 6 and 10 do work. When you add the 4
sides of the rectangle together to find the perimeter, you
get 32. Again we are looking for a perimeter of 32m so this
is correct. They student should be able to identify that
these 2 factors work!
10m
6m
6m
10m
Step 1:
Find the factors of 60:
60:
Students can make
a list or chart of the
factors and check to
see if each set
works.
Perimeter:
1 x 60
122m
2 x 30
64m
3 x 20
46m
4 x 15
38m
5 x 12
34m
6 x 10
32m
Finding the solution
To answer the original question, “ What is the
length and the width of the dining room?”
Don’t forget…
The word problem states that the width is longer
than the length, which indicates that the bigger
number will represent the width.
The Answer:
Attend to Precision
This ties in with attending to precision because it
forces the student to be precise. The students
must understand the specific formulas to find
the perimeter and area of a shape and be able to
apply it. In this specific example, they have to
know the exact factors of 60 and be able to list
them out. They also have to be precise when
calculating their measurements to find the
length and width of the given shape.