Building Materials (Grade Levels: 5  8)
Building Materials
 Community Geometry
 Career Connections  More Math Concepts
Student
Activity (PDF File)
Answers
(PDF File)
One
aspect of architecture and construction is determining
how much building material you need. Calculating the
amounts of the various materials involves using a lot
of mathematics.
Pouring
a foundation
1. When you buy concrete, it comes in a unit called
a cubic yard. A cubic yard of concrete is enough concrete
to fill a cube that is 3 feet on each side. How many
cubic feet of concrete are in a cubic yard?
2.
When you build a building, you have to pour a foundation
for the walls to sit on. Suppose you want to pour a
foundation for a playhouse with an outside dimension
of 5 feet by 3 feet and a foundation that is 1 foot
wide and 1 foot deep. How many cubic feet of concrete
will you need?

5 + 5 + 1 + 1 (count the long sides first then
add the remaining blocks on the short sides) 

5 + 2 + 4 + 1 (count the sides as you go around
the rectangle) 

5 + 5 + 3 + 3  4 (count the complete sides and
then subtract the four corner blocks that each counted
twice) 
All
of these make sense depending on your strategy.)
3.
Now, suppose you want to pour a foundation for a rectangular
building with an outside dimension of 20 feet by 40
feet and a foundation that is 1 foot wide and 1 foot
deep. How many cubic feet of concrete will you need?
4.
How many cubic yards of concrete will you need?
5.
When you pour the foundation, it leaves an open rectangle
on the inside. What are the dimensions of this rectangle?
6.
In addition to pouring the concrete for the walls of
this foundation, the foundation you want requires you
to pour enough concrete inside the walls to make a floor
6 inches thick. How many cubic feet of concrete do you
need?
7.
How many cubic yards of concrete will you need make
the floor?
Building
a floor
One
way to build a floor (that is not sitting on the ground)
is to use joists. These are boards that lay on their
sides under the floor and run in the same direction
(parallel) to one of the sides. The rule when building
floors is that you need a joist to start and another
joist every 16 inches in a building, and if this does
not come out even, you need to add an extra joist. The
building you are working on is 20 feet by 40 feet.
8.
Suppose you want to have a joist run the same direction
as the 20foot side. This means you will need one joist
to start and joists every 16 inches along the side that
is 40 feet. How many joists would you need?
9.
If we laid these joists end to end, how long would they
be?
10.
Suppose we wanted to run the joists the same direction
as the 40foot side. How many joists would we need?
11.
If we laid these joists end to end, how long would they
be?
