Math-in-CTE Lesson Plan
Lesson Title: The Foundations of Building
Lesson #: AM02
Occupational Area: Agriculture
CTE Concept(s): Calculate cost of materials, determine cost of materials, use
a tape measure, calculate volume of concrete.
Math Concepts: Computation in context, convert measurement units,
calculating perimeter/area/volume of a rectangle, circle, triangle.
Lesson Objective:
Student will demonstrate a working knowledge of:
*Translating word phrases and sentences into
expressions and equations and vice versa. (Pass:
Algebra I, Standard 1, Objective 1)
*Using the formulas from measurable attributes of
geometric models (perimeter, circumference, area and
volume), science, and statistics to solve problems within
an algebraic context. (Pass: Algebra I, Standard 2,
Objective 8a)
*Drawing and analyzing 2- and 3-dimensional figures.
(Pass: Geometry, Standard 2, Objective 2) and its
application in agriculture power and technology, while
recognizing it in other contexts.
Supplies Needed:
Link to Additional Materials:
Agriculture Mechanics AM02 Downloads
TEACHER NOTES
(and answer key)
THE "7 ELEMENTS"
1. Introduce the CTE lesson.
What types of materials are used in This lesson is anticipated to take
building/construction?
about a week to complete.
Of these, we will work specifically on
concrete which is used for floors, walls, Have the students make a list. We
drainage systems, walkways, patios, are looking for steel, lumber,
footings, foundations, and anchoring concrete, etc.
systems.
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Students need to be told that
is measured in cubic yards
Why do we need to know how to concrete
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calculate volume in cubic yards for (yd ). If the material is concrete, they
need to make sure their final result is
concrete?
in these units.
1) It allows us to estimate the cost of
the materials prior to a project
which in turn allows us to make
decisions relating to scaling up or
down or even scrapping the project
do to budgeting reasons,
2) We can cross check the supplier’s
figures to make sure the proper
amount will be delivered and
billed.
2. Assess students’ math awareness You may either divide the class into
as it relates to the CTE lesson.
groups using the think-pare-share
When we talk about pouring or running method, or just record answers from
concrete, we start by building a form in the class in a general discussion.
which to pour it. The form is usually The shape of a cube is basically that
cubic, rectangular, or cylindrical in of a box with equal sides.
shape.
The size of a cubic yard is 1 yd x 1
What is the shape of a cube?
yd x 1 yd.
What is the size of a cubic yard?
V = length x width x height (depth).
What is the formula for determining 1 yard = 3 feet
volume?
1 foot = 12 inches
How many feet are in a yard?
Most forms are measured in feet or
How many inches are in a foot?
inches (which need to be converted
When getting our volume in cubic yards, to feet), but concrete is measured in
cubic yards. So, if a cubic yard is 1
why do we divide by 27?
yd x 1 yd x 1yd and 1 yard = 3 feet,
then a cubic yard is also 3 ft x 3 ft x
3 ft and when we multiply 3 x 3 x 3
we get 27.
Use a model made of pvc pipe or
boards and colored string to
reinforce how 27 is obtained in the
formula. This may help if the
students forget the number 27, and
help trigger their memory of how to
figure this divisor.
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3. Work through the math example
embedded in the CTE lesson.
When we start calculating the volume of
your given form, we find the area by
multiplying your length and width
(usually in feet). Most likely, the height
or depth will be in inches. This must be
converted to feet and then multiplied by
the answer from the other two (length
and width). Then, to convert from cubic
feet to cubic yards (if the material is
concrete), this answer must be divided
by 27.
L
W
H
LxWxH
27
Use the formula to find the amount of
concrete needed to fill a form that is 60
ft long by 40 ft wide by 6 inches deep.
60feet
40ft
6 in
Change 6 inches to feet
6 in. ÷ 12 in. = 0.5 in.
Use formula, multiply the three
dimensions, then divide by 27.
(60 ft) x (40 ft) x (.5 ft)
27
Answer: 44.44 yd3
(For more problems see “Concrete”
worksheet).
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4. Work through related, contextual
math-in-CTE examples.
Find the amount of concrete needed for Change 4 inches to feet.
a sidewalk from a house to a driveway
that is 12 feet long, 3 feet wide, and 4 4 in. ÷ 12 in. = 1/3 ft.
inches thick.
Multiply the dimensions, then divide
by 27.
(12 ft) x (3 ft) x (1/3 ft)
27
Answer: .44 yd3
Emphasize that this time answer is
to be in cubic feet and there will be
Find the volume in cubic feet of a wheat no need to divide by 27. Just
truck bed that is 20 feet long, 7 feet multiply the three dimensions.
wide, and 4.5 feet deep.
(20ft) x (7 ft) x (4.5ft)
Answer: 630 ft3
Note: It may seem more logical to
give this answer in bushels but we
are dealing with “non-grain"
Once again, answer is to be in cubic
Find the volume in cubic feet of the city feet.
swimming pool, if the dimensions of the Volume = (101 ft) x (42 ft) x (7 ft)
pool are 101 feet long, 42 feet wide, and Volume= 29,694 ft3
7 feet deep.
5. Work through traditional math
examples.
Multiply dimensions. Do not divide
Find the volume in cubic feet of a by 27.
rectangular prism that is 6 feet long, 4 (6 ft) x (4 ft) x (2 ft)
feet wide and 2 feet high.
Answer: 48 ft3
For additional problems see “Math”
problems worksheet.
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6.
Students
demonstrate
understanding.
their For class field trip, the teacher may
create groups for students to work in
Students are assigned the task of or do individually.
finding the measurements of an existing
structure at their home (ex. sidewalk,
patio, etc) and determining the amount
of concrete used in building that
structure.
Class will take a short field trip to find
the measurements of an existing
structure around the campus or school
farm (ex. sidewalk, tennis court, etc)
and determine the amount of concrete
used in building that structure.
7. Formal assessment.
1.
Find the amount of concrete Convert 6 inches to feet.
needed to pour a driveway that is 6 in. ÷ 12 in. = 0.5 in.
40 feet long, 25 feet wide, and 6
Multiply the dimensions and divide
inches deep.
by 27. (Material is concrete.)
(40 ft) x (25 ft) x (0.5 ft)
27
Answer #1: 18.52 yd3
2.
3.
Find the amount of concrete (3 ft) x (3 ft) x (3 ft)
needed to pour a base for an
27
antenna tower that measures 3 Answer #2: 1 yd3
feet by 3 feet by 3 feet.
(Concrete)
Find the volume in cubic feet of a (5 ft) x (3 ft) x (1 ft)
(Do not
rectangular prism that is 5 feet divide – answer requested in ft3)
long by 3 feet wide by 1 foot high. Answer #3: 15 ft3
For additional test questions see
Material Costs Test.
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