Math-in-CTE Lesson Plan
Lesson Title: Don’t Fence Me In
Lesson #: AM01
Occupational Area: Agriculture
CTE Concept(s): Calculate cost of materials, determine the costs of a project,
and identify the units of measurement by which various materials are sold,
setting steel post, laying out fence lines.
Math Concepts: Percent, computation in context, convert measurement units,
calculating perimeter/area/volume of a rectangle, circle, and triangle.
Lesson Objective:
PASS Algebra I, Standard 2, Objective 8b: Process
Standard I, Objective 2: Algebra I, Standard 3, Objective
b: Algebra I, Standard I, Objective I: Geometry, Standard
2, Objective 4.
Supplies Needed: Calculator, Pencil, Paper
Link to Accompanying Materials: Agriculture Mechanics AM01 Downloads
TEACHER NOTES
(and answer key)
1. Introduce the CTE lesson.
Make a rectangular pen out of
electric fence posts behind Ag
The time has come to ‘Fence Me In’.
We need to build a 5-strand barbed wire building or in shop.
fence around a 40-acre field. Where
would you begin when solving this
problem? What formulas might you
need to know? Refer to the drawing of
your acreage and cost tables to help
you solve this problem. You will be
finding the perimeter of your acreage,
computing the total cost of fencing it
and determining the percentages of
costs.
THE "7 ELEMENTS"
2. Assess students’ math awareness
as it relates to the CTE lesson.
What is perimeter?
Perimeter is the distance around the
outside of a shape or figure.
How is perimeter found?
Perimeter is found by adding the
lengths of all sides.
How many feet in a yard?
Three feet equals one yard.
What does the term ‘linear feet’ Linear feet measures the length of a
mean?
two dimensional object.
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How do you determine the total feet Total Feet of wire = (Perimeter) ·
and cost of wire?
(Number of wire on fence).
Cost of Wire = (Total Bundles of
wire) · (Cost per bundle)
Total number and cost of posts?
How will you determine how many
posts you will need?
Total Number of Posts =
(Perimeter/(Distance between
posts)) - 12 preset corners
Cost of posts = (Number of posts) ·
(Cost per post)
How will you determine the
percentage of each cost? Keep in
mind that the distance between
every post will be 8 feet.
Cost percentage of wire = ((Cost of
wire)/(Total Cost)) · 100
Cost percentage of posts = ((Cost of
posts)/(Total Cost)) · 100
3. Work through the math example
embedded in the CTE lesson.
Let’s work through a couple of
similar examples.
Pass out student worksheet.
1.) Let’s find the perimeter of a hog pen
that is 8 yards wide and 12 yards
long.
2.) Just to make it interesting, let’s
express our perimeter in feet. To do
that, we need to convert our yards to
feet. *Remember that there are 3
feet in 1 yard.
8 · 3 = 24 feet
12 · 3 = 36 feet
So now we know our dimensions in
terms of feet. Now use the formula
used to find perimeter:
P = 2(length) + 2(width)
P = 2(36) + 2(24)
P = 72 + 48
P = 120 feet
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3.) Using the same information in the
last example, let’s suppose we want
to put a 2-wire electric fence around
our hog pen. We need to calculate
how many feet of wire we need to do
this. Remember that we found our
perimeter to be 120 feet. So, if each
wire must go around the pen, that Students will need to know how
means we need 2 · 120 or 240 feet many feet of wire are in a bundle.
of wire. If this wire is sold by We used 100 ft.
bundles and each bundle contains
100 feet of wire, how many bundles
will we need? 240/100 = 2.4. Since
we can’t buy 0.4 of a bundle, we will
need to buy 3 bundles in order to
have enough wire.
4.) We need to also calculate how many
posts we will need, right? Assuming
that each post is 6 feet apart, how
many would we need?
120 feet divided by 6 feet = 20 posts
5. & 6.) Now let’s figure the cost of our
wire and posts. Use your cost tables This worksheet was not intended to
to do this.
stand alone. We need to use cost
tables. If these are unavailable,
20 posts · $2 per post = $40
please supply costs of:
3 bundles · $20 per bundle = $60
$2 per post
$20 per bundle
7.) So the total cost for our fence would
be $40 + $60, which is $100.
8). Finally, we are ready to build a 5strand barbed wire fence around a
40-acre field. Let’s refer to our Second page of worksheet.
diagram and note that our corner
posts are set and were donated by
Allen Bass, local welder.
a.) We need to begin by finding the
perimeter of our field.
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P = 2(width) + 2(length)
P = 2(220) + 2(880)
P = 440 + 1760 = 2200 yards
Notice that our perimeter is in terms of
yards. For practical purposes, we
need to convert this to feet.
Remembering that there are 3 feet in
a yard, we can do this by multiplying
2200 yards by a ratio equal to one
that contains feet and yards.
 2200 yards  3 feet 
  6600 feet


1

 1yard 
The yards cancel out, leaving you
with a number in terms of feet.
b.) Now that we know the perimeter in
feet, we can determine how many
posts we need. The simplest way to
do this is to divide the perimeter by
the distance between the posts.
Number of posts =
6600 feet
 825
8 feet
Remember that our corner posts
were donated and already set, so we
need to subtract these off.
825 – 12 = 813 total posts
c.) Next, we need to figure out how
much wire we need. Since this wire
is along the perimeter of our field,
the amount of one strand of wire will
be the same as the perimeter, which
is 6600 feet. Because we have 5
strands, we need to multiply the
amount needed for 1 strand by 5.
Total wire = 6600 feet · 5 = 33000 ft.
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When we go to our wire, we will see
that it is sold by the bundle. Barbed
wire is sold in bundles that contain
600 feet of wire. So to figure out
how many bundles we need, we
have to divide the total amount of
wire needed by 600 feet.
33000 feet
 55 bundles
600 feet
Once again, if this information is not
readily available in cost tables,
supply this information to the
students:
600 feet per bundle
$2.29 per post
This works out nicely, however; we
need to take into consideration that
we will be wrapping the wire around
the corner posts and we may have
breakage and have to repair it,
which will require more wire. So
when we go to buy our wire, we
need to buy one more bundle in
order to insure that we have enough
wire for our project.
$34.95 per bundle
Make sure students understand that
they need to add one more bundle to
allow for breakage and extra wire to
wrap around the posts.
d.) We’re ready to go buy our materials.
Use your cost tables to help you
determine this. Remember that if
you were doing this on your own,
you would need to compare prices at
several places to insure minimal
cost. Let’s compute the cost of our
posts first.
813 posts · cost per post =Total cost
813 posts  $2.29  $1861.77
e.) Now let’s figure the total cost of our
wire. Remember that we decided
that we should buy an extra bundle,
so we need 56 bundles altogether.
56 bundles · cost per bundle
= Total cost
56 bundles  $34.95  $1957.20
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Total cost is found by adding the
individual costs.
Post cost + Wire cost = Total cost
$1861.77 + $1957.20 = $3818.97
f.) Finally, we’re ready to compute the
cost percentages. In other words,
we are going to figure out what
percentage of our total cost was
posts and what percentage was
wire. Let’s find the percentage of
the cost of posts first.
Total post cos t
 100  % of cos t
Total cos t
$1861.77
 100  48.75%
$3818.97
Let’s find the percentage of the cost
of the wire.
Total wire cos t
 100  % of cos t
Total cos t
$1957.20
 100  51.25%
$3818.97
Note that the cost percentages of
each add up to 100%. If they hadn’t,
we would have known that we had
made a mistake.
4. Work through related, contextual
math-in-CTE examples.
Class discussion.
Ask students to determine the
difference in total feet of wire if they
were to build a 4-wire fence instead of a
5-wire fence. What would the cost be if
the posts were wooden instead of tposts?
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5. Work through traditional math
examples.
These problems can be used as
chalkboard examples or see
1. Find the perimeter of a rectangle traditional math handout attached.
whose length is 90 feet and width 1. P = 2(90ft) + 2(60ft)
is 60 feet.
P = 180ft + 120ft
a) 150 feet
P = 300 ft
b) 5400 feet
c) 300 ft
c) 300 feet
d) 540 feet
e) none of the above
2. How many yards are in 743 feet?
a) 2229 yards
2. 743/3
b) 247.6666 feet
b) 247.6666 ft.
c) 61.91666 yards
d) 247.6666 yards
e) none of the above
3. If the perimeter of a rectangular
corral is 296 yds., and the length
of the corral is 196 ft., what is the
width of the corral in feet?
3. 296 yds · 3 ft/yd = 888 ft.
P = 2(length) + 2(width)
888ft = 2(196ft) + 2(w)
888ft = 392ft + 2(w)
496ft = 2w
w = 248ft
6. Students demonstrate their
understanding.
See worksheet.
Students are to complete the
worksheets.
Transport students on a field trip to view
and discuss other types and styles of
fences. The style of the fence has a
direct correlation to the cost of building
the fence.
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7. Formal assessment.
Additional perimeter problems were
developed for unit and semester exams.
1. Find the perimeter of a cattle lot 1. 264 ft.
that is 60 ft. by 72 ft.
P=2(length) + 2(width)
P=2(60) + 2(72)
P=120 + 144 = 264 ft
2. Find the total cost of the above
electric fence with two wires.
The posts are set 12 feet apart.
The electric fence posts are
$2.25 each. The wire comes in
bundles 100 ft. long @ $25 per
bundle.
2. $199.50
22 posts · 2.25 =$ 49.50
Perimeter needs to be doubled
for two wires.
264 ft · 2 = 528
528/100=5.28 bundles
6 bundles @ $25 = $150.00
Add posts to wire.
$150.00 + $49.50 = $199.50
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