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Math-in-CTE Lesson Plan
Lesson Title: Octagon Hay Feeder
Lesson #: AM07
Occupational Area: Agriculture
CTE Concept(s): Use a tape measure, use a carpenters square, construct
projects and equipment using an arc welder.
Math Concepts: Computation in context, rate, scale drawing, map model,
apply geometric properties, function, equation, model problem situation, use
algebra to solve problems
Lesson Objective:
Translate word phrases and sentences into expressions
and equations and vice versa. (Pass: Algebra I, Standard
1-1)
Solve linear equations by graphing or using properties of
equality. (Pass: Algebra I, Standard 1-6A.)
Draw and analyze 2- and 3-dimenzional figures. (Pass:
Geometry, Standard 2-2)
Use geometric tools (e.g., protractor, compass, straight
edge) to construct a variety figure. (Pass: Geometry,
Standard 2-6)
Supplies Needed:
Link to Accompanying Materials:
Agriculture Mechanics AM07 Downloads
TEACHER NOTES
(and answer key)
THE "7 ELEMENTS"
1. Introduce the CTE lesson.
Due to the high demand of round bale
feeders in our community, we are going to
construct octagon bale feeders, not round.
Due to the nature of an octagon, we need
to look at a new approach to building
these feeders. Although we will utilize the
pipe bender to construct the angles for the
octagon, we could also use the cutoff saw
to build the same angles, or even a miter
saw to cut wood projects.
First we need to determine the angle of an
octagon and how to draw it on paper. We
will draw the octagon and use a ratio to
scale the picture to the optimum size.
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Due to the nature of this project,
a wood project may be more
“user friendly” than using metal.
This could be a picture frame…
2. Assess students’ math awareness as
it relates to the CTE lesson.
Question the class. Define:

Octagon – eight sided polygon

Complimentary angles – two
angles whose sum is 90

Perpendicular – two lines
intersecting in a 90° angle.

Polygon – A union of segments
connected end to end, such that
each segment intersects exactly two
others at its endpoints.

Proportion – a statement that
expresses ratios which are equal.

Unit of measure

Linear feet or inches – measures
length of 2-D object

Does anyone know the formula for
finding the angle of an octagon?

How can we find the optimum
diameter of the bale feeder?

What is the diameter of a round
bale?

From a drawing, how will we
determine the actual dimensions of
the bale feeder?


In discussing the complimentary
angle, be sure the students know
that a triangle has 180° total. For
example, start with a right
triangle with a 20° angle. To find
the third angle C, you can say
180°= 90° + 20° + C. Now
subtract 90° from both sides
gives 90° = 20° + C. Then
subtract 20° from both sides
gives 70° = C.
Examples can be quickly drawn
on chalkboard to give students a
visual.
For a 7 ft diameter feeder the
sides will be 2.9 ft and for a 6 ft
diameter feeder the sides will be
2.5 ft.
angle = (N-2) · 180°
N
Will the angle for a small octagon be
the same angle for a larger one?
How will we “build” the angles of the
octagon?
What would we do to find the angle
to be cut using the cutoff saw?
2
(Where N is the number of sides)
Take them to shop and show on
miter or cutoff saw with scrap
material. In addition, transfer the
angle with a sliding T bevel to the
saw.
3. Work through the math example
embedded in the CTE lesson. Now
that we have our formula we will find the
angle of an octagon:
angle = (N-2) · 180°
· is the same as multiply (x)
N
(N = # of sides of the polygon)
Angle =
(8  2)180 6(180) 1080


 135 
8
8
8
The use of a protractor and T
bevel may be used to transfer the
angle to the saw.
Next we need to practice constructing a
135° angle of various sizes (e.g. 6 inch).
Construct an octagon on paper. Using our
drawing we can take the welding rods and
bend them to an exact fit of the drawing
and welding them together to form a scaled
model of the feeder.
Now we need to address the conversion
from scale to actual. The students will
determine the ratio of the scale to actual.
To make this process easier we will have
the students build their model on a 1:12
scale.
For example:
1
7

gives us 1x = 7(12) so x = 72.
12 x
Therefore, the measurement of their model
will take the place of the 7 in the above
example to find the actual measure of the
feeder.
When a pipe bender is not available or for
extra instruction where a cutoff saw would
be more applicable to a project, we will
address building the angle with the cutoff
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saw. Special care needs to be taken to
allow ample time for this to “click” for the
students. Have the students look from the
perspective of the saw, the middle of the
octagon. Using the picture and scale that
was constructed earlier, the students may
get a hands-on approach to learning. If this
approach does not develop into the correct
findings then one must use the
Pythagorean theorem, which will be familiar
to some students. Draw a line from the
center of the octagon to one of the
“corners” of the octagon.
Then draw
another line from the center of the octagon
perpendicular to one of the sides adjacent
to the “corner”. See the example:
Mathematically, the line segment
AB bisects the angle “B” (cuts the
angle in half). So the 135° is cut
into 67.5°.
A
B
Looking at the triangle, we can see the
different perspectives to view the
angles. “A” being the saw perspective
and “B” is our perspective. The saw
perspective is looking at the compliment
of B, thus 90° - 67.5°= 22.5°.
For a 7 ft diameter feeder, the sides will
be 2.9 ft. For a 6 ft diameter feeder, the
sides will be 2.5 ft.
Now the students may go to the shop
and produce the feeder.
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**** Optional formula that
maybe used to challenge the
more “advanced” students to
find the length of the sides is
2r · tan(180°/N) where r is
the radius and N is the
number of sides.
4. Work through related, contextual
math-in-CTE examples.
angle = (N-2) · 180°
What is the angle of an equilateral triangle?
N
Square?
Rectangle?
Pentagon?
(N = the number of sides)
Hexagon?
60°, 90°, 90°, 108°, 120°
5. Work
examples.
through
traditional
math
Find the complimentary angles of 20º; 45º;
70º; 45º; 53º
37º;
A classroom has 3 girls and 9 boys. If
21 boys
another classroom has the same ratio, how
many boys are in the class if there are 7
girls?
6.
Students
understanding.
demonstrate
their
Students will construct one level of the bale Scrap material (wood or metal)
feeder.
would be useful to make these
In addition, students may also construct the “smaller” projects.
various shapes, pentagon, hexagon,
heptagon (7), nonagon (9), or decagon(10),
to construct a picture frame or similar
projects.
7. Formal assessment.
Problems will be on unit and/or semester
tests as necessary.
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