Math-in-CTE Lesson Plan Template
Lesson Title: Cuts and Measurements
Author(s):
Emily Gehrig
Phone Number(s):
(541) 308-6765
Deb Glover
Lesson #
E-mail Address(es):
[email protected]
[email protected]
(541) 566-2335
Occupational Area: Welding
CTE Concept(s): Cutting Tool Efficiency
Math Concepts: Add and Subtract Fractions, Simple Equations
Lesson Objective:
Determine which cutting tool is the most efficient for a given job.
Supplies Needed:
2’ flat bar, O/A Cutting Torch, Plasma, Chop Saw, Band
Saw, Ironworker (any cutting tools you may have in your shop).
THE "7 ELEMENTS"
TEACHER NOTES
(and answer key)
1. Introduce the CTE lesson.
Script-“How many of you have ever been
working on a building project, you knew that
you would need exactly 6 (for example) feet of
material. After you make all of your cuts and
start building, you are just 1 inch to short.
Has this ever happened to you? I know it has
happened to me! Today we are going to learn
how to keep that from ever happening again.”
Objective: Determine which cutting tool is the
most efficient for a given job.
2. Assess students’ math awareness as it Give each student three pieces of licorice.
relates to the CTE lesson.
Have them cut the licorice into three pieces to
match the following lengths:
“You all have been given three pieces of licorice.
Using your ruler and scissors cut the three pieces
 4½“
of licorice to match the measurements on the
 2¼“
board. After you have completed your cuts bring
 6 5/8 “
the licorice up to my table to compare your Prior to the lesson cut poster board pieces to
licorice lengths to the poster board templates. If match the above lengths as well. After the
your licorice matches the template, you may eat students cut their licorice to length, have
it. If it does not match you need to try again. If them compare the licorice to the templates
your licorice is cut to short leave it with me, so I you have cut.
can eat it, you will get a new piece to start from.”
At this point asses the student knowledge of
fractions. If the cuts are not correct, you may
need to review measurement. If the cuts
closely resemble the template, the student is
ready to move on.
Math-in-CTE Technical Assistance
3. Work through the math example embedded Prior to the lesson, accurately cut flat bar into
in the CTE lesson.
two foot lengths.
“You will be working in partners. Each group
needs a piece of this pre-cut metal. The metal
you are getting is called flat bar. It is 2 inches
wide, a quarter inch thick, and 2 feet long. In
our shop there are four types of equipment
you can use to cut this size of metal.
Prepare the names of the cutting tools in your
shop on small pieces of paper to place in “the
hat.” Students will draw for their tools from
this hat.
Each pair of students will need a tape
measure and soap stone, or a Sharpie
Q: Who can tell me what equipment we can use marker.
to cut this metal?
Strategically divide students into partners.
A: (Answer will depend on what equipment you One math savvy student with a struggling
have in your shop). In our shop we can use student.
the plasma, O/A cutting torch, chop saw, and
On the board write the following cut lengths:
the band saw.
1. 2”
Great job!
2. 1 ½”
Each group will use one of these pieces of
3. 2 ¼”
equipment. We will draw, from a hat, which
piece of equipment your group will be using.
4. 3 7/8”
On the board there are seven cut lengths. In your
group, you will measure the first cut length,
make the cut, then measure the second
length, make the cut, measure the third length,
and so on. Do not make all of your marks
prior to cutting!!! Keep all pieces, and mark
them with your name and cut length.
5. 1 ¾”
6. 2 5/8”
7. 3 3/8”
4. Work through related, contextual math-in- Complete questions 1-4 on the board in front
CTE examples.
of the class. For questions 5-7 have the
students attempt to work on their own.
“On the white board write your names and under
your names write the length of the remaining Method #1
piece of flat bar.
1.) 24” - 2” = 22”
Q: Notice that no one has the same answers.
2.) 22” - 1 ½ = 20 ½ ”
What are some thoughts on why the remaining
3.) 20 ½ ” – 2 1/4” = 18 ¼ ”
flat bar is a different length in each group?
A: Measured incorrectly, cut in the wrong place, 4.) 18 ¼ “ – 3 7/8 = 14 3/8”
some equipment is more accurate than other 5.) 14 3/8” – 1 ¾” = 12 5/8”
equipment.
6.) 12 5/8” – 2 5/8” = 10”
Now using the cut lengths on the board please
figure how long the remaining flat bar should 7.) 10” – 3 3/8” = 6 5/8”
be.
Example: The first cut length is 2”, so if you start Method #2
with the 24”, you cut 2” off, you are left with
2 + 1 ½ + 2 ¼” + 3 7/8” + 1 ¾” + 2 5/8” + 3
__? (22”)
3/8” = 17 3/8”
Now that you know how much flat bar is
remaining, and theoretically how much should be 24 – 17 3/8” = 6 5/8”
remaining subtract the remaining from the
Math-in-CTE Technical Assistance
theoretical total.
To determine total waste:
Q: How can we determine how much material Theorectical Total-Actual Total=Total Waste
was wasted on each cut?
A: Divide the total waste by the number of cuts
To determine the waste per cut:
(in this case there were 7 cuts).
Total waste/Number of Cuts=Amount of
Waste per Cut
5. Work through traditional math examples.
See attached worksheet.
To give you guys some practice please complete
this worksheet.
6. Students demonstrate their understanding.
Q: Judging by the lengths remaining from your
bars, what can you tell me about the efficiency
of the cutting tools used?
A: Answers may vary. The bar that is the longest
was probably cut by the most efficient cutting
tool, for this specific job.
Q: Why is this information important for us to
understand?
A: If you are trying to cut a piece of metal into
four equal pieces, and you cut on the wrong
side of the line your last piece will not equal
the same size as the other pieces. Or…if you
are working for a manufacturer and you don’t
include the lost material, due to cuts, you may
very well cost your employer a lot of money.
Different pieces of cutting equipment will cause
lesser or greater amount of cut loss.
Depending on the piece of equipment you use
your job may be more accurate. However,
there will be times when the most efficient
piece of equipment for one job will not work for
another job. Example: The chop saw works for
flat bar, but not for sheet metal.
7. Formal assessment.
Formal assessment will be done on a unit
test.
Important notes: There is some prep work that needs to be done prior to the lesson. Attached is the
scanned step by step answer key to the math problems, and a worksheet to check for understanding.
Math-in-CTE Technical Assistance