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Lesson Plan
Course Title: Principles of Manufacturing
Session Title: Manufacturing Mathematics
Performance Objective:
At the end of this lesson, the student will be able to apply basic mathematic formulas to solve
problems found in the manufacturing business by completing all of the handouts for this lesson.
Specific Objectives:
 List different costs and explain
 Identify the basic units of measurement used in manufacturing
 Evaluate drawings for sizes of material
Preparation
TEKS Correlations:
This lesson, as published, correlates to the following TEKS. Any changes/alterations to the
activities may result in the elimination of any or all of the TEKS listed.
Principles of Manufacturing:

130.322(c)(17)(A)(B)(C)(D)(E)
…demonstrate communication techniques consistent with industry standards;
…locate relevant information needed to solve problems;
…apply mathematics concepts to solve manufacturing problems;
…analyze science principles used to solve problems;
…use the appropriate units of measure.

130.322(c)(15)(A)(B)(C)
…apply an engineering approach to problem solving to improve a manufactured product;
…apply critical-thinking strategies to the analysis of proposed solutions;
…apply decision-making techniques to engineering solutions.
Interdisciplinary Correlations:
Algebra I:

111.32(c)(1)(B)(C)(D)(E)
…gather and record data and use data sets to determine functional relationships
…describe functional relationships for given problem situations and write equations or
inequalities to answer questions arising from the situations;
…represent relationships among quantities using concrete models, tables, graphs,
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diagrams, verbal descriptions, equations, and inequalities;
…interpret and make decisions, predictions, and critical judgments from functional
relationships.

111.32(c)(11)(C)
…analyze data and represent situations involving exponential growth and decay using
concrete models, tables, graphs, or algebraic methods.
Teacher Preparation:
Teacher should review the Manufacturing Mathematics PowerPoint presentation, notes and
Excel Board Footage Worksheet. The handouts Manufacturing Mathematics, Material Cost, and
Board Footage should be printed for this lesson.
References:
“Mathematics for Manufacturing Student Workbook” By Bridge to Advanced Technological
Education and Employment
http://www.uic.edu/cuppa/techbridge/PDF/MathforManufacturing_100300.PDF
Instructional Aids:
1. Manufacturing Mathematics PowerPoint presentation
2. Excel Board Footage Worksheet
Materials Needed:
1. Pencil
2. Notebook
3. Manufacturing Mathematics handout
4. Material Cost handout
5. Board Footage handout
Equipment Needed:
1. Computer
2. Data projector
Learner Preparation: None required
Introduction
Introduction (LSI Quadrant I):
ASK: Have you ever wondered when, or if, you would ever use the math that you are learning?
ASK: Have you ever asked yourself why you should have to learn all these formulas?
SAY: Today, we are going to explore when, how and why math is necessary in manufacturing.
SAY: Calculating a pay check or figuring the cost to make a project are just several ways that
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math is used in manufacturing.
SAY: The Manufacturing Mathematics PowerPoint presentation that I will show will give you
ways that mathematics is used in all manufacturing companies.
SAY: You will be asked to use the information to complete some worksheets for a grade.
SAY: Hopefully, when you have completed this lesson, you can answer the questions that you
have had about the need to learn mathematics.
SHOW: Manufacturing Mathematics PowerPoint presentation
Outline
Outline (LSI Quadrant II):
Instructors can use the PowerPoint presentation, slides, handouts, and note pages in
conjunction with the following outline.
MI
Outline
Notes to Instructor
I. Introduction
A. Manufacturing Mathematics
B. Terms
C. Labor cost
D. Material cost
E. Machine cost
F. Product cost
G. Profit
H. Measurement units
I. Unit Cost
Begin Manufacturing
Mathematics
PowerPoint
II. Board Footage Formula
A. Board Footage
B. Square Footage
C. Linear Footage
A. Slides 13-23
Slides 1-12
Students write the
different costs in their
notes.
B. Slides 24- 27
C. Slides 28- 30
Resources:
Slides 31-32
.
III. The student practices using the formulas
Students will complete
the Manufacturing
Mathematics, Material
Cost, and Board
Footage handouts.
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Verbal
Linguistic
Logical
Mathematical
Visual
Spatial
Musical
Rhythmic
Bodily
Kinesthetic
Intrapersonal
Interpersonal
Naturalist
Existentialist
Application
Guided Practice (LSI Quadrant III):
The teacher will monitor the students as they work with the Manufacturing Mathematics
handout.
Independent Practice (LSI Quadrant III):
The students will work on the other handouts.
Summary
Review (LSI Quadrants I and IV):
Question: What is math used for in Manufacturing?
Answer: Allow the students to explain what they have learned.
Question: Can anyone tell me the formula for figuring board footage? Labor cost?
Material cost?
Answer: Allow students to give the formulas.
Question: Why is it necessary to have a set of plans?
Answer: Allow students to give their reasons.
Evaluation
Informal Assessment (LSI Quadrant III):
The teacher will watch the students and listen to the discussion.
Formal Assessment (LSI Quadrant III, IV):
The handouts will be graded.
Extension
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Extension/Enrichment (LSI Quadrant IV):
After the worksheets have been completed and collected, the teacher should lead a discussion
using the following questions:
1. Looking at the operating cost to machine 400 parts, do you think it is possible for the
company to save money? If so, how?
2. How do you think the company could expedite the time it takes to package 3,000 sets of
tools?
3. What do you think is the most expensive part of running a manufacturing company and
why?
4. What do you think would happen to a manufacturing company whose workers could not
complete basic math computations?
Students should design a project, and using the formulas, figure out how much material is
needed and what the cost will be.
Copyright © Texas Education Agency, 2012. All rights reserved
Name_____________________________________________
Date______________ Period _________
Flexible Manufacturers are to package 3,000 sets of tools. It takes three
minutes to organize and package the sets. If five people are working to
package the sets how much time will it take to complete the job?
The workers are paid $9.50 per hour. What is the labor cost for this job?
Number of hours worked ___________
Labor Cost __________
CNC lathe machine time cost $25 dollars per hour to
operate. The machine produces 400 parts in an eight
hour shift. What is the machining cost per part?
Answer _____________________________
The Flexible Manufacturers are asked to produce 1,000 4 X 6 plastic frames. The frames are
made from a sheet of 1/4 thick plastic 4” wide and 14” long. The sheet material used to make
these frames is 48” wide and 96” long. How many sheets of material will it take to produce
the order of frames? Each sheet cost $25.00 and labor cost per frame is $.75. What is the cost
of labor? What is the cost of the materials?
Number of sheets needed for job? __________
What is the material cost per frame? _______
What is the total cost per frame? ___________
Copyright © Texas Education Agency, 2012. All rights reserved
Name_____________________________________________
Use the measurements on the drawing
to fill in the chart. The chart will help
you with the measurements for finding
the board footage for the bookcase.
Date______________ Period _________
33
3/8”
11
A
TXWXL
Board Footage
1” X 12” X 12”
B
All material is 3/4” in thickness*
except the back is 1/4” plywood
12
C
12
C
12
C
12
C
B
51
Use this space to show your work. Use the back if
needed.
10
3
32
Part
Name
Quality
Thickness
D
Width
Length
Board
Footage
A
Top
B
Side
C
Shelf
D
Foot
Back
*
material less than 1” in thickness is
figured at 1” in the formula
Copyright © Texas Education Agency, 2012. All rights reserved
Name_____________________________________________
Date______________ Period _________
Answer the following questions in the answer blanks. The blank space below the question is a place for you to figure the answer.
Smith Lumber Company filled an order of 45 sheets of oak plywood. The sheets have 32
square feet in them (4’ X 8’ sheet). The company was going to produce cabinets out of the
plywood. Each cabinet needed 15 square feet of plywood. How many cabinets can be built
out of the plywood ordered?
Answer ________________________
Conner Nut and Bolt Company received an order for 300 of each of the items listed in the
chart. The chart shows the cost of each. Figure the cost of the order.
Part
Cost
Nut
$0.25
Lock
Washer
$0.12
Flat
Washer
$0.04
Bolt
$0.75
Answer _____________________
36”
ABC Cabinet Company was contracted to build
fifty wood framed mirrors. The mirror frame
size is twenty four inches tall by thirty six inches
long. What is the cost to make the mirror if the
frame material cost 75 cents per foot and the
mirror glass is a dollar per square foot?
32”
24”
22”
Answer __________________________
Copyright © Texas Education Agency, 2012. All rights reserved
Name_____________________________________________
Date______________ Period _________
Figure the board footage for the Shelf Coat Rack.
A
C
B
B
D
Shelf Coat Rack
24
All material is 3/4” thick
6
1 1/2
dowels 1/2” dia. 3” long
5
3
6
5
4
4 1/2
5
2
22 1/2
Part
Name
Quality
Thickness
3
1/2”
dia
Width
Length
Board
Footage
A
Top
B
Side
C
Back
D
Dowels
4”
Answer ________________________
Copyright © Texas Education Agency, 2012. All rights reserved
Name_____________________________________________
Date______________ Period _________
Flexible Manufacturers are to package 3,000 sets of tools. It takes three
minutes to organize and package the sets. If five people are working to
package the sets how much time will it take to complete the job?
The workers are paid $9.50 per hour. What is the labor cost for this job?
Answer
3,000 sets X 3 minutes each = 9,000 minutes for all sets
Labor Cost
$9.50 X 30 hours = $285 per person
$285 per person X 5 people = $1425
9.000 minutes / 5 people = 1800 minutes
Number of hours worked __30 hours___
Labor Cost __$1425____
1800 minutes / 60 minutes per hour = 30 hours
CNC lathe machine time cost $25 dollars per hour to
operate. The machine produces 400 parts in an eight
hour shift. What is the machining cost per part?
Answer
400 parts / 8 hours = 50 parts per hour
$25.00 per hour / 50 parts per hour = $0.50 per part
Answer _$0.50 per part_______________
The Flexible Manufacturers are asked to produce 1,000 4 X 6 plastic frames. The frames are
made from a sheet of 1/4 thick plastic 4” wide and 14” long. The sheet material used to make
these frames is 48” wide and 96” long. How many sheets of material will it take to produce
the order of frames? Each sheet cost $25.00 and labor cost per frame is $.75. What is the cost
of labor? What is the cost of the materials?
Answer
4” X 14” = 56 sq inch of plastic per frame
$25.00 / 82 = 0.30 cost of plastic per frame
$0.30 + $0.75 = $1.05 total cost per frame
56” X 1000 = 56,000 total sq inches plastic needed
48” X 96” = 4608 sq inches of plastic per sheet
56,000 / 4608 = 12.15 sheets of plastic
Number of sheets needed for job? __12.15____
What is the material cost per frame? _$0.30___
What is the total cost per frame? _$1.05______
Copyright © Texas Education Agency, 2012. All rights reserved
Name_____________________________________________
Use the measurements on the drawing
to fill in the chart. The chart will help
you with the measurements for finding
the board footage for the bookcase.
Date______________ Period _________
33
3/8”
11
A
TXWXL
Board Footage
1” X 12” X 12”
B
12
C
12
C
12
C
Side 1 * 10 * 51 ÷144 = 3.54 *2 = 7.08
12
C
Shelves 1 * 10 * 32 ÷ 144 = 2.22 * 4 = 8.89
3
All material is 3/4” in thickness*
except the back is 1/4” plywood
B
51
Use this space to show your work. Use the back if
needed.
Answer
Top 1 * 11 * 33 ÷ 144 = 2.52
10
Foot 1* 3 * 32 ÷ 144 = 0.67
Back 32 * 51 = 11.33 Sq Ft
32
Part
Name
D
Quality
Thickness
Width
Length
Board
Footage
A
Top
1
3/4”
11”
33”
2.52 bd ft
B
Side
2
3/4”
10”
51”
7.08 bd ft
C
Shelf
4
3/4”
10”
32”
8.89 bd ft
D
Foot
1
3/4”
3”
32”
0.67 bd ft
Back
1
1/4”
32”
51”
11.33
Sq Ft
*
material less than 1” in thickness is
figured at 1” in the formula
Copyright © Texas Education Agency, 2012. All rights reserved
Name_____________________________________________
Date______________ Period _________
Answer the following questions in the answer blanks. The blank space below the question is a place for you to figure the answer.
Smith Lumber Company filled an order of 45 sheets of oak plywood. The sheets have 32
square feet in them (4’ X 8’ sheet). The company was going to produce cabinets out of the
plywood. Each cabinet needed 15 square feet of plywood. How many cabinets can be built
out of the plywood ordered?
Answer
45 * 32 = 1440 sq ft total sq ft of order
1440 ÷ 15 = 96 Cabinets
Answer __96__________________
Conner Nut and Bolt Company received an order for 300 of each of the items listed in the
chart. The chart shows the cost of each. Figure the cost of the order.
Part
Cost
Nut
$0.25
Lock
Washer
$0.12
Flat
Washer
$0.04
Bolt
$0.75
Answer
.25 + .12 + .04 + .75 = 1.16 per group
$1.16 * 300 = $346.
Answer ___$346______________
36”
ABC Cabinet Company was contracted to build
fifty wood framed mirrors. The mirror frame
size is twenty four inches tall by thirty six inches
long. What is the cost to make the mirror if the
frame material cost 75 cents per foot and the
mirror glass is a dollar per square foot?
32”
24”
22”
Answer
24” + 36” + 24” + 36” = 120” inches perimeter
120” ÷ 12” = 10’ changing inches to feet
10’ * $0.75 = $7.50 cost of wood for the frame
22” * 32” = 704 sq inches
704” ÷144 = 4.9 sq ft
4.9 * $1.00 = $4.90 cost per mirror
$7.50 + $4.90 = $12.40 total cost for mirror
Answer _$12.40________________
Copyright © Texas Education Agency, 2012. All rights reserved
Name_____________________________________________
Date______________ Period _________
Figure the board footage for the Shelf Coat Rack.
A
C
B
B
D
Shelf Coat Rack
24
All material is 3/4” thick
6
1 1/2
dowels 1/2” dia. 3” long
5
3
6
5
4
4 1/2
5
2
22 1/2
Part
Name
Quality
Thickness
Width
Length
Board
Footage
A
Top
1
1”
6”
24”
1 bd ft
B
Side
2
1”
5”
6”
.42 bd ft
C
Back
1
1”
6”
D
Dowels
3
1/2”
dia
22.5” .94 bd ft
4”
A. 1” X 6” X 24” ÷144”
=
1.00 bd ft
B. 1” X 5” X 6 “ ÷144” = 0.21”
2 parts .21” X 2
= 0.42 bd ft
C. 1” X 6” X 22.5” ÷144” = 0.94 bd ft
Total
= 2.36 bd ft
Answer _____2.36 b f___________
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