Math for Manufacturing
Practicum in Manufacturing
Lesson Plan
Performance Objective
Upon completion of this lesson, each student will gain a better understanding regarding how to solve math
problems as required in a manufacturing environment by completing the activities and quiz.
Specific Objectives
The student will be able to
 Identify specific lengths on a standard tape measure
 Add and subtract fraction problems
 Add and subtract problems with decimals
 Convert fractions to decimals
Terms
 English Standard Measurement System- the system of measurement used in the United States
(adopted from the English imperial measurements) based on the number 12 and inches, feet, and yards
as basic standards of lengths.
 Whole number- a number that has no fraction or decimal; for example, 0, 1, 2, 3, 4, 5, 6, 7, 8, etc.
 Decimal- is defined as a system of numbers or currency where everything is based on the number 10,
or on parts of 10.
 Simplify- used in math to combine numbers into lower or fewer numbers.
 Reducing- occurs when a fraction is changed into its lowest terms; for example, 3/6 can be reduced to
1/2.
 Prime number- a number that can only be divided by itself and the number one.
 Proper fraction- a fraction written where the numerator is less than the denominator.
 Positive number- a number with a value greater than zero.
 Numerator- the top number or symbol of a fraction.
 Mixed number- a number that contains both a whole number and a fraction.
 Lowest common denominator- to reduce a fraction; where the smallest number is found that can be
evenly divided by all denominators in the problem.
 Fraction- a set of numbers that expresses part of a whole; it contains a numerator and a denominator.
 Difference- the result found when numbers are subtracted.
 Improper fraction- a fraction where the numerator is larger than the denominator.
Time
This lesson should take approximately 12 class periods (45 minutes each).
Preparation
TEKS Correlations
1
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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.
Practicum in Manufacturing
 130.330 (c)
o (2) The student applies concepts of critical thinking and problem solving. The student is
expected to:
(A) analyze elements of a problem to develop creative and innovative solutions;
(B) critically analyze information to determine value to the problem-solving task;
(C) compare and contrast alternatives using a variety of problem-solving and criticalthinking skills; and
(D) conduct technical research to gather information necessary for decision making.
English Language Arts and Reading, English I
• 110.31 (b)
o (24) Listening and Speaking/Listening. Students will use comprehension skills to listen
attentively to others in formal and informal settings. Students will continue to apply earlier
standards with greater complexity. Students are expected to:
(A) listen responsively to a speaker by taking notes that summarize, synthesize, or
highlight the speaker's ideas for critical reflection and by asking questions related to the
content for clarification and elaboration;
(B) follow and give complex oral instructions to perform specific tasks, answer
questions, solve problems, and complete processes; and
(C) evaluate the effectiveness of a speaker's main and supporting ideas.
Discrete Mathematics for Problem Solving
• 111.46 (c)
o (1) Mathematical process standards. The student uses mathematical processes to acquire
and demonstrate mathematical understanding. The student is expected to:
(A) apply mathematics to problems arising in everyday life, society, and the workplace;
(B) use a problem-solving model that incorporates analyzing given information,
formulating a plan or strategy, determining a solution, justifying the solution, and
evaluating the problem-solving process and the reasonableness of the solution;
(C) select tools, including real objects, manipulatives, paper and pencil, and technology
as appropriate, and techniques, including mental math, estimation, and number sense
as appropriate, to solve problems;
(D) communicate mathematical ideas, reasoning, and their implications using multiple
representations, including symbols, diagrams, graphs, and language as appropriate;
(E) create and use representations to organize, record, and communicate mathematical
ideas;
(F) analyze mathematical relationships to connect and communicate mathematical
ideas; and
(G) display, explain, and justify mathematical ideas and arguments using precise
mathematical language in written or oral communication.
2
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Accommodations for Learning Differences
It is important that lessons accommodate the needs of every learner. These lessons may be modified to
accommodate your students with learning differences by referring to the files found on the Special
Populations page of this website (cte.unt.edu).
Preparation
 Review and become familiar with the terminology, website links, and the slide presentation.
 Have materials, slide presentation, and websites ready prior to the start of the lesson.
References
Webster’s new compact office dictionary (2003). New York, NY: Houghton Mifflin Harcourt Publishing Co.
Instructional Aids
 Math for Manufacturing slide presentation and notes
 Warm-up Activity (Slide 3)
 Manufacturing Math Terms and Definitions handout for each student
 Manufacturing Math Terms and Definitions Answer Key
 Manufacturing Math Quiz for each student
 Manufacturing Math Quiz Answer Key
 Additional Manufacturing Math Activities
o Drawings I, II, III, IV
o Understanding a Drawing
o Understanding a Drawing Answer Key
o Production Cost
o Machining: Punch Plans and Rubrics
o Measurement Worksheet
o Precision Measurement Worksheet
o Manufacturing Math
Introduction
The main purpose of this lesson is to give students an understanding of math calculations commonly used in
the manufacturing workplace.

Say
o Accurate math calculations are critical in a manufacturing environment.

Ask
o What math calculations do you use in your everyday life?

Say
o Math calculations help ensure the correct quantity of raw materials are purchased for the production
process.
3
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
Show
o Photos of manufacturing processes and raw material storage locations.
Outline
MI
OUTLINE
I.
NOTES TO TEACHER
Introduction of lesson
A. Manufacturing Math slide
presentation
B. Bell work activity
C. Warm-up activity
Begin the Manufacturing Math
slide presentations.
I.
How to use a standard measuring
ruler
Warm-up Activity:
Leadership Terms and Definitions
handout
II.
Calculating fractions
A. Addition
B. Subtraction
III.
Calculating decimals
A. Addition
V.
Subtraction
A. Converting fractions to decimals
VI.
Manufacturing Math Quiz
VII.
Assign additional math activities
A. Drawings I, II, III, IV
B. Understanding a Drawing
C. Production Cost
D. Machining: Punch Plans and
Rubrics
E. Measurement Worksheet
F. Precision Measurement
Worksheet
G. Manufacturing Math
Have students work on the Bell
Work Activity. (Slide 2)
Students (in pairs) will teach each
other the terms and definitions.
They may do computer-based
research to look up the meaning.
(Slide 3)
Each slide is meant to be
discussed. Have some background
knowledge, and challenge the
students to make some
contributions to the discussion.
Administer quiz and grade using
answer key.
Explain and assign the additional
math assignments.
4
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Multiple Intelligences Guide
Existentialist
Interpersonal
Intrapersonal
Kinesthetic/
Bodily
Logical/
Mathematical
Musical/Rhythmic
Naturalist
Verbal/Linguistic
Visual/Spatial
Application
Guided Practice
The teacher will present the Math for Manufacturing slide presentation and will have the students complete
the assignments.
Independent Practice
Students will complete the math assignments and worksheets.
Summary
Review
 The standard increments on a ruler
 The differences in calculating like and unlike fractions
 Converting fractions to decimals using a calculator
Evaluation
Informal Assessment
The teacher monitors during activities to check for understanding.
Formal Assessment
 Daily grade on assignments
 Manufacturing Math Quiz
Extension
Students will research and write a 150-word essay on one of the most commonly used computer software
programs, which is used by top manufacturing companies to track and calculate the quantities of raw
materials used during the manufacturing process.
5
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Name_____________________________________Date_______________________Class____________
Math
Terms and Definitions
Directions
Use the internet to research the definitions to the math terms below.
1. Decimal
2. Difference
3. English Standard Measurement System
4. Fraction
5. Improper fraction
6. Lowest common denominator
7. Mixed number
8. Numerator
9. Positive number
10. Prime number
11. Proper fraction
12. Reducing
13. Simplify
14. Whole number
6
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Math
Terms and Definitions
Answer Key
1. English Standard Measurement System- the system of measurement used in the United States
(adopted from the English imperial measurements) based on the number 12 and inches, feet, and yards
as basic standards of lengths.
2. Whole number- a number that has no fraction or decimal; for example, 0, 1, 2, 3, 4, 5, 6, 7, 8, etc.
3. Simplify- used in math to combine numbers into lower or fewer numbers.
4. Reducing- occurs when a fraction is changed into its lowest terms; for example, 3/6 can be reduced to
1/2.
5. Prime number- a number that can only be divided by itself and the number one.
6. Proper fraction- a fraction written where the numerator is less than the denominator.
7. Positive number- a number with a value greater than zero.
8. Numerator- the top number or symbol of a fraction.
9. Mixed number- a number that contains both a whole number and a fraction.
10. Lowest common denominator- required to reduce a fraction; where the smallest number is found that
can be evenly divided by all denominators in the problem.
11. Fraction- a set of numbers that expresses part of a whole; it contains a numerator and a denominator.
12. Difference- the result found when numbers are subtracted.
13. Improper fraction- a fraction where the numerator is larger than the denominator.
14. Decimal- a numerical system where everything is based on the number 10, or on parts of 10.
7
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Name_____________________________________Date_______________________Class____________
Math Quiz
Directions
Name the fraction at each arrow in each diagram below.
1.
___________________
2.
__________________
Complete the calculations below. Find the least common denominator and reduce the answers where
applicable.
3.
4.
_1 + _3 = ____
6
8
12 + 14
11 11
=
5.
11 – 8_ =
13 13
6.
_8 - _7 =
13 18
____
____
____
8
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Complete the calculations below.
7.
6.135
+ 9.044
8.
91.274
+ 34.312
9.
95.24
- 48.56
10.
59.984
- 46.394
Convert the following fractions to decimals.
11.
1/16 = _____
12.
7/8 = _____
9
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Math Quiz
Answer Key
Directions
Name the fraction at each arrow in the diagrams below.
1.
Answer: 15/16
2.
Answer: 9/16
Complete the calculations below. Find the Least common denominator and reduce the answers where
applicable.
3.
_1 + _3 = ____
6
8
4.
12 + 14
11 11
=
5.
11 - _8
13 13
=
6.
_8 - _7 =
13 18
____
Answer: 13
24
Answer: 26
11
____
Answer: _3
13
____
Answer: _53
234
Or, 2 and
_4
11
10
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Complete the calculations below.
7.
6.135
+ 9.044
Answer: 15.179
8.
91.274
+ 34.312
Answer: 125.595
9.
95.24
- 48.56
Answer: 46.68
10.
59.984
- 46.394
Answer: 13.590
Convert the following fractions to decimals.
11.
1/16 = ___
12.
7/8 = ___
Answer: .0625
Answer: .875
11
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Drawing I - Punch
Drawing II - Small Hammer
12
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Drawing III – Tablet Computer Stand
Drawing IV – Welded Angle Shelf
13
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Name __________________________________________Date_______________ Period ____
Understanding a Drawing or Plan
Directions
Refer to Drawing I, II, III, and IV and answer the questions.
Punch
1. What length are the punches?
______________
2. What is the diameter of the punch?
______________
3. What is the length of the taper on the center punch?
______________
Small Hammer
4. How many parts does the hammer have?
______________
5. What is the size of the metal used to make the handle?
______________
6. What size piece of metal will it take to make the hammer head?
______________
7. What do the numbers ¼ - 20 X ¾” mean?
______________
___________________________________________________________________
8. What is the total length of the hammer assembled?
______________
Tablet Computer Stand
9. What is the size of the piece of sheet metal needed to make the stand? _____________
10. How tall will the stand be when bent into shape?
_____________
Welded Angle Shelf
11. How many pieces of metal are needed to produce the shelf?
______________
12. What is the total amount of angle used to make the shelf?
______________
13. What size piece of 3/16” plate metal will be used for the shelf bottom? ______________
14. The cost of 3/16” plate is $0.50 per foot.
What is the cost of the shelf bottom?
______________
15. The cost of ¾” angle iron is $0.25 per foot.
What is the cost for the shelf frame?
______________
14
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Understanding a Drawing or Plan Answer Key
Directions
Refer to Drawing I, II, III, and IV and answer the questions.
Punch
1. What length are the punches?
___5 inches____
2. What is the diameter of the punch?
____1/2 inch____
3. What is the length of the taper on the center punch?
___1 ½ inches___
Small Hammer
4. How many parts does the hammer have?
___3__________
5. What is the size of the metal used to make the handle?
__1/2” dia. by 3”_
6. What size piece of metal will it take to make the hammer head?
_3/4” X ¾” X 3”__
7. What do the numbers ¼ - 20 X ¾” mean?
______________
__1/4” by 20 threads ¾” long_______________________________________________
8. What is the total length of the hammer assembled?
Tablet Computer Stand
__8 ¼”________
(The threads screw in 1 ½” 9 ¾” – 1 ½”)
9. What is the size of the piece of sheet metal needed to make the stand? __6” X 17”____
10. How tall will the stand be when bent into shape?
____5”_______
Welded Angle Shelf
11. How many pieces of metal are needed to produce the shelf?
_____9________
12. What is the total amount of angle used to make the shelf?
_204” / 17’_____
13. What size piece of 3/16” plate metal will be used for the shelf bottom?__12” X 44”____
14. The cost of 3/16” plate is $0.50 per foot.
What is the cost of the shelf bottom?
___$1.83______
15. The cost of ¾” angle iron is $0.25 per foot.
What is the cost for the shelf frame?
____$4.25_____
15
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Name __________________________________________Date_______________ Period ____
Production Cost
Production Cost
The customer wants 1000 drive punches manufactured. You will have to calculate the total
cost to manufacture the punches. Use the chart below to figure the cost. Show your work.
1/8 CHAMPER
TAPER TO 1/4 DIA.
1 1/4
/2 DIA. TOOL STEEL ROD
5
DRIVE PUNCH
Materials
½” X 12’ tool steel
bar
Cost
$25.00
Production Cost Chart
Operations
Cost
Machine ¼” dia.
$0.50 each
Time
2 minute each
Cut off
$0.05 each
½ minute each
Heat treating
$0.25 each
3 minute each
Polishing
$0.10 each
5 minute each
The cut off operation waste ¼” of material for each cut.
______________________________________________________________________________________
1. How many bars of ½” are needed to make 1000 punches?
__________________
(Round up to a full 12’ bar)
2. How much time does it take to make one punch?
__________________
3. How much does it cost to make one punch?
__________________
4. What is the cost of the metal to make one punch?
__________________
5. How many punches can be made from a 12 foot bar?
__________________
6. What is the total cost to make all 1000 punches?
__________________
7. What process takes the longest time to perform?
__________________
8. What could be done to decrease production time?
__________________
______________________________________________________________________________
9. The production time to complete all punches is 10 days. Office charges and electricity are
added at $100 per day. What are the costs of the 1000 punches?
__________________
16
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Production Cost Answer Key
Production Cost
The customer wants 1000 drive punches manufactured. You will have to calculate the total
cost to manufacture the punches. Use the chart below to figure the cost. Show your work.
1/8 CHAMPER
TAPER TO 1/4 DIA.
1 1/4
1/2 DIA. TOOL STEEL ROD
5
DRIVE PUNCH
Materials
½” X 12’ tool steel
bar
Cost
$25.00
Production Cost Chart
Operations
Cost
Machine ¼” dia.
$0.50 each
Cut off
Heat treating
Polishing
The cut off operation waste ¼” of material for each cut.
$0.05 each
$0.25 each
$0.10 each
Time
2 minute each
½ minute each
3 minute each
5 minute each
_____________________________________________________________________________
1. How many bars of ½” are needed to make 1000 punches?
_____35___________
(Round up to a full 12’ bar)
2. How much time does it take to make one punch?
_____10.5 minutes_____
3. How much does it cost to make one punch?
______$0.90________
4. What is the cost of the metal to make one punch?
______$0.89________
5. How many punches can be made from a 12 foot bar?
______28____________
6. What is the total cost to make all 1000 punches?
____$1790___________
7. What process takes the longest time to perform?
__Polishing___________
8. What could be done to decrease production time?
__________________
____Shorten the polishing time by using more people or machines________________________
9. The production time to complete all punches is 10 days. Office charges and electricity are added
at $100 per day. What are the costs of the 1000 punches?
____$2790_________
17
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Name ___________________________________________ Date_______________ Period ____
Machining: Punch Plans and Rubrics
Center Punch
Measurement
Section
Drive Punch
Points
Measurement
Section
Total length
Total length
End taper
End taper
Taper length
¼” dia. end
Finish
Finish
Grade
Grade
Points
18
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Name _________________________________________ Date_______________ Period ____
Hammer
Measurement
Section
Points
Measurement
Section
Handle length
Head length
Handle taper
Head taper
Handle thread
Assemble
Shaft length
Finish
Shaft threads
Grade
Points
Shaft threads
19
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Name ______________________________________ Date________________ Period ______
Measurement Worksheet
Directions
Use the diagram below to complete the measurement shown at each arrow.
1. ________
6. ________
2. ________
7. ________
3. ________
8. ________
4. ________
9. ________
5. ________
10. ________
20
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Measurement Worksheet Answer Key
Directions
Use the diagram below to complete the measurement shown at each arrow.
1. __7/16______
6. __2 and 1/4______
2. __13/16______
7. __2 and 1/2______
3. __1 and 1/16______
8. __2 and 7/8______
4. __1 and 9/16______
9. __3 and 3/8______
5. __1 and 15/16______
10. __3 and 13/16___
__
21
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Measurement Chart
Fractions / Decimals / Metric Equivalents
Sheet Metal Gauge Size Chart
Fraction
1/16
1/8
3/16
1/4
5/16
3/8
7/16
1/2
Decimal
0.0625
0.125
0.1875
0.250
0.3125
0.375
0.4375
0.500
Metric
1.587
3.175
4.762
6.350
7.937
9.525
11.113
12.700
Fraction
9/16
5/8
11/16
3/4
13/16
7/8
15/16
1
Decimal
0.5625
0.625
0.6875
0.750
0.8125
0.875
0.9375
1.0000
Metric
14.287
15.875
17.462
19.050
20.637
22.225
23.812
25.400
Inch
0.0478
0.0359
0.0299
0.0239
0.0179
0.0149
0.0120
Metric
1.204
0.912
0.759
0.607
0.455
0.378
0.305
Standard Steel Gauge
Gauge
3
6
8
10
12
14
16
Inch
0.2391
0.1943
0.1644
0.1345
0.1046
0.0747
0.0598
Metric
6.073
4.935
4.176
3.416
2.657
1.897
1.519
Gauge
18
20
22
24
26
28
30
Cutting Speed Chart
Material Type
Feet per Minute
Meter per Minute
Mild Steel
100-125
30-38
Cast Iron (medium)
60-80
18-24
Alloy Steels
65-120
20-37
Carbon Steel
70-130
21-40
Stainless Steels
75-130
23-40
Bronzes
80-150
80-150
Aluminum
250-350
75-210
Brass
300-700
90-210
22
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Name ______________________________________
Date___________ Period ___
Precision Measurement Worksheet
Convert the following fractions to equivalent decimals.
1. ½ = _____________
6. 1/16
= _____________
2. ¾ = _____________
7. 3/8
= _____________
3. 1/8 = _____________
8. 9/16
= _____________
4. ¼ = _____________
9. 15/16 = _____________
5. 7/8 = _____________
10. 3/16
= _____________
Add the following measurements.
11. 0.250 + 0.500 = ______________
16. 0.0625 +0.125 = ______________
12. 0.125 + 0.250 = ______________
17. 0.3125 + 0.0625 = ______________
13. 0.500 + 0.250 = ______________
18 0.4375 + 0.500 = ______________
14. 0.75 + 0.125 = ______________
19. 0.625 + 00.625 = ______________
15. 0.500 + 0.375 = ______________
20. 0.500 + 0.750 = ______________
Calculate the revolutions per minute for the following parts. (Use the chart for the cutting
speeds for the material.)
21. The material is brass with a diameter of 2.25 inches.
22. The material is aluminum with a diameter of 3.5 inches.
23. The material is mild steel with a diameter of 3.5 inches.
24. The material is mild steel with a diameter of ¾ of an inch.
25. The material is carbon steel with a diameter of 3/8 of an inch.
23
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Precision Measurement Worksheet Answer Key
Convert the following fractions to equivalent decimals.
1. ½ = ____0.500____
6. 1/16 = ____0.0625____
2. ¾ = ____0.750____
7. 3/8
= ____0.1875____
3. 1/8 = ____0.125____
8. 9/16
= ____0.5625____
4. ¼ = ____0.250____
9. 15/16 = ____0.9375____
5. 7/8 = ____0.875____
10. 3/16
= ____0.1875____
Add the following measurements
11. 0.250 + 0.500 = ____0.750____
11. 0.250 + 0.500 = ______________
12. 0.125 + 0.250 = ____0.375____
12. 0.125 + 0.250 = ______________
13. 0.500 + 0.250 = ____0.750____
13. 0.500 + 0.250 = _____________
14. 0.75 + 0.125 = ____0.875____
16. 0.0625 +0.125 = ____0.1875____
15. 0.500 + 0.375 = ____0.875____
20. 0.250 + 0.750
17. 0.3125 + 0.0625 = ____0.3750____
18 0.4375 + 0.500 = ____0.9375____
19. 0.625 + 00.625 = ____1.250____
= ____1.000____
Calculate the revolutions per minute for the following parts. (Use the chart for the cutting
speeds for the material.)
21. The material is brass with a diameter of 2.25 inches.
RPM = 300 * 4 / 2.25 RPM = 533
22. The material is aluminum with a diameter of 3.5 inches.
RPM = 250 * 4 / 3.5 RPM = 285
23. The material is mild steel with a diameter of 3.5 inches.
RPM = 100 * 4 / 3.5 RPM = 114
24. The material is mild steel with a diameter of ¾ of an inch.
RPM = 100 * 4 / 0.75 RPM = 533
25. The material is carbon steel with a diameter of 3/8 of an inch.
RPM = 70 * 4 / 0.375 RPM = 746
24
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Name___________________________________________
Period__________
Date___________________
Manufacturing Math
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?
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?
Number of hours worked _____________
Labor Cost _____________
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 costs
$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? _____________
25
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Name___________________________________________
Period__________
Date___________________
Board Footage
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.
33
3/8”
11
A
C
V
B
Board Footage __T X W X L__
1” X 12” X 12”
12
All material is 3/4” in thickness*
except the back is 1/4” plywood.
12
C
12
C
12
C
Use this space to show your work.
Use the back if needed.
C
B
51
10
3
D
321
Part
Name
Quality
Thickness
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.
26
Copyright © Texas Education Agency, 2015. All rights reserved.
Name___________________________________________
Period__________
Date___________________
Material Cost
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
Nut
Lock
Washer
Flat
Washer
Bolt
Cost
$0.25
$0.12
$0.04
$0.75
Answer________________________________
____
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?
Answer____________________________________
27
Copyright © Texas Education Agency, 2015. All rights reserved.
Name___________________________________________
Period__________
Date___________________
Figure the board footage for the Shelf Coat Rack.
A
C
B
B
D
Shelf Coat Rack
All material is 3/4” thick.
24
6
1 1/2
dowels 1/2” dia. 3” long
5
3
6
4
5
4 1/2
5
2
22 1/2
Part
Quality
Name
A
Top
B
Side
C
Back
D
3
Dowels
Thickness
1/2 ”
dia.
Width
Length
Board
Footage
4”
Answer_______________________________________
28
Copyright © Texas Education Agency, 2015. All rights reserved.
Name___________________________________________
Period__________
Date___________________
Manufacturing Math Answer Key
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
Labor Cost:
3,000 sets X 3 minutes each = 9,000 minutes for all sets
$9.50 X 30 hours = $285 per person
9.000 minutes / 5 people = 1800 minutes
$285 per person X 5 people = $1,425
1800 minutes / 60 minutes per hour = 30 hours
Number of hours worked ___30 hours___
Labor
Cost ___$1,425___
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?
29
Copyright © Texas Education Agency, 2015. All rights reserved.
Answer
4” X 14” = 56 sq inch of plastic 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
4608 / 56 = 82 frames per sheet
$25.00 / 82 = 0.30 cost of plastic per frame
$0.30 + $0.75 = $1.05 total cost per frame
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_____
30
Copyright © Texas Education Agency, 2015. All rights reserved.
Name___________________________________________
Period__________
Date___________________
Board Footage Answer Key
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.
33
3/8”
11
A
C
V
Board Footage __T X W X L__
1” X 12” X 12”
12
All material is 3/4” in thickness*
except the back is 1/4” plywood.
12
C
Use this space to show your work.
Use the back if needed.
12
C
Answer
12
C
Top 1 * 11 * 33 ÷ 144 = 2.52
3
B
Foot 1* 3 * 32 ÷ 144 = 0.67
Back 32 * 51 = 11.33 sq ft
B
51
10
D
32
Side 1 * 10 * 51 ÷144 = 3.54 *2 = 7.08
Shelves 1 * 10 * 32 ÷ 144 = 2.22 * 4 =
8.89
C
Part Quality Thickness
Name
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.
31
Copyright © Texas Education Agency, 2015. All rights reserved.
Name___________________________________________
Period__________
Date___________________
Material Cost Answer Key
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
Answer __96 cabinets__
45 * 32 = 1440 sq ft total sq ft of order
1440 ÷ 15 = 96 cabinets
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
Answer
Nut
$0.25
.25 + .12 + .04 + .75 = 1.16 per group
Lock
$0.12
Washer
$1.16 * 300 = $346.
Flat
$0.04
Washer
Answer ___$346___
Bolt
$0.75
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?
Answer ___$12.40___
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
32
Copyright © Texas Education Agency, 2015. All rights reserved.
Name___________________________________________
Period__________
Figure the board footage for the Shelf Coat Rack.
Date___________________
Answer Key
A
C
B
B
D
Shelf Coat Rack
All material is 3/4” thick.
24
6
1 1/2
dowels 1/2” dia. 3” long
5
3
6
4
5
4 1/2
5
2
22 1/2
Part
Quality
Name
A
1
Top
B
2
Side
C
1
Back
D
3
Dowels
Thickness
1”
Width
Length
6”
24”
Board
Footage
1 bd ft
1”
5”
6”
.42 bd ft
1”
6”
22.5”
.94 bd ft
1/2 ”
dia.
A Top 1” X 6” X 24” ÷ 144” = 1.00 bd ft
B Side 1” X 5” X 6” ÷ 144” = 0.21”
2 parts .21” X 2 = 0.42 bd ft
C Back 1” X 6” X 22.5” ÷ 144” = 0.94 bd ft
Total = 2.36 bd ft
4”
Answer ___2.36 bf___
33
Copyright © Texas Education Agency, 2015. All rights reserved.