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Math for Manufacturing

Practicum in Manufacturing

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).

TEKS Correlations

Preparation

Lesson Plan


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 critical-thinking 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.


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

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.

Introduction


Show o Photos of manufacturing processes and raw material storage locations.

Outline

MI

OUTLINE

I. Introduction of lesson A. Manufacturing Math slide

presentation B. Bell work activity C. Warm-up activity

I. How to use a standard measuring

ruler

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

NOTES TO TEACHER

Begin the Manufacturing Math

slide presentations.

Have students work on the Bell Work Activity. (Slide 2) Warm-up Activity: Leadership Terms and Definitions handout 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.


Multiple Intelligences Guide

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.

Review

The standard increments on a ruler

The differences in calculating like and unlike fractions

Converting fractions to decimals using a calculator

Informal Assessment The teacher monitors during activities to check for understanding. Formal Assessment

Daily grade on assignments

Manufacturing Math Quiz

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.

Existentialist

Interpersonal

Intrapersonal

Kinesthetic/

Bodily

Logical/

Mathematical

Musical/Rhythmic

Naturalist

Verbal/Linguistic

Visual/Spatial

Application

Summary

Evaluation

Extension


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


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.


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. 5. 6.

_1 + _3 6 8

=

____

12 + 14 11 11

=

____

11 – 8_ 13 13

=

____

_8 - _7 13 18

=

____


Complete the calculations below. 7. 8. 9. 10. Convert the following fractions to decimals. 11. 12.

6.135 + 9.044

91.274 + 34.312

95.24 - 48.56

59.984 - 46.394

1/16 = _____

7/8 = _____


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. 4. 5. 6.

_1 + _3 6 8

=

____

Answer: 13 24

12 + 14 11 11

=

____

Answer: 26 _4 11 11

11 - _8 13 13

=

____

Answer: _3 13

_8 - _7 13 18

=

____

Answer: _53 234

Or, 2 and


Complete the calculations below. 7. 8. 9. 10. Convert the following fractions to decimals. 11. 12.

6.135 + 9.044 Answer: 15.179

91.274 + 34.312 Answer: 125.595

95.24 - 48.56 Answer: 46.68

59.984 - 46.394 Answer: 13.590

1/16 = ___ Answer: .0625

Answer: .875 7/8 = ___


Drawing I - Punch

Drawing II - Small Hammer


Drawing III – Tablet Computer Stand

Drawing IV – Welded Angle Shelf


Name __________________________________________Date_______________ Period ____

Directions

Refer to Drawing I, II, III, and IV and answer the questions.

Understanding a Drawing or Plan

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? ______________


Directions Refer to Drawing I, II, III, and IV and answer the questions.

Understanding a Drawing or Plan Answer Key

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? __8 ¼”________

Tablet Computer Stand (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_____


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

1 1/4

TAPER TO 1/4 DIA.

/2 DIA. TOOL STEEL ROD 5

DRIVE PUNCH

Production Cost Chart

Materials Cost Operations Cost Time

½” X 12’ tool steel

bar

$25.00 Machine ¼” dia. $0.50 each 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? __________________


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

1 1/4

TAPER TO 1/4 DIA.

1/2 DIA. TOOL STEEL ROD 5

DRIVE PUNCH

Production Cost Chart

Materials Cost Operations Cost Time

½” X 12’ tool steel

bar

$25.00 Machine ¼” dia. $0.50 each 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? _____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_________


Center Punch

Measurement Section Points

Total length

End taper

Taper length

Finish

Grade

Drive Punch

Measurement Section Points

Total length

End taper

¼” dia. end

Finish

Grade

Name ___________________________________________ Date_______________ Period ____

Machining: Punch Plans and Rubrics


Name _________________________________________ Date_______________ Period ____

Hammer

Measurement Section Points Measurement Section Points

Handle length Head length

Handle taper Head taper

Handle thread Assemble

Shaft length Finish

Shaft threads Grade

Shaft threads


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. ________


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___

__


Measurement Chart Fractions / Decimals / Metric Equivalents

Sheet Metal Gauge Size Chart

Standard Steel Gauge

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

Fraction Decimal Metric Fraction Decimal Metric

1/16 0.0625 1.587 9/16 0.5625 14.287

1/8 0.125 3.175 5/8 0.625 15.875

3/16 0.1875 4.762 11/16 0.6875 17.462

1/4 0.250 6.350 3/4 0.750 19.050

5/16 0.3125 7.937 13/16 0.8125 20.637

3/8 0.375 9.525 7/8 0.875 22.225

7/16 0.4375 11.113 15/16 0.9375 23.812

1/2 0.500 12.700 1 1.0000 25.400

Gauge Inch Metric Gauge Inch Metric

3 0.2391 6.073 18 0.0478 1.204

6 0.1943 4.935 20 0.0359 0.912

8 0.1644 4.176 22 0.0299 0.759

10 0.1345 3.416 24 0.0239 0.607

12 0.1046 2.657 26 0.0179 0.455

14 0.0747 1.897 28 0.0149 0.378

16 0.0598 1.519 30 0.0120 0.305


Name ______________________________________ Date___________ Period ___

Precision Measurement Worksheet

Convert the following fractions to equivalent decimals.

Add the following measurements.

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.

1. ½ = _____________ 2. ¾ = _____________ 3. 1/8 = _____________ 4. ¼ = _____________ 5. 7/8 = _____________

6. 1/16 = _____________ 7. 3/8 = _____________ 8. 9/16 = _____________ 9. 15/16 = _____________ 10. 3/16 = _____________

11. 0.250 + 0.500 = ______________ 12. 0.125 + 0.250 = ______________ 13. 0.500 + 0.250 = ______________ 14. 0.75 + 0.125 = ______________ 15. 0.500 + 0.375 = ______________

16. 0.0625 +0.125 = ______________ 17. 0.3125 + 0.0625 = ______________ 18 0.4375 + 0.500 = ______________ 19. 0.625 + 00.625 = ______________ 20. 0.500 + 0.750 = ______________


Precision Measurement Worksheet Answer Key Convert the following fractions to equivalent decimals. 1. ½ = ____0.500____ 2. ¾ = ____0.750____ 3. 1/8 = ____0.125____ 4. ¼ = ____0.250____ 5. 7/8 = ____0.875____ Add the following measurements 11. 0.250 + 0.500 = ______________ 12. 0.125 + 0.250 = ______________ 13. 0.500 + 0.250 = _____________

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

6. 1/16 = ____0.0625____ 7. 3/8 = ____0.1875____ 8. 9/16 = ____0.5625____ 9. 15/16 = ____0.9375____ 10. 3/16 = ____0.1875____

16. 0.0625 +0.125 = ____0.1875____ 17. 0.3125 + 0.0625 = ____0.3750____ 18 0.4375 + 0.500 = ____0.9375____ 19. 0.625 + 00.625 = ____1.250____ 20. 0.250 + 0.750 = ____1.000____

11. 0.250 + 0.500 = ____0.750____ 12. 0.125 + 0.250 = ____0.375____ 13. 0.500 + 0.250 = ____0.750____ 14. 0.75 + 0.125 = ____0.875____ 15. 0.500 + 0.375 = ____0.875____


Name___________________________________________ Date___________________

Period__________

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?

Labor Cost

$9.50 X 30 hours = $285 per person

$285 per person X 5 people = $1425

Labor Cost



Labor Cost



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 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? _____________


Name___________________________________________ Date___________________

Period__________

Board Footage

Part Name

Quality Thickness Width Length Board Footage

A Top

B Side

C Shelf

D Foot

Back

Labor Cost



Labor Cost



Labor Cost



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.

Board Footage __T X W X L__ 1” X 12” X 12” All material is 3/4” in thickness* except the back is 1/4” plywood.

3

321

12

12

51

10

11

33

12

12

3/8” A

C

V C

B

B

C

C

C

D

*Material less than 1” in thickness is figured at 1” in the formula.

Use this space to show your work. Use the back if needed.


Name___________________________________________ Date___________________

Period__________

Material Cost

Labor Cost



Labor Cost



Labor Cost



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________________________________

____

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____________________________________

Answer the following questions in the answer blanks. The blank space below the question is a place for you

to figure the answer.


Name___________________________________________ Date___________________

Period__________

Part Name

Quality Thick- ness

Width Length Board Footage

A Top

B Side

C Back

D Dowels

3 1/2 ” dia.

4”

Labor Cost



Labor Cost



Labor Cost



Figure the board footage for the Shelf Coat Rack.

A

6

4

1 1/2

4 1/2

24

2

5 5

5 dowels 1/2” dia. 3” long

22 1/2

3

Shelf Coat Rack All material is 3/4” thick.

D

C

B

B

6

Answer_______________________________________


Name___________________________________________ Date___________________

Period__________

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

3,000 sets X 3 minutes each = 9,000 minutes for all sets

9.000 minutes / 5 people = 1800 minutes

1800 minutes / 60 minutes per hour = 30 hours

Labor Cost



Labor Cost



Labor Cost



Labor Cost:


$285 per person X 5 people = $1,425

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?


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_____


Name___________________________________________ Date___________________

Period__________

Board Footage Answer Key

Part Name

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

Labor Cost



Labor Cost



Labor Cost



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.

Board Footage __T X W X L__ 1” X 12” X 12” All material is 3/4” in thickness* except the back is 1/4” plywood.

3

32

12

12

51

10

11

33

12

12

3/8” A

C

V C

B

B

C

C

C

D

*Material less than 1” in thickness is figured at 1” in the formula.

Use this space to show your work. Use the back if needed. Answer

Top 1 * 11 * 33 ÷ 144 = 2.52

Side 1 * 10 * 51 ÷144 = 3.54 *2 = 7.08

Shelves 1 * 10 * 32 ÷ 144 = 2.22 * 4 =

8.89

Foot 1* 3 * 32 ÷ 144 = 0.67

Back 32 * 51 = 11.33 sq ft


Name___________________________________________ Date___________________

Period__________

Material Cost Answer Key

Labor Cost



Labor Cost



Labor Cost



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

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___

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

Answer the following questions in the answer blanks. The blank space below the question is a place for you

to figure the answer.


Name___________________________________________ Date___________________

Period__________

Part Name

Quality Thick- ness

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” 22.5” .94 bd ft

D Dowels

3 1/2 ” dia.

4”

Labor Cost



Labor Cost



Labor Cost



Figure the board footage for the Shelf Coat Rack. Answer Key

A

6

4

1 1/2

4 1/2

24

2

5 5

5 dowels 1/2” dia. 3” long

22 1/2

3

Shelf Coat Rack All material is 3/4” thick.

D

C

B

B

6

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 Answer ___2.36 bf___

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Math for Manufacturing Lesson Plan - data.cteunt.orgdata.cteunt.org/.../7.1-math-for-manufacturing.pdf · Math for Manufacturing ... Lesson Plan . 2 Copyright © Texas Education Agency,