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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).
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
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.
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.
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
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_______________ 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 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_________
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.
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
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
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
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___