Mathematics; Secondary Education; Tests; Textbook

DOCUMENT RESUMEED 112 088AUTHORTITLECE 004 854Picot, DonaldApplied Mathematics--Machine Shop; A TeachersGuide.INSTITUTIONSPONS AGENCYRutgers, The State Univ., New Brunswick, N.J.Curriculum Lab.New Jersey State Dept. of Education, Trenton. Div. ofNOTEVocL'tional Education.97p.EDRS PRICEDESCRIPTORSME- 0.76 HC- 4.43 Plus Postage*Curriculum Guides; *Individualized Curriculum;Instructional Materials; Lesson Plans; *Machinists;*Mathematics; Mathematics Instruction; MathematicSMaterials; Post Secondary Education; PracticalMathematics; Secondary Education; Tests; TextbookAssignments; Trade and Industrial Education; UnitPlanABSTRACTThe outline of mathematics skills provides forindividualized instruction by allowing each student to completeperformance tests which indicate the point at which his instructionshould start. The course is divided into two parts; one coveringoperations with whole numbers, decimals, fractions, and percentage;the other dealing with ratio, proportion, square roots, fundamentalgeometry, and trigonometry with practical applications. The skills inpart one are prerequisite to successful completion of part two whichmeets the performance requirements of the second class machinistclassification. The outline contains lists of texts for both parts onwhich the skills and assignments are based and a pretest forproficiency credit for part one. The course is structured in units(13 in part one, 10 in part two) which are divided into lessons. Foreach lesson specific performance objectives with correspondingassignments from the texts are indicated. Quizzes for some lessonsand tests for each unit (actual forms) are included. An evaluationform for each unit has space for lesson, quiz, and unit test gradesand a percentage formula for using these three types of scores intabulating a final grade. *************************Documents acquired by ERIC include many informal unpublished* materials not available from other sources. EPIC makes every effort ** to obtain the best copy available. Nevertheless, items of marginal ** reproducibility are often encountered and this affects the quality ** of the microfiche and hardcopy reproductions ERIC makes available** via the ERIC Document Reproduction Service (EDRS). EDRS is not* responsible for the quality of the original document. Reproductions ** supplied by EDRS are the best that can be made from the *******************************

State of New JerseyDepartment of EducationDivision of Vocational EducationAPPLIED MATHEMATICSMACHINE SHOPA Teachers GuideBehavioral ObjectivesIndividualized CurriculumDonald Picot, InstructorCharles Green, SuperintendentWarren County Area Vocational & Technical High SchoolWashington, New JerseyVocational-TechnicalCurriculum LaboratoryRutgers - The State UniversityBuilding 4103 - Kilmer CampusNew Brunswick, New Jersey

DIVISION OF VOCATIONAL EDUCATIONSTEPHEN POLIACIK, ASSISTANT COMMISSIONERCURRICULUM LABORATORYRUTGERS - THE STATE UNIVERSITYBUILDING 4103 - KILMER CAMPUSNEW BRUNSWICK, NEW JERSEY4

CONTENTSMachine Shop Applied Mathematics IPageIntroduction to Mathematics I1Reference Books for Mathematics I2Pretest3Unit I- NumbersUnit II- Addition of Whole Numbers and Decimals611Unit IIISubtraction of Whole Numbers and Decimals14Unit IVMultiplication of Whole Numbers and Decimals17Unit VDivision of Whole Numbers and Decimals21Unit VI- Common Fractions25Unit VII- Addition of Fractions29Unit VIII - Subtraction of Fractions32Unit IX- Multiplying Fractions35Unit X- Division of Fractions38Unit XI- Fraction Problems Involving Combined Operations41Unit XII- Decimal Fractions44Unit XIII - Percentage47Machine Shop Applied Mathematics IIIntroduction to Mathematics II50Reference Books for Mathematics II51Unit I52Unit IIRatio and Proportion- Squares, Square Roots, and Their Application555

PageUnit III- Regular Polygons59Unit IV- Circles63Unit V- Arcs and Circles-66Unit VI- Fundamentals of Trigonometry69Unit VII- Use of Trigonometric Tables74Unit VIII- Solution of Right Triangles77Unit IX- Practical Applications of Trigonometry84Unit X- Computing Taper per Unit of Length89ii

INTRODUCTIONMACHINE SHOPAPPLIED MATHEMATICS IThe following is a performance outline for Machine Shop Mathematics I.Each student must demonstrate a capability in all the performances listedto complete the course. These math skills will equip the student to makethe necessary calculations for machine tool operation, for personal needs,and as a prerequisite to Machine Shop Mathematics II.The outline is constructed for individual instruction. All studentswill start the course by completing tests until they reach their presentlevel of performance. Each individual's instruction will start at thatpoint and continue until he has mastered the performances outlined.Completion of this course of study will permit the student to pursueMachine Shop Mathematics II or take the option of other electives.Much of the learning will be under the student's own direction. Hisprogress will depend largely on his personal effort and ability.Eachclass member is expected to give his best effort, using class time to maximum advantage. The benefit each student receives from the instructor'sguidance, advice, and knowledge wal depend to a large degree on a matureattitude on the part of each individual and the class as a whole.The student must be convinced that the level of his math skills willhave a direct impact on his shop progress. The Machine Shop course reliesstrongly on 4powledge of math and other related subjects. Specific shopperformance requirements cannot be met without these background courses.This course should be an easy step-by-step learning process thatshould be easily mastered by the conscientious and able student. Whenhe has mastered his related and shop skills, he will be recommended for aRemind the students: "You 'learn so thattrial "earning" in the trade.you may earn'".4,*1

REFERENCE MATERIALSFORCOURSE OF STUDY OUTLINEMACHINE SHOPAPPLIED MATHEMATICS I1.Basic Mathematical Skills (BMS)Loyce C. GossageMcGraw-Hill Book Company2.Mathematics for Technical and Vocational SchoolsStade, Margolis & BoyceJohn Wiley and Sons, Inc.3.Basic Vocational Mathematics IC. M. SantoliVocational-Technical Curriculum LaboratoryRutgers - The State University4.Essential Business Mathematics (EBM)Llewellyn R. SnyderMcGraw-Hill Book Company5.Business and Consumer Arithmetic (B&CM)Olson and McNallyPrentice Hall, Inc.2

NameDatePRETESTMachine Shop Applied Mathematics INOTE TO STUDENT:A.B.C.To earn credit for Math I, proficiency must be shown inall sections.Reduce to lowest terms:Answer below:1.14/161.2.24/322.3.6/83.4.3 10/164.5.16/645.Convert to the required fraction:6.1/2 to 4ths6.7.1/2 to 10ths7.8.3/8 to 32nds8.9.5/8 to 64ths9.10.7/8 to 16ths10.Add and reduce to lowest terms:11.1/2 1/411.12.3/16 1/812.13.1 1/4 1/413.14.7/8 1/1614.15.10 1/8 1/3215.039

D.E.Multiply and reduce to lowest terms:16.3/4 x 516.17.2/3 x 5/717.18.3/4 x 8/918.19.8/11 x 5/1219.20.2 1/2 x 3 1/420.Divide and reduce to lowest terms:22.3/42/321.522.23.1 l equivalent correct to 3 decimal places:3/426.27.5/1627.28.1 5/828.29.1/3229.30.1/6430.Add.Give answers in decimals.31.1.500 .250 - .531.32.250 1/232.33. 2.875 .125 - 3.033.7/8 .125 - 0.75034.34.35. 1.015 .625 - .04535.4

IH.Find the percentage:36.50% of 336.37.5% of 337.38.1% of 10038.39.6% of 50039.40.10% of 1,00040.

COURSE OF STUDY OUTLINEMACHINE SHOPAPPLIED MATHEMATICS ISpecific PerformancesAssignmentsUnit I - NumbersLesson 1. Meaning of Numbersa. Defines a digit as asingle number.a)Basic Vocational Math,Part I,page 2.b. Defines a unit as ab)BVM-I, page 3.c)BVM-I, pages 3 & 4Groups multiples of tenin the tens position.d)BVM-I, pages 5 & 6Etc.e)Lesson 1 - QuizBVM-I, pp. 7-13Handout I-1single one.c. Defines the place valueof a number in terms ofits position in relationto the decimal point.d. Places numbers in theproper numerical position.Groups the numbers 2-9in the units position.6

NameDateMACHINE SHOPAPPLIED MATHEMATICS IQuizUnit I, Lesson 11. A digit is the same as (choose one)a)b)a unita single numbera single objectany number of objectsc)d)2. Give the place value for the seven places preceding the decimal point.11I0000000,oi!*DecimalPointAnswer3. There areunits in the tens place.4. There aretens in the hundreds place.5. There arehundreds in the thousands place.7A a)-11. !J

COURSE OF STUDY OUTLINEMACHINE SHOPAPPLIED MATHEMATICS IUnit ILesson 2Lesson 3(continued)Reading and Writing Whole Numbersa. Refers to any number group byname such as: units, tens,twenties, hundreds, andthousands.a) BVM-I, pages 14-16b. Arranges numbers in groups ofthree digits beginning fromthe decimal point and placesa comma between each group.b) BVM-I, pp. 17-19BVM-I, p. 20, drill #1c) Lesson 2, Quiz - BasicMath Skills, pp. 3 & 4prob. 1-10, prob. 31-38,prob. 42 and 43.Rounding Off Numbersa. Defines rounding off as thesimplifying of a numbera) BVM-I, pp.23 and 24.b. Rounds off by selecting thedesired place, omits allnumbers to the right of thatplace, substituting zeros.b) BVM-I pp. 24 (bottom) -26(prob. 1-5 each)If the last remaining numberon the right is1. Five or greater,adds 1c) Lesson 3 Quiz BVM-Ip. 27 (1-5)2. Four or less, leaversthe sameLesson 4Unit Testa) Handout-Unit I test8

NameDateMACHINE SHOPAPPLIED MATHEMATICS I.',Unit I - TestWrite the following numbers in numerals with commas inserted. (10 pts each)1. Twenty-four1.2. One hundred thirty-five2.3. Two thousand, nine hundred and nine3.4. Fourteen million, six thousand and ten4.5. One hundred one thousand and one5.Round off the following numbers to the third place before the decimal.(10 pts .9.04 l.A.c.)

Name:Applied Mathematics IEvaluation sheet for - Unit I - NumbersTitleLesson #Level(Quiz -Comment)1Meaning of Numbers (Lesson 1)2Reading & Writing Whole Numbers Quiz - Lesson 23Rounding Off Numbers4Unit TestEvaluation:IAlBjCJDLesson 25%Quiz 25%Test 50%Unit GradeDate completed.14 rb.,.)10a

Unit II - Addition of Whole Numbers and DecimalsLesson 1.Introduction to Additiona. Defines the numbers beingadded as the addend andthe answer as the sum.Lesson 2.Addition Factsa. Demonstrates memorizationof the 100 primary combinations of the digits(0,1.9).Lesson 3.a) Business and Consumer Math.pp.59-60. Work prob. 1-20b) EBM, p. 16, work prob.l -13c) BMS, p. 137, part A,prob. 1-10Checking Additiona. Uses the reverse-ordermethod to check addition.Lesson 5.a) BMS, p 11, part 4A (Thisis a speed exercise; seeyour instructor beforestarting.)b) BMS, p 195, part A Quiz(see above instructions.)Addition of Larger Numbersa. Aligns the decimal point ina vertical column.b. Finds the sum of long columns.Lesson 4.a) Basic Math Skills, p. 9Unit Test11EBM, p. 13BMS, pp 17-18c) EBM, p. 16, part Ba)b)

NameDateMACHINE SHOPAPPLIED MATHEMATICS IUnit II - TestFind the sum; check your 2513)3.75049.254).8121.0613.531.0075)Ten (10) points each.,3.31256)40.16 108.67 54.047 80.0313.5007)2.8 9.04 16.009 28.17648).58 95.4 16.009 1.0079)1.0025 .7514 .3095 .200010.00010.0001510)1.062 .438 .500 1.312Write answers 5

Applied Mathematics IName:Evaluation sheet for Unit ITAddition (f WholP NnmhPrs k DocimalsTitleLesson #Level1Introduction to Addition2Addition Facts (Quiz - Les. 2)3Addition of Larger Numbers4Checking Addition5Unit TestAB CDEvaluation:Lesson 25%Quiz 25%Test 50%Unit GradeDate completed13Comment