Ermarmps - ERIC · · 2014-01-27Ermarmps. DOCUMENT RESUME. SE 020 947. DiBello, Louis V.; ......

ED 128 175

AUTHORTITLE

INSTITUTICN

SPONS AGENCYP U3 DATEN OTE

AVAILABLE FROM

EDRS PRICEDESCRIPToRS

I Ermarmps

DOCUMENT RESUME

SE 020 947

DiBello, Louis V.; Lnd OthersCatalogue of PLATO Mathematics L.nsons for CommunityColleges and Adult Education.Illinois Univ., Urbana. Compu er- ased EducationLab.National Science Founda-. t Washington, D.C.Nov 75126p.; Not available in hard copy due to marginallegibility of lesson descriptions throughout originaldocumentPLATO Publications, Computer-Based Education ResearchLab, 252 Engineering Research Lab, University ofIllinois, Urbana, Illinois 61801 ($6.10 prepaid)

MF-$0.83 Plus ?ostage. EC Not Available from EDRS.Adult Education; Algebra; *Community Colleges;*computer Assisted Instruction; Computers; Geometry;Higher Education; *Instruction; *InstructionalMaterials; Lesson Plans; *Mathematics Education;Number Systems; Trigonometry*PLATO; Programmed Logic for Automatic TeachingOperations

ABSTRACTThis catalog presents brief descriptions of all

lessons developed by the PLATO project for community colleges andaeldt education. One hundred siN lessons are available forccmputey-based use. Topics range from elementary arithmetic toftmction theory and trigonometry. For each of these lessons, thiscatalog presents the title, code name, author' and a description of

the lesson. Lesson descriptions include notations of grade andsubject area, amount of student tine and computer space needed, astatememt of the lesson objectives, and a delineation of the lessonsequence. For most lessons, sample computer displays are pictured.Three programs_which allow students to comment upon lessons andteachers to gain information concerning student progress are also

provided. (SD)

* ************* ** * *4***** ** * ***********************

Documents acquired by ERIC include many informal unpublished

* materials not available from other sources. ERIC makes,every effor* 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. Reproductio *

* supplied by EDRS are the best that can be made from the original.* 444 ***************************************************************** *

.1-fryt NI' Of fttPl"tf

,4A f-Nn 0,,,%1TtJ ft OF

cATALOGUE OP

PLATO MATHEMATICS LESSONS

for CornnwnitY Colleges

and Adult Education

cOmpiled by

Louis V. DiBelloTamar kbeliovich Weaver

Keith Bailey

Community COlZege Mthemtics Group

November 1975

Copyright November 1975

by Board of Trustees,University of Illinois

All rights reserved. No part of this book nay bereproduced in any form or by any means without per-mission in writing from the authors.

This manuscript was prepared with partial supportfrom the National Science Foundation (USNSF C-723)and the University of Illinois at Urbana-Champaign.

4

ACKOJLEDGEMENTS

We thank R. T. Gladin, photographer, CoordinatedSciences Laboratory, and W. Wilson, graphic specialist,Computerbased Education Research Laboratory, for theirhelp in the preparation of this catalogue.

We offer special thanks to Sibyl Fellum, typist,for her competence and pltience In general, and for thefine work she has done oh this catalogue.

we also wish to thank the individual lesson authorsprovided written descriptions of their lessons.

TABLE OF CONTENTS

Page Number

Intr duction 1

Lesson Descriptions

A. Whole Numbers

Speedway . . [speedway] . . Al

Signed Numbers

Introduction -- Thermometer, Sea Level . [signex] Bl

Adding and Subtracting on the Number Line . [signum] . B2

[signadd] . 84

[signsub] . 85

Eggdropper 4 0 [ccegg] . 86

Exercises -- Adding and Sub ac- ng [signprac] . . 87

Double Signs (Flipping) and

File Name

Add Aon of Signed Numbers .

Subtracting Signed Numbers .

Multiplication (Patterns) . [signmult] . as

Multiplication (using the running an ) [run] . 89

Division of Signed Numbers . . [divide] . . 511

Addition, Subtraction, andMultiplication of Signed Numbers . [bank] . . B12

Signed NuMber Word Problems onTemperature and Sea Level . . [wordp] . 513

Signed Numbers Games -- West . [west2] . 814

C. Divisors and Multiples of Whole Numbers

]Divisibility Rules/Reducing Fractions [diVr Cl

Finding the Greatest Common Divisor [gcd]

Prime Factorization of Whole Numbers . (primefac] . C3

Claim Game [claim] . C4

D. Fractions

IntrodUction to Fractions [frint] . 1D1

Equal Fractions [frdrill] . D2

Fractions on the Number Line . [rfrac] . D3

Exercises -- Arithmetic Operations. [fraeprac]on Fractions . . . . .. . D4

Exercises -- Equal Fractions; mixedNumbers . . . . . [fracfun] D5

6

File Name Page 4uird_

Execises Reducing Fractions . [reduce] . . D6

Adding and Subtracting Fractionswith Unlike Denominators [lcd] . D7

Graphic Experim,mts with Fractions [frac2] . DB

[darts]Dart Game . D9

Introduction to Rati [ratios] D10

E. Decimals

Decimal Skills: Introduction . [dec] . . El

Reading and Wri ing Decimals . . . . [dec11 . . E2

Adding and Subtracting Decimals . E3

Multiplying and Dividing Decimals . . .

. [dec21 .

[dec3] . . E4

Rounding and Comparing Decimals . . . [dec4] . . . E5

Keeping a Balancd Checkbook . . . . [ckn] . . E6

F. Percent

Introduction to Percent , [per] . . P1

Percent-Decimal-Fraction Conversions [per11. . F2

Word Problems w th Percent . . . [per2] . . F3

C. Arithmetic Review

Math Review Drills I . . [mars] . . GI

Math Review Dri ls II . . r . G2mars4] .

Square Root

Finding the Square Root . . . . [sqrt] . . . H1

I. Set Theory

Introduction to Sets . [ccset] . . Il

J. Algebraic Expressions

Symbols of Grouping . . . [niath95c] . 31

Word FLoblems Drills I . . - [marsl] . 32

Evalmating Algebraic Expressions . . . . J3[eac]

The Distributive Law , . . [dist] . 34

Collecting Like Terms . . [collect] . . 35

K. Exponents and Radicals

Introduction to Exponents . . . [exp3] . . . . KI

Laws of Exponents . . Dnath95b] . . K2

Powers and Roots of Natur-1 Numbers . . [nath95f] . . . K3

7

File Name Page Number

Introduction to Radicals . [frac] . . K4

Addition of Radicals . [matb95d] . 1(5

Irrational Numbers . [math951] . K6

L. Adding, Subtracting, and MultiplyingAlgebraic Expressions

Introduction to Polynomials . . [algex] . Ll

Binomial Products: (x ± 2)(x - 3 ) etc. [quadl] . L2

Binomial Products: (a + b) (a b) etc. [park2] . L3

Math Special Produ_ s [math95e) . L4

Crossword Puzzle on A'JabraicVocabulary [puzl]

Factoring

Factoring Quadratic Polynomials [quad2] . M1

Factoring Polynomials [math95a] . M2

N. Solving Linear Equations

Solving Linear Equations . [solvel] . . N1

Word Problems Involving Linear Equations [wordl] . N2

n. Alg-biaic Fractions

Reducing Algebraic Fractions . [math95g] . 01

Multiplying Algebraic Fractions [math95h] . . 02

Finding the Least Common Multiple ofAlgebraic Expressions . . [math95i] . 03

Adding Algebraic Fractions . [math95j] . . . 04

Solving Fractional Equations . [liml] . . 05

P Plotting Points

How to Plot Points .

Q

[remttt] . P1

Tic-Tao-Too . . . . . . [ccttt] . . P2

Battleship [ccbattle] P3

Plotting Points Checkup

Graphing Straight Lines

Graphing Straight Lines -- Table ofValues . . . .

Intercept of Straight Lineq

Slope of a Line

Point-Slope Form .

0 0 0

3.

[cctttest] . . P4

[linel] . pi

aine21 = = . Q2

(line2a] . . Q3

[line1a] . Q4

File Name Page

Graphing Any Line in the Form

y = mx b [line3] . Q5

. Q6The Lines y ;_ and x [line4]

Graphing Lines in the Form

ax ± by c = 0 . .[1ine5]

More Exercises on Linear Equations and

traight Lines . . . . 0 . [line71

Simultaneous Equations

Introduction to Systems of Equations . [simequ] . 111

Independent Systems of Equations and

Numbers of Solutions .0 . [simequ1] . R2

. Q7

. Q8

How to Write Solutions to Systems

of Equations .. [simegula] . R3

Solving 2 x 2 Systems by Graphing (simequ2] 0 . R4

Introduction to Algebraic Methods of

Solving 2 x 2 Systems . . . . Esimequ31 . . R5

Solving 2 x 2 Systems by Substitution rsimequ43 . R6

Solving 2 x 2 Systems by the Addition-

Subtraction Method .. . . . . [simequ5] . R7

Exercises on Solving 2 x 2 Systems of

Equations .[simegu6] . R8

Posttest for Simultaneous Equations [simtest] . R9

9. Quadratic Equations

Solving Quadratic Equations by Factoring . [quad3] . S1

Solving Quadratic Equations by Completing

the Square . . .[math95M1 . . S2

Solving Quadratic Equations by Fac oring [solquad] . 53

T. FUnction PlOtting

Function PlOtter =[ccplot] . T1

Three-Dimensional Function Plo er [plot3l .

trio Conversion

Introduction to the Metric System . [liter] .

Trigonometry

Introduction to Trigonometry _ [intro ig1] V1

Similar Triangles and PythagoreanTheorem . . . . . . [trigi] . , V2

Special RigUt Triangle . [trig2] . . V3

9iv

File Na_e Page Number

The Sine of an Angle . . [triq3] . . V4

The Cosine and Tangent of an Angle [trig4] , . . V5

Right Triangles [trig5l . V6

Solving Oblique Triangles

Sine of Angles Greater than 90 Degrees .

Word. Problems with Trigonometry

[trig6] . . V7

[trig7] . V8

[word2j . V9

W. Scientific Notation

Scientific Notation . . . .[scienot]

X. Logarithms

Introduction to Logarithms [ XIcclog)

Y. Blide Rule

Slide Rule . . . . . . [srl] = . Yl

Z. Basic Probability

introduction to Probability . [ccprobl . . Zl

Index File

Cononunity College Math Index . [mathco] AA1

BB. Notes Files

studnotes [studnotesl . . BB1

studnotesr . . [st',Anotesr) 1382

Math Notes . . [mathnotes] BB3

10

INTRODUCTION

The Community College Mathematics Project

It would take many pages to mention each person who has been involvedin the development and implementation of the PLATO Community CollegeMathematics courseware. In most cases, the initial authoring of a PLATOlesson has been followed by cooperative review procedures involvinginstructors and PLATO staff, and by the collection and analysis of usageand lesson data. Special recognition is due to the following persons whohave served as lesson authors, programmers and/or r viewers:

Peter AshDan AndersonKeith BaileyRobert BaillieDick BennettJames BoweryRose Brolrm

teve BrayndickDonald CohenRuth ChabayLouis DiBelloSharon DugdaleJerry GlynnFrances KennedyDavid KibbeyDavid LassnerBen LathanErrol MagidsonLaVerne McFaddenAllan MeersRichard NeapolitanGary PeltzCerro]. Steve Robinson

Shin SaitoBonnie A. SeilerNoa ShindermanDonald ShirerMartin SiegelDan SleatorPaul ThompsonCharles WeaverTamar A. WeaverMitsuru Yamada

Kennedy-King College, ChicagoParkland College, ChampaignCERL, UrbanaCUL, UrbanaParkland College, ChampaignRegional Health Resource Center, UrbanaKennedy-King College, ChicagoMalcolm X College, ChicagoCERL, UrbanaCERL, UrbanaCERL, UrbanaCERL, UrbanaCERL, UrbanaCERL, UrbanaCERL, UrbanaCTRL, UrbanaKennedy-King College ChicagoKennedy-King College, ChicagoParkland College, ChampaignWright College, ChicagoWright College, ChicagoMalcolm X College, ChicagoChicago Urban Skills Institute, ChicagoMalcolm X College, ChicagoCERL, UrbanaMalcolm X College, ChicagoValparaiso University, Valparaiso, INCERL, UrbanaCERL, UrbanaParkland College, ChampaignCERL, UrbanaCERL, UrbanaMalcolm X College, Chicago

This project is part of the Community College Project directed byDaniel Alpert and coordinated by Pauline Jordan. It is the responsibilityof the Community College Mathematics Group at CERL, Urbana, under thedirection of Louis V. DiBello, to coordinate the development and implementationof the courseware, to collect and interpret formative data on the lessons,

11

2

and to keep the individual authors informe of the results of the data

analyses. It is the responsibility of the individual authors to make

needed revisions, to keep the lessons in working order, and to provide

for the collection of data in their lessons. Usage of the mathematics

lessons is facilitated by the PLATO site coordinators, Errol Magidson of

Kennedy-King College, Nitsuru Yamada of Kalcolm X College, RichardNeapolitan of Wright College, Elise Spencer Gorun and Carroll Steve

Robinson of the Chicago Urban Skills rnstitute and Robert Grandey of

Parkland College.

Ca alogue

This catalogue contains short descriptions of the PLATO lessons that

are available under the Community College Mathematics Project. It should

serve instructors as a guide for incorporating PLATO courseware into their

teaching activities. On-line access to these lessons is available throughthe PLATO lesson "mathcc", which provides an updated index to all community

college mathematics lessons, as well as an indication of their current

status.

In an attempt to provide a clearer idea of what these PLATO lessons

are, we have included photographs of vaxian prints of selected screen

displays. In nany cases, screen displays in PLATO lessons are built up

in a sequence of steps. New text or graphic perts of a display are often

added after the student has responded to a qaestion or otherwise indicated

he is ready to proceed. To illustrate this process, and to show some of the

interactive capabilities of the PLATO system, we have selected one frame

from the fraction lesson "rfracu. Each stage in the development of the

final screen display has been varian printed and photographed below. The

reader should keep in mind that the varian prints presented in the body of

this catalogue usually represent an intermediate stage in the dynamic

development of the screen displays.

1 2

The varian prints loelow and on the next page hc,w the s p LJ1VQ 1rdin one exercise actiNity in the frac ticm leson "rfra.c". In the fir5 t foursteps, the student's attention is dixected tc the correspondence betweenthe denomina tar and the way in which tile nturdoer line is divided -

13

Lee 't kir-AA& ow/ frsettOtts with

etteweei intent 4

ew mice Qlf orwit is Obeh pore, '4 okflovk the 4 to 1,4

LI,4

r eet,, 01.,n y,te Etr-

, 7, 7Ntt tr-47,t

Soo,re oat

a

t 1,o I fv=5, ,t; 2 tp7r,.tt.

,i VI nt

-, t--, 4

J

4

; o.r4b.4

1

leoste some feset terW with

*wow tweet. 4

4

1

24

4140 4 0 3 tOottho over ft7 I.

Hoo. KoAoh or ni t s each pftrt ?

No../ tIve 4 to 3/ 4

Use the I or kees to move the,

prem. wlien you re done.

Now the student is asked to move apointer to 3/4. (instructions aregiven at the bottom of tbe

When the student has moved the poixiterand pressed LA3, he is given thecurrent location of the pointer-Here, the pointer is at 2/4 ims-teadof 3/4 so he must try ag-ain.

Now the pointer was correctly. movedto 3/4. The point was then Labeled.Next, the student would be asked tcmove the pointer to another fracticnwith denominator 4...

14

LESSON DESCRIPTIONS

15

File

Au

speedwaySpeedway

Bonnie Ander _n Seller1 Elementary Math Group, CERL

611

HOW ds,t 41 toget er-

4

4

6

* 2801c bok

Yakt had ellaacai thitanqtr,rf ra,:e ted-a,

Objective:Student quic41y and accurately answers one-digit addition, subtraction,

multiplication, and division problems.

1. Game format. Tbe s udent works ten problems (for each "race")and wins if he beats his previous tine.

2. Missed problens are repeated and difficulty level is adjustedaccording to performance.

Grade Level: Basic mathematics Student Time: open

Subject_Area: Aritbnetic ecs: 6020

S ecial Notes:The student is provided graphs and Charts of his performance whichhe can use to decide where he needs nom practice.

1.6

31

Pile Name: signexIntroduction -- Thermometer Sea. Level

Author: Tamar Abeliovich Weaver, CUL

is Dif /tif,TVP

r a I iht se

t ettt_,t v SI

iv tI IS 1 tIcs at& 1=',7..1

Ob ective:1. To present a quick and easy introduction to the number line and signed

numbers by usimg temperature and sea level.

Description:1. A pretest gives the student the chance to skip all or part of the

Lesson.2. There are two sections: 1) temperature and 2) sea level. In each

section the student sees a number scale (a thermometer in section 1and a sea level scale in section 2) and answers several easy questionson reading scale values and differences between scale values.

Grade Level: Basic mathematics Student TiMe: 5 - 10 minutes

Subject Area: Arithmetic

17

ecs: 1860

52

File _Name: signumAdding and Subtracting on the Number Line

Author: Tamar Abeliovich Weaver, CERI

rit

Objectives:1. To introduce the number line2. To teach order on the number3. To teach a number line model4. To present practice problems

Ta,a _t.art, at C

Move th r.-ainter t.Pp thg fIrt rgter

ri,ve p,,t-ytar p. Djtil-PpttCT-- ha

1t1K01-: 1A 11111. A

and the negative numbers.line.of adding and subtracting signed numbers.on adding and subtracting signed numbers.

1. A pretest lets the student skip all or part of the lesson.

2. After a short introduction to the number line, the student is taught

to move a pointer along the number line. The negative nuMbers are

introduced as points that are integral distances to dhe left of 0.

3. Order on the number line is introduced (as -2 -5).

4. Then the student is taught a number line model of adding and subtracting

signed numbers. This arithmetic model is used to introduce each new

type of signed number problem. Once each type is introduced, the

student is given problems of that type until he can answer then': cor-

rectly without help. The help consists of either stepping the student

through with the number line model, or presenting a diagram of the

problem on the number line.

Grade Level: Basic mathematics


18

Student Tim 45 minutes

ecs: 5787

B3

File Nan signumAdding and Subtracting on the Number Line

Author: Tamar Abeliovich Weaver, CERL

th1 ph-zkril.,.4 th.e uita-

V--dd tait Zi Td dttad-ztiwyet tc tht ht. tht 0dvdr-Tti.

dds 1 -1, Nc :T.

TT, 5tdrtd et .11.

add-, thd r IF eF t th 10-tt huilt-t* Ill thi

(-1 1D,b11Fha--T tat -1..

w_iffildvd with tat 54-11k

-1 -3 '4

1

r-

lid Itit :f

.1,LE ,

Irwt 7,1.1.i, 51 gn t.

19

0iede

demddibtr ti-ist tad ricft , 1 ,-Itt0-1.! r _iv

Thid .4141 da-T-bld,r0 I Old -Tht.tad ad,: 'thy-put a

5L-13FRICTION IS TRE PENEPSE "F 111116ITI-11.

IR(1,11 d riEf7STTIvE ti.d leftttit -1.rd f I'

ttart with a3.il

SUBTRT-d:T a rxcre=ahvE t-Tt he ..4f.:.ette tiE3- t tc.tee,:e. the

p,C0

B4

File Name: signaddAddition of Signed Numbers

Author: Taniar Abeliovich Weaver, CERL

Ob'e tives:1. To introduce the number line and the negative numbers.2. To teach order on the number line.3. To teach a number line model of adding signed numbers.4. To present practice problems on adding signed numbers.

Description:1. A pretest lets the student skip all or part of the lesson.2. After a short introductioa to the number line, the student is taught

to move a pointer along the number line. The negative numbers areintroduced as points that are integral distances to the left of 0.Order on the number line is introduced (as -2 > -5).Then the student is taught a number line model of adding signed numbers.This arithmetic model is used to introduce each new type of signed num-ber problem. Once each type is introduced, the student is given problemsof that type until he can answer them correctly without help. The helpconsists of either stepping the student through with the number linemodel, or presenting a diagram of the problem on the number line.

Grade Level: Basic mathematics Student _T e: 35 minutes

SubjectArea: Arithmetic

Special Notes:

ecs: 5880

1. This lesson contains the parts of lesson "signum" that involve addition.

2. The sequence of lessons "signadd" and "signsub" is equivalent to lesson

"signue, but the order of presentation of the topics is different.

3. Refer to the description of lesson "signum"that also occur in lesson "signadd".

for several screen displays

as

File Name: signsubSubtracting Signed Numbers


Objectives:1. To teach a number line model of subtracting signed numbers.

2. To present practice subtracting and adding Signed numbers.

Description:1. A pretest lets the student skip all or part of the lesson.

2. The student is taught a number line model of subtracting signed numbers.The student gets exercises until he can do them without any help.

3. The help consists of either stepping the student through with the numberline model, or presenting a diagram of the problem on the number line.


Subiect Area: Arithmetic

Stadua Time: 25 minutes

ecs: 4800

Special Notes:1. This lesson should be preceeded by lesson "signadd".

2. The sequence of lessons "signadd" and "signsub" is equivalent to le-s-n"signam", but the order of presentation of the topics is different.

3. Refer to the description of lesson "signum" for several screen displaysthat also occur in lesson "signsub".

B6

File e: ooeggEggdropper

Author: Mitsuru Yamada, Malcolm X College

MICIcohter 13. now .t4E) les)pter tiiit Move, .

place th. oprrlI

SOVCC M

Ht11=',Pter kt lk ..

Hz .111

rij. thc w.k.115 !o

To provide p ac ice in addition and subtraction of signed numbers .

Desc4ptjonThe student specifies a move for a helicopter along the namber line,or specifies the location of an limbrella on the number line. In both

oases the helicopter drops an egg. Its target is a man on the number

line.

Grade Level: Basic mathematics Student Time: 5 - 10 minutes

agraELNEas: Arithmetic ecs: 742

37

File Name: signpracExercises -- Adding and Subtracting

Auth Tamar Abeliovich Weaver, CERL

Obiective:To provide drill practice in adding and suand a posttest for these skills.

acting signed numbers

Description:1. Randomly generated problems in adding and subtracting signed numbers

are given. The student must answer seven in a row correctly on first

or second try. For help, the number line model prepared in lesson"signum" is used when the student calls for it.A drill with "eggdropper" on the number line involves adding and sub-tracting signed numbers.To finish the lesson the student has to go through a posttest foradding and subtracting signed numberp.The student can choose any of the three sect ons in any order, and asoften as he likes.

Grade Level: Basic mathematics Student Time: 30 minu

Subj.ect Area: Arithmetic ece: 3923

Special Notes:This lesson should be used after lesson "signum".

te-

Be

File Name: signmultDouble Signs (Flipping_ and Multiplication (Pat eris)

Author- Tamar Abeliovich Weaver, CERL

. --4 r-7 =6 =4 -4 -3 -2 -I

Pr444 Lt 7'

OF.43,461T41 44 44.

v44-4

Nrit4

tvm

th,t opp,:e,-.1Tr

P4-43% LA@ t4, !lip It r.' 4144

IT CHM 44=4:I 1.

Objectives:1. To provide a concrete visual model for getting rid of double signs.

2. To provide a simple introduction to the rules for multiplying signed

numbers.

Description:There are two sect ons:a. Flipping: The student is given an arrow on the number line that

represents a signed number. He can press LAB to flip the arrowabout the origin and he is taught that this represents minus theoriginal signed number. By using this flipping model the studentis required to answer questions like -(+3) = ? and -(-2) = ?, etc.

b. Patterns: The student fills in the answers to:2 x 2 = 2 x (-2) =

1 x 2 = 1 x (-2) =

0 x 2 = and then 0 x (-2) =

(-1) x 2 = (-1 ) x (-2) =

(-2) x 2 = 2 x (-2)

These patterns provide an easy introduct on to the rules(negative) x (positive) = (negative) and (negative) x (ne a ive)(positive).

G ade Level: Basic mathematics Student Time: 15 minutes

Sublect Area: Arithmetic

24

2370

B9

File Name: runMultiplication (using the running man)

Author.: Abeliovich Weaver, CERL

pas. lee.%New the man le running 9 seeds per sogonol to the LEFI

We NI I I find hie Ipeet ion 2 gosonsiePFTER he tot to

1

Time .

SO hi* 1004tio1*.2),

Ns, t T

1.15th t11.5 then rWn it

.14 -10

AFTER d.

5 runnIng 5 yArd LEFT.

L/4 fitS1 hi5 IsCoti,sh 2 ,t0,4$ BEFOPE ho 1.t to g.

5popl.

S hi5 ii .10

Cgr,est.Fre55 COTH to. .54-* 010 Man be

NE,J

ANIWINIMIMUIV

Objective:1. To tea h multiplication of signed numbers by using a concrete visual

model.

pesgription:1. A pretest lets the student skip parts cf the lesson.2. A model of a man running along the number line is used to teach multi-

plication of signed numbers. His speed is positive or negative accor-ding to whether he runs to the right or left; his time is positive ornegative according to whether it is after or before ffl, and his position

is interpreted as the product of speed and time.

3. Once the multiplication problems are introduced by using this model,

more problems are presented without the model, and the model is used

for help if the student needs it. The student works problems of eachtype until he can answer without asking for help.

Grade Level: Basic mathematics Student Time: 45 minutes


25

ecs: 4677

Pile Name:

B1C

runMultiplication (using the running man)

A.0 her: Tamar Abeliovich 'Weaver, CERL

Whlt Ot,t t't I I j Of I ,s"00,, SZ

For g soCordO5Er0fE _ wi II

100o. 4 Tht o ortono 2 t-ot=rOo bEFORE OAp0.4 tr $)/srdt por tOCAOO to tho RIGg4T.

For Z. oeconte BEFCVE m .P Z5O 1115 lOOotl,,o 15 gl

( 2!) x 0- 5Latat 15 th.l. fIfO I,xoti.=r

SO (-1) (0) 10

Pro51

-r

page

leditoeciet men g-_: to m I WItixot * *2 minod it ie 2 1104OrdS AFTER ILmago. -s einoe it id yerde per s000nd to the LEFT.

ite nit* 0 time* 5 verde to the LEET, -So hie letstion ib by; (4.2 x - 5)

What Is the eon's loco =IN Ok

So (.2)0-5) -10

.11 .5

simo.56:1*

AFTER O.

26

B11

File Name: divideDivision of Signed Numbers


Z7Z127:::2;2,7.2:1717",,M-7:

L-101 - 5 ) -2 .-A-

caMigrAseseraGin-ILIRIVE)X?:7-aA"-W-Vaz

Objective:To present an introduction and practice on division of signed numbers.

Description:1. Division is introduced as the inverse operation of multiplication, and

multiplication is used as a check.2. Sign rules for division are given as the same as those for multiplication.3. As a help sequence, the student is sent to the section of lesson "run"

that provides practice in finding the factors that yield a given product.



2 7

ecs: 580

B12

File_Name: bank umps out to bank2)Addition, Subtraction, and Multiplication of SignedNumbers.

Autho Donald Cohen and Jerry Glynn, Elementary M-th Group,CERLmodified by Tamar Abeliovich Weaver and Robert

CERL

=E

Ob'ective:To teach arithmetic of signed numbers and provide practice in adding

and multiplying signed numbers.

Description:1. There are five sections:

a. Introduction -- checks and billsb. Adding signed numbersc. Addition exercisesd. Multiplying signed numberse. Multiplication exercises

2. In these lessons signed number arithmetic is modeled by sending

receiving checks or bills.3. In sections b and d each arithmetic problem is associated ith a story

problem invclving checks and bills.

4. In sections c and e a sequence of arithmetic problems without the money

stories is given.


Sub'ect Area: Arithmetic

2 8

ecs: bank 3481

bank2 1990

B13

File Name: werdpSigned Number Word Problems on Tempe ature andSea Level


-7 'ZIZtalf000113:27.;7,11177::37.17":2T.:.-,..-.--.77r..7,741=1-7:.-......"1-1.732

I

11-;4.1 I ta th.t e,trte., that.11 1 t th,t.

Objective:To practice word problems involving subtraction of signed numbers=

Descrip_tion:

1. There are two types of problems:a. Temperature Changesb. Sea Level Differences

2. The student sees the picture of the problem and as feedback he seeswhat his response looks like

Grade Level; Basic mathematics Student Time: 15 minutes

Su1iect Area: Arithmetic ecs:

29

1736

1314

Fi e N- west2Signed Numbers Game -- West

A th : Bonnie Anderson Seiler, CT1RL Elementary Math Group

FMMEMEIMErr7r,:7:4;a412,IVE a Turn_

Your nurnbtrat 2+1+4(I=

Objective:To provide practice in a game format in combining signed numbers byusing the four arithmetic operations with or without parentheses.

Desc ption:1. The game consists of a race between a stage coach and a locomotive.

The student plays against another student or against PLATO.2. Moves are made by combining three signed numbers using the four

arithmetic operations.

Grade Level= Basic mathematics Student Time: 15 minutes

Supiect ea: Arithmetic ecs: 5700

3 0

cl

File 1amc: diqrDivisibility Rules/Reducing Fractions

Au tho r_ ErYci Magidson, Kennedy-King Ccalege

11-6, (31 1,,av (.4.

I. rli?1, Iri,. t .,==y i

3,1y tt f On, it ,6 31616 I

r6t3,66666 313 3

r4.11,htf it cliv161616 Ly 1 ii tbit 1 t ^:11W

t163I 41

Jav16136166 I,

1, t ,

.

Objectives:1. To teach the student the rules for divisibility by 2, 3 5, 10,

4, 6, 9 and to drill the student in their use.2. To teach the student to use these divisibility rules __11 reducing

fractions.

Desc iption:There are eight sections:a. Numbers divisible by 2b. Numbers divisible by 3C. Numbers divisible by 5d. Numbers divisible by 10e. Reducing fractions quicklyf. Numbers divisible by 4g. Numbers divisible by 6h. Numbers divisible by 9

Grade Level: Basic mathi_atice Student Time: 60 minUtes

Subject_ -ea: Arithmetic ecs: 4118

SPecial Notes:Optional topic : Finding the Greatest Common Divisor

31

C2

File Mare: godFinding the Greatest Common Divisor

Author: Errol Magidson, Kennedy-King Cillege

r, fdr- f irdirr, 171.0 bias di!vibbib,1 by TN-,anifinnt EocI he.,4c-,an thf,,--...7n ;4" am fro,tt 1 C*Fl.

2 4Frabt th4 LPPLIP.42

Firtt, livido Thin 5f1ALLEP

Snii-or41, f iinur redfoir,d4r T-IfIO

th4 DIVI,OOP tkid pllunt

'1,11,1+,1= I f.:I et, , ce, tio

hi,gyininn

4 74

(±i

I A

1811-Z.7.LNfLa 7zr-,=1,61.

Pront Eixencin*

Find Lbn er-eftt,t 11,47.1,,n1 ,j1 V171, V3CD: th

Tont t4II PLATO AnoT volii 1410T uldted.For ,Anipl if w4nT PLAN: dpvide 5 int.-, Z2,

f-i.e5; - 5 ..5F ZZ' 5.

che=n1 CFCD.

Or Ic trot rrIct c,-:

(-our requ4nt;

Ob'ective:The student will be able to find the greatest common divisor of anyfraction so he can reduce it when possible.

Descri1. Introduction2. PLATO reduces student-constructed fractions3. Practice exercise test

Grad2 Level: Basic mathematics Student Time: 60 minutes

Sub ect Area: Arithmetic ecs: 2141

N-

kutho

C3

primefacPrime Factorization of Whole Numbers

Keith Bailey, CERL

711=12101911110,c':I,x--- ,You haus 4 problems to go.

If the given owele r ,s i105 p61155, oe will 15660, k5.

Fire 4,11 of voor feetorn ortme/ ii

cho,We foefor which in riot prima: *I

1-!,"1t61 6 55 :5 prOduOt ot

smaller netweal nwbbere. 6

We will keep 1,-a

12

11 5 .

You 04V# 4 p444144,4 40 to.

If the 0,Yen Wil ACtO

f,ra all Of v44, fa4t4r4 prime y oh

o,e done

be will keep trodk of our work here.

12

12 = 4

T5,5 15 the Prime Factor FOOt er, of 11.

MQ-1:LV.:1=iiMMME7Sigil

ObjectiveTo teach how to find the prime factorization of natural numbeto teach the definition of prime numbers.

Description:1. (section a) Definition of factor with exercises.2. (section b) Definition of prime.3. (section c) The student is stepped through the process of finding

prime factorizations.4. (section d) The student is asked to give the prime factorization and

can use several steps.5. (section e) Quiz over the abcve topics. The student must pass this

quiz to complete the lesson.6. (section f) The student call choose any natural number from 2 to 10,000

and the prime factorization will be given to him.

Grade Level: Elementary algebra Student Time: 35 minutes

Subject_Area: Algebra ecs: 3170

Special Notes:Each section can be accessed fron an index. If the student fails thequiz, appropriate sections for review are noted on this index.

c4

File Name: claimClaim Game

Authors: Charles Weaver CERL, and Bonnie Anderson Seiler,

OERL

CLAIM CAME

4 14 11 I.: 14

4 V I 1

Objective:To pract ce factoring natural numbers.

E=ltiacm1. The gal _ is for two players either two friends or a student against

PLATO. The two players take turns picking numbers from the board(see figures above). As each number is picked, it is removed fromthe board and added to the player's score.

2. His opponent may then increase his own score by CLAIMing the numberson the board that are factors of the original number. When allnumbers have been removed from the board, the player with the highestscore win3.

Grade Level: Basic mathematics Student T' e: 15 minutes

Subject.Area: Arithmetic ecs: 2272

Special.Notes;PLATO plays poorly against poor players.

3 4

Di

File N' e: ZrintIntroduct n to Fractions

Authorz Keith Bailey, CERL

Ire r. th ,1=

tyrt

t;_7.7._;. :4"

,-t I

. 1 th.- 1,, I I

5-zongrp. '..MIZEZSMEAMME/METZ:Micz.=r)7.47,,airza7,7;

Objective:

To introduce the concept of a frac ion and to teach the distinctionbetween the numerator and denominator of a fraction.

Description:1. The student is taught to represent a fraction by divided and shaded

squares -- e.g., to represent 4/5, divide each square in the groupinto five equal parts and shade four of the equal parts.

2. The student is asked to represent a given fraction and also to givethe fraction represented by a given picture of shaded squares.Once this representation has been learned, the student uses it tocompare fractions and to add fractions with like denominators.


Subject_Area: Arithmetic

35

Student Time: 60 minutes

ecs: 3194

D2

File Name: frdrillEqual Fracti

Author: Keith Bailey) CERT.,

PALE: If

deck., r.tc,vt .1,1

Th-,5 t-IN1 we will le. I-Z

r ,

r,zova=

Th5f 55,55 15 tV5 fltt TpflI

,1 5155_5. t, ,,,5t 5 1 A ft-7

Ob'ective:To provide instruction in writing equal fractions.

292SEiELiaa: n nxc n c1. The rule = is derived by multiplying --by a fraction equal

d dxc d c

to 1. This rule is drilled in several different ways, then the studentbuilds a table of common fraction equalities such as 1/2 = 2/4,1/3 = 2/6, etc.

2. The notion of factor is introduced and used for reducing fractions.3. A drill is given in which the student is asked to write a fraction wi h

a given denominator equal to a given fraction -- e.g., 2/3 .= ?/12.


gabitf.rt.: Arithmetic

3 6

ecs: 4236

D3

iJe Name: rfracFractions on the Number Line

Author: Keith Bailey, CERL

lecet soma r,actione with

denominator 4

Hew many porta a I divideae4h unit into, 4 0

pFeoa NENT to divide EACH unit nto 4 equal parte.

31125=5:1rwasisur,p21:L.-.74:nligsal

,7;w77.7,TIMIM:31EarAzilir415:,57....Tyczamr,

Let I ,ot t,me fre,tti,65 with

denomivatF 4

IJ. tho t, raf,ve

,r5, whh

'.7-14MicaMMEMMEmMirm2=MMatlaus%iMetwrim.

Obiectives:1. To teach how to locate fractions on the number line.2. To show how this model can be used for comparing fractions, deter-

mining equivalent fractions, converting improper fractions to mixednumbers.

3. To demonstrate the relationship between division and fractions.

Description:(sections a - e) The number line is introduced and, for a givenfraction, the student is asked how to subdivide each unit length andthen move a pointer to locate the fraction. Given a subdivided number-line, the student is asked to use a fraction to give the location ofthe pointer.

2 (section f) A labeled numberline for a certain denominator is given.The student is asked to move the pointer to locate fractions whosedenominators are multiples of the first denominator.

3. (section g) The student can choose two denominators and the corres-ponding labeled number lines are shown for comparison.

4. (section h) For an improper fraction on the number line, the studentis asked to give the corresponding mixed number.

5. (section i) The relationship between division and fractionsdemonstrated.

1


Subject Area: Arithmetic 37


ecs: 3707

04

File Name: fracpracExercises -- Arithmetic Operations on Fractions

Auth, - Keith Bailey, CERLprogrammed by David Lassner, CERL

Objective:To provide drill practice and checkup quiz on the four arithmeticoperations on fractions.

Description:1. There are six sect2.ons:

a. Addition of Fractions with Like Denominatorsb. Subtraction of Fractions with Like Denominatorsc. Multiplication of Fractionsd. Division of Fractionse. Addition and Subtraction of Any Fractionsf. Mixed Exercises

2. Each section has three options:a. Instruction: a brief statement of the appropriate rule, and a

typical problem of the given type that the student is steppedthrough.

b. Practice: five problems of the given type -- at any time thestudent can press DATA to get the rule on the screen or HELP tostep through his problem.

c. Checkup: a quiz of six problems. The student has mastered thesection if he answers five correctly out of six.


Subjec ea: Arithmetic

3 8

Student Time: 60 minuteS

ecs: 3446

7171.VE177.71iirteallE

D5

Ei e Nam fracfunExercises -- Equal Fra ns; Mixed Numbers

Author: Keith Railoyl CERLprogrammed by David Lassner, CERL

Objective:To provide drill practice and checkup quiz in reducing fractions,writing equal fractions and m_l_xed number conversions

Descri tion:1. There are three sections:

a. Reducing Fractionsb. Writing an Equal Fractionc. Mixed Number Conversions

2. Each section has three options:a. Instruction: a brief statement of the appropriate rule, and a

typical problem of the given type which the student is steppedthrough.

b. Practice: five problems of the given type -- at any point thestudent can press DATA to get the rule on the screen, or HELPto step through the given problem.

c. Checkup: a quiz of six problems. The stude t has mastered thesection if he gets five correct out of the


Subject Area: Arithm tic

3 9

ecs: 3887

D6

File Nam reduceExercises -- Reducing Fractions

Author: Mitsuru Yamada, Malcolm X College

Ob'ective:To provide practice n reducing fract ons.

DescriptJon:1. There are two sections:

a. PLATO selects the fraction to be reduced.b. The teacher selects the fraction to be reduced.

2. In both sections, once the fraction is given, the student is asked toname a common divisor of tne numerator and denominator, then to reducethe fraction by that divisor. Definitions of terminology are availableby pressing DATA.

3. The student may work as many problems as he wants in ei.ther section.



4 0

ees: 1650

D7

File_Name; lcdAdding and Subtracting Fractions with UnlikeDenominators

Author: Errol Magidson, Kennedy-King College

-411=11111NOMIIIIIIIIP111 ,

3- 4

la4t t.414 514155.11. .18rt.r..att..4 4,1 044. it t.'heir, 4.4 vat 511" ttrtlefl'

6

3

15t, 511115 31-40 3.41440,,,att ,3

tie ketr.41 104tti,r, Int tit

1,111,5t 15 ,..,4,11- i3t,FaTICIaT Ii tt,4w-ti;,1441"

4

,"I. 44tIF ir th,Iti,TZ4t3TIF o'itprot--a

t

Th. t

PPF.t,'41.tt,t'i44 4

11 t 1511 1' ,Et5.1

Prot,

tiac, thIA rr-t. T pat ,t.ut'Pts I 511,11.11 5. PfCI 5 4..,41 i 44 ir t tit 4.

.3 341 4 3 .71'

-I

13,444, -=',44att: 14413034r ar.;ni:

t:431-I ICr 10 si. 4.14rt It tt:0 4t4r1 ,4t ,at 1444FII ,147 4i

Objective:To teach the student how to add or subtract fractions with unlike

denominators.

Description:1. There are four sections:

a. Steps to Finding a Solutionb. Finding a Common DenominatorC. Finding the New Numeratorsd. Having PLATO solve student-constructed problems

2. Pre- and posttest are available.


$ ject Area: Arithmetic ecs: 5006

DS

File Name: frac2Graphic Experimen s with Frac ions

Keith Bailey, CERL

1-1-ir -7 LW I I -

777: 77-a- 71- 17,

Fiatt -rta." -"" h,

Enter the fre,;t L.n .rniient to etert with,Yatin tractIon micet te lea, thenend tht dent.minet.1, nIwIJ be lee, then 21> 2 7 747i enter a number went

nwltitly th-t r.cie erd de.r

2 " 67 7 7 7 71 7 aiv. 7 3 a1Y, Z1 parte

z

Objective:To use squares, rectangles1 and the number line to eavelop an under-standing of fractions.

Description:1. (section a) A divided square is used to show equivalent fractions.2. (section e) Lists of equivalent fractions are generated for the

student's choice of two fractions. This can be used for findingcommon denominators.(section f) The student is asked to subdivide unit lengths on thenumber line so that a bar can be measured.

4. (sections b, c, d, g) The student uses the number line to draw andmeasure rectangular bars.

Grade Level: Basic mathematics Student Time: open


Special Notes:This lesson is not ready for classroom use and is only intended forpilot testing some ideas.

ecs: 2984

File Name: dartsDart Game

Author': Sharon Dugdale, David Kibbey, Elementary Math Group,CERL

Objective:To provide practice in locating fractions on the number line.

12sEiLizam:1. A vertical number line with several balloons at different locations

is displayed. Only integer points on the line are labeled.2. The student enters a fraction or expression and a dart is shot to

that location. If any part of the balloon is touched by the dart,the balloon "bursts."

3. The student's task is to break all the balloons.

Grade Level: Basic mathematics Student Time: open-ended

Subject __ea: Arithmetic ecs: 4935

5pecia1 Notes:The number line and the size of the balloons vary depending on theperformance of the student.

4 3

D10

File Name: ratiosIntroduction to Ratios

Author: Barbara Lederman, Cotimiunity College Math Group

eMS; rati o 3 7.. 4

WIDENS: fractional form=

uOtrt colon: 34

QUICK Jelli

urtt th.g foil- M IOU In WOWS:

rritl 7.f 5 to 6

_siie hat an engine of 40 horsepos an ngine of 75 borsepauer

at it the rato of the hortepower of thefirst to the hortepOueo of the 1.tebni?

eettv hes Ito and Lou has SICWhat is retio of Loo't money tOBetiv't nomryi

ISM Ok

of enp circle i

ralg is I0 .

Wet it the ratio of the circumferenceftr_ F

SOCOnd7(-1 NT! C 2wr)

000rrrrry g000

Objectiye:To provide a short introduction to ra 1-s.

Descr tion:Introduction to ratios: notation, terminology, writing ratios,expressing ratios in lowest terms.


Subject Area: Arithmetic ecs- 2800

4 4

El

File Name: decDecimal Skills: Introduction


Objective:To provide an overall rationale, set of objectives and index tolessons deci, dec2, dec3, dec4, and ckbk.

Description:This lesson contains four sections:a. Rationale for decimals lessonsb. Lesson objectivesc. Definition of "decimal"d. The index for the decimal lessons


Subject Area: Arithmetic eos: 1500

4 5

E2

File Name: dealReading and Writing Decimals


51:s 4 IP:! 11..1,1

I I 1

; f fiints1,5

Ob ective:1. To enable the student to read and write decimals using place and point

methods.

Description:1. There are five major sections:

a) Introductionb) Reading the place value chart0 Relationship between place value and fractional sized) Reading decimal numbers (place and point methods)

e) Writing a decimal number2. In addition there are pre- and posttests in this lesson.

3. Each section has instruction and exercises.


Subject Area- Arithmetic

4 6

ecs: 5712

E3

File Name: dec2Adding and Subtracting Decimals


11,

Objective:To enable students to add and subtract decimals.

Description:1. There are three major sections:

a. Lining up decimals for adding and subtractingb. Adding decimalsc. Subtracting decimals

2. In addition, there are pre- and posttests.3. Each section has instruction and exercises.


Subject Area: Arithmetic ecs: 5278

4 7

E4

File Name: dec3Multiplying and Dividing Decimals


PrAtfJ, E.OrC4 1

fte tie ee-ieed re,int wili he

in th th.e tkMe'aF,I

795.7 8873 . 70602461Orees .HE1P7if you can'tfin4 the

ensue,

Witiezien in e t NuMtth of mietakeei 4

Let's coneldeh you an OVeht if yOu can foe 5

An 5 ncw cornett- You will be fitieen help Ohnuld

you- mien 3-

qe,Aficl kfInt 1,4a;

I 59

. las r2. 9662

Pret

fibi Tie

. . . . the ieret t _he pla.e

ant t IMIlft r ACIMOI pOint I

-HELP- beellaLle

NfuMbOr 0-, a r rti nietekeni

Let'S iou en e.rfrt if yOu can get a

An A rOA. Vu will be riven help ehieuldy,i M155 3-

Objective:To enable the student to multiply and divide decimals.

Description.1. There are two major sections:

a. Multiplication of Decimalsb. Division of DecimalsEach section has instruction and exercises.There are pre- and posttests.


Subleot ea: Arithmetic

4 8

ecs: 5911

E5

File Name: dec4Rounding and Comparing Decimals

Author: Errol Magidson Kennedy-King College

Objectives:1. To enable the student to round off decimals.2. To enable the student to convert fractions or mixed numbers to

decimals and vice versa.3. To enable the student to compare decimals and fractions.

Description:1. There are five major sections:

a. Rounding off decimalsb. Changing fractions to decimalsc. Changing mixed numbers to decimalsd. Changing decimals to fractionse. Comparing fractions and decimals

2. Each section contains instruction and exericses. The lesson contains

pre- and posttests.


Subjeot Area.: Arithmetic ecs: 5963

E6

File Name: ckbkKeeping a Balanced Checkbook

Author. Errol Magidson, Kennedy-King College

Objectives:1. To enable the student to use his decimal skills to keep a balanced

checkbook.2. To provide a practical setting for the student to strengthen his

skills at adding and subtracting decimals.

Description:1. There are three sections:

a. How entries are made in a checkbookb. Finding balance after deposits or checksC. Making entries in your own checkbook

2. Checking account and money transactions are simulated for the s Wents.



5 0

Fl

File N perIntroduction to Percent

Author: Errol Magidson Kennedy-King College

Objective:To provide overall rationale, set of objectives, and index to lessons

perl and per2.

Description:There are four sectxa. Rationaleb. Lesson Objectivesc. Definition of "percent"d. Index to Percent Lessons


Sub'ect Area: Arithmetic

S uden Time: 10 mintes

ecs 1500

F2

Ft

File Name: perlPercent-Decimal-Frac on Conversions


Pt4T

CC:IttALI

That

ALAIL4t trt r,w

=HELP- 4.-a t 1st I

1F .4.1441-t it Tu 4,4 jet 4

(214 .t I I L:-.s I i

miss 3

Ob'

P.raottce Ell-tme 3

PLATO'%

t, a per,:eHt;

FFt4CTIi4I 3 1 5

-HELP- -,Jti.,t1

PVT.:DJ: 324 't

PLATO F.F Taws.

f3_114t4_tr I P t r3t1 1 NOALtr 71 rat tT.44t

L# n .:Ort4iAr y.ttt 411 Feft iTt 4

In a 14111 Lt iiven sh,uId.1-7b

ctive:To enable the student to convert from one to another among percents,decimals, and fractions.

Description:1. There are three major sections:

a. Introductionb. Converting from decimals to percents and vice versac. Converting from fractions to percents and vice versaEach section has instruction and exercises.The lesson has pre- and posttests.

Grade Level: Basic mathematics Stud n Time; 60 minutes


F 3

File Name: per2 (jumps out to per3 and per4)Word Problems with Percent


SOLUTION) part . .% $2so 040,4 ChArge 10% to a decirtli

tent . .18 8200 then multiply.)$218

ppoix_Em

Eath number it. ri,:el in the appr,priate thttrionel,

Thm mombmr Fme-0 to 1tP1 ETTM7. 1Prebo -NEXT--;

the,1 Nt TITO-bale t,- nn PLATO slvebtTm Fr

Firaet

Solve theoe problems:

4

ppomcm! 16ur bargained with tbe galemmanto pay 44% of hie Original olleni

Ifpaid 812.15. what was the

aalesman's original offer?

Identif.

the number i

Number i

113 n yOur problem, Ifirt prest iho qwe5t,on mark

Perbet 4911

hateFart I, 422.85

0115140r1 Ullt,Ur

--7t1 3

15 in A, r!,.

-HELM. ave,liable

Wm-ter :1 mItheko.; aWel 1 4 M1 atAX00

Objective:

To enable the student to solve word problems involving percent.

Description:1. There are four sections:

a. Introduction to percent word problems.b. Magic triangle method for solving word probl s with percent.c. More difficult word problems with percent.d. Problems using simple interest.Each section provides instruction and exercises.The lesson has pre- and posttests.


Subject Area: Arithmetic ecs: per2 4738per3 1776per4 4201

G1

File Name: marsMath Review Drills I

Author : Shin Saito, City Colleges of Chicago, andNoa Shinderman, Malcolm X College

orAtes

411

he4. 4 1.f t

rivet 1,, tv tIhte. ,n the efreet, t the I sit Sr r ight

rettt,O the

t3,411_

$ probloas dsse. ttht het's, 4 pe- 1

50Ivet 127.6 5.411 m

ritet hr. ur. the je,116.61 Ards. To do so, ro.votho I riont.er on the scross to tits left r.2ht

th7 ks, 'a° .

Pre66 ,hoh1s2Iffsl

are .4 .127.6

8.41$

tepe in the anstser,

Objective:To pre ent review practice with help on fractions and decimais.

Description :

1. There are six sections:Fractionsa. Multiplicationb. DivisionDecimalsc. Addition (paper and pen needed)d. Subtraction (paper and pen needed)e. Multiplication (paper and pen needed)f. Division (paper and pen needed)

2. In each section there is a short explanation of how to work theproblem type indicated on the index. The section then consists ofworking exercises in that problem type. Help is availabie to showthe student hoW to work on exercises. He must, however, do fourexercises without help to complete the section.

Grade Level: Bas c mathematics Student Time: 35 minutes


54

ecs: 2788

G2

File Name mers4Math Review Drills II

Auth Shin Saito, City Colleg. of Chicago, andNoa Shinderman, Malcolm X College

,-yari .',:::,:,:a7,-,f;' .0:11011r=r4", .-S-':.:"-7: .72%71611W '=a--.771.7W ;,=zzttz-

_

6013*2

117,3**

*(*4)1 414

9 * 4LIIVAt 47**

mt Igro-

6 arable*

_dcaable a_

344t44 d th*: 4****41,,n.n t1-1 Anno,r.

.3 z = =3

Queue., 1

* 7 * 3 -44

ate f t heI er

Ob'ective:To present review practice with help on signed nurr±ers and powers often.

Descri tion:1. There are five sections:

Signed Numbersa. Addition and Subtractionb. Double Signsc. Multiplicationd. More Addition and SubtractionThe Powers of Tene. Multiplication and Division

2. In each section there is a short explanation of how to work the problemtype indicated on the index. The rest of the section consists ofworking exercises of that problem type. Help is available to see howto work a given exercise. The student must, however, do six exerciseswithout help to complete the section.



Hi

File_Meme: sqrtFindina the Square Root

Author: Tamar Abeli v.ich Weaver, CERL

,

I

,t1o, r

wg =An =r6, Tripdr-g th5t Y-,a a alae

k5 21,1,3 ==.1 nre .f.t 4,10. It it§F rui I e,1,11t

13.4

,ard th.t ri15 ,.; '

V`, H

Objective:

To provide three methods for finding square roots:a. Guessing and Adjustingb. Newton's Methodc. The Square Root Algorithm

Description:The student gets an index from which he cat dhoose one method and/orsee an explanation of why the nethod works. Each technique is taught ,

by helping the student through the steps.

Grade Lev Basic mathematics


5 6

EI2A2nt_Time: 30 nhinUtes

ecs: 3470

I 1

File Name: ccsetIntroduction to Se

Tamar Abeliovich Weaver and Louis V. DiBello, CERLprogrammed by Tamar Abuliovich Weaver, CERL

Objective:To provide an introduction to set theory including a discussion of

sets, subsets, elements of a set, and the three operations: union,

intersection, and complementation.

Description:1. Each topic is presented via a short description and examp e.

2. Practice exercises are given which include help and error feedback.

3. The student must correctly complete four exercises in a row for each

topic.

Grade _Level: Intermediate aigebra Student Time: 2 -inu s

Sub'ect Area: Albegra

57

ecs: 2524

J1

'le e: math95cSymbols of Grouping

Authoxs: Mitsuru Yamada, Malcolm X College, Steven Brayndick,Malcolm X College, and Shin Saito, City Colleges ofChicago

.;ggauxmage:::

tal

Thir* th1

au:_rux-'..11c7L;;21a-g-z..k....::41;zaTig.R

To present easy nuzerica1 problems involving order of operations andparentheses.

-415tr.Y04


a. Addition and subtraction without parenthesesb. Addition and subtraction with parenthesesc. Operations without parenthesesd. Operations with parenthesese. Backward drill

2. In each section the student is asked to evaluate arithmetic expressions.Some sections contain expressions with parentheses, while others do not.The student may press DATA to be given a sequence of questions andarrows which lead him through the evaluation in steps; or he may pressHELP to be shown how to perform the evaluation. He must perform tenevaluations without HELP to complete a section.

Grade Level: thexnatics Student Time: 30 minutes


58

ecs: 2941

32

ile Narne mars1Word Problems Drills

Author: Shin Saito, City Colleges of Chicago

-',7-251211121=11

Prcits -ItCLP. I f

FYgo, -C447+3- for

rf.,Tp-e tt-w 4,4,7 r -It

tU t 1

wilt )4e 4.4.414 4 4,

Rrect -Rap- fPros,. =DATA. for etxtte htnts tcerd DOivirt

Typft the apprfln-e rorevpreeflion

Jyri yet thitth.. ffit itz t.er hc.1.0t, t-ttNt ntaby tni lyehe lye In

If Jt0 tivvelr 30 fl,11v, h rut. jii±t ttultittlytar

..1:a^rilir"..4.1t.202:17-1V4:4.1."41-1=c4=2.at"TECZi4:974...;

Ob'ective:To enable the student to translate simple

and arithmetic expressions.

.Z7rrStUt..151fT,M.,attivn21117441A7KPa

problems into algebraic

Description:There are two sections:a. Beginning Exercises I

b. Rate Problems IIEach section consists of ten word problems. At the beginning, the

problems are arithmetic. At the end it is necessary to solve a linear

equation to solve the problem. The student can obtain the correct

answer by pressing HELP. However, he must solve all problems without

help to complete the section.

Grade Level: Elementary Algebra Student Time: 15 minutes

Subject Area: Algebra

5 9

ecs: 3164

J3

N= eacEvaluating Algebraic Expressions

Author: ol Magidson, Kennedy-King College

""Tr

Lok

01,45 z e.-4.24rea-p the .4u6ht

Auehtit.5 t Oen dtvi det he 7

tho c,1 ar1.1 5....f.112 2514 .1' q

.401-1 =4I71ltqsr,

E FwE$1; 1qJ! 2

rt,r tt,

Obleotive:The student will be able to evaluate algebraic expressions by sub-stituting numbers for unknowns and then computing the solution.

Desc pt _

1. Introduction2. Arithmetic Operations: review3. Order of Operations4. Reading Algebraic Expressions5. Writing Algebraic Expressions6. Substitution

Grade Level: Elementary Algebra Student Time: 60 minutes

Subject Area: Algebra ecs;

S ecial Notes:Pretest and posttest are available.

6 0

3769

34

File Name: distThe Distributive La

Author: Tamar Abeliovich Weaver, CERLprogrammed by Robert Baillie, CERL

r L'_"7 irri-F7Air

1. To provide a graphic model for the distributive law.

2. To provide practice on the distributive law with signed numbers and

variables.

Description:1. A model of dots in rows and columns is used to get the rule

ax (b + c) ax1D-1-ax c.2. The student assigns signed numbers to a, b, and c and applies this

rule.3. A simple example of repeated addition is provided as an alternative

justification of the rule.4. The student is given practice exercises in applying the law with

signed numbers and variables.

Grade Level: Elementary Algebra Student_Iiime: 30 minutes

SAj_ect Area: Algebra

61

ecs: 4831

File N- e: collectCollecting

Author: Tamar Abelprogrammed

j5

Like Terms

ovich Weaver, CERLby Robert Baillie, CERL

Obje- iv-1. To introduce the following terminology: like terMs, x-term, constant.2. To provide practice in simplifying algebraic expressions by collecting

like terms.

Description:After introducing the vocabulary, the student answers simple questionson identifying x-terms and constants. The distribution law is used toopen parentheses and like terms are collected to simplify the results.

Grade_ Level: Elementary albegra Student Time: 25 minutes

Subject Area: Algebra ecs: 3790

Apecial Notes:The distributive law is a prere isite available in lesson "dist").

6 2

File Name: exp3Introduction to Exponen

Au Carroll (Steve) Robinson, C i a

Institute

t1t,t

f

t. 1 1 01.*T and E'..f1t11T

t gi1FLE

1! I h£,1k 1 1,1Y1 11, ion form.

1MTLIEntallairMINKEV;.Th7-11',S:Allti--TC.6.31EIMMIEU ET,

Oblective:To provide an

Skills

Tt f.10--11 I

19,19

10 10

10-10

14.14

t9l9111 10

1010

141g

19

10

Iff

14

i0

IP

1-1

I

10.te.'1.0.12

iff

14,14

3 10; 14

11.14.1,1 4.4.11114

A 4,k,.1. IA', 601i) tr,t,l4 k

, 4 313r. 14

t

- tep ti"=,%41,F-i-hrirp. LEt F'T -01w.*

oduction and drill and practice on exponen s.

Dtsk/Lak:There are six sections:a. What Is an Exponentb. Practice Writing Exponential Notation

c. Practice Writing Multiplication Notation

d. Calculating Numerical Valuee. Practice Calculating Numerical Valuef. Final Quiz

Grade_Lev _ High School and above Student Time: SO - 60 minutes

Sul....`eg.L.612A: Algebra ecs 4140

Special Notes:1. A section covering the SUPER key prcedes the index.

2. A student is only required to pass the final quiz to comp

lesson.

6

K2

File_Name: ,4

Laws of Expon nts

Author: Richard Neapolitan, Wright College

6 prab I wt, pi1w hlp.Eva ludte th,r, 1.1166.m6g 0-.ffemiklon; 4 (xYz3)

r

flthts

page

fl

Oblective:

To present practice with help on exponent problems.

Description:1. There are seven sections:

a. Writing an expression in exponential formb. Writing an expression without exponentsc. Multiplying exponential expressions in one variabled. Multiplying exponential expressions in three variablese. Dividing exponential expressionsf- Expressions (one variable) to a powerg- Expressions (multiple variables) to a power

2. In each section the student is first shown how to perform the taskindicated on the index page. He must then successfully perform thattask six times to complete the section. He may, however, request HELPat any time to receive assistance on a given problem. The HELP consistsof being shown how to perform the task in steps.

Grade Level: Intermediate algebra

Subject Algebra

6 4


ecs: 2207

File N-me: math95fPowers and Roots of Natural Numbers

Authors: Shin Saito, City Colleges of Chicago, andRichard Neapolitan, Wright College

Objective:To present practice with help on roots of natural numbers.

Description:1. There are five sect ns;

a. Powersb. Introduction to Radicalsc. Radicandsd. The Principal Square Roote. The Principal Cube Root

2. Section a teaches the student the concept of a power. The student mustfind four powers without HELP to complete the section. He may, however,request HELP to find a given power. The HELP consists of a sequence ofquestions and arrows which lead him through the steps involved.

3. Section b introduces him to the concept of roots and radicals.4. Sections c, d, and e test him on the concepts indicated on the index.

The format and requiraments to complete these sections are exactly thoseof section a.

Grade Level: Intermediate algebra Student Time: 30 minu es

SUbject Area: Algebra

6 5

ecs: 2339

K4

fracIntr duction to Radicals I

Authors: Shin Saito, City Colleges of Chicago, and RichardNeapolitan, Wright Colleges

ffer==,:nRia ,E=7.=

Objective:To provide an introduction and practice on radic

Description:1. Thare are five sections:

a. Properties of Radicalsb. Simplifying a ST-are Rootc. Simplifying a Square Root with a Fractiond. Simplifying a Cube Roote. Simplifying a cube root with a Fraction

2. Section a contains the statement of four properties of radicals used inthe following four sections.

3. In each of the last four sections the student is first shown how tosimplify the radical type indicated on the index. The student must thensimplify radicals of that type himself. The student may press HELP toreceive a series of questions which will lead to the simplification ofa radical. He must, however; simplify four radicals without HELP tocomplete the lesson.

Grade Level: Intermediate algebra Student Time: 30 minutes

Subject Area: Albegra ecs: 4673

K5

File Name: math95dAddition of Radic

Authors: Shin Saito) city Colleges of Chicago andRichard Neapolitan, Wright College

Preblema l.rt 4 PrOblogg.done(gi .1p)1 0.

ti gum:

Elweltent

4.--r 2.1-1-

Perform the a&1itin on fl-,t,, th, renult r.tu

By pregging;HELP, wil; give you gid iA golving theLne- wiI1 evpInin rvvr to uv,r1f: the grrf,

EIPTB, letg you review the Introdution togilowg you to tic back ta the table.

l'7?"11lartilISSTP7S 711EMEMITtt'-MM"..r..%.543:E.

Objective:To present practice with help on addition of radicals.

1. There are four sections:a. Addition of Radicalsb. Adding Similar Radicalsc. Adding Two Radicalsd. Adding Several Radicals

2. In section a the student is shown how to add sim lar radicals and shownhow tc combine radicals which can be simplified into similar radicals.

3. In section b, he must add similar radicals. He must do four problemswithout HELP to complete the section. He may, however, request HELPat any time, to work a given problem. The HELP consists of a sequenceof questions and arrows which lead him through the problem in steps.

4. In sections c and d he must add radicals which are not similar. The

criteria and HELP are similar to that of section b.

Grade Level: Intermediate algebra Student Time: 30 minutes30

Subiect Area: Algebra

6 7

ecs: 3478

K6

File N- e: math95lIrrational Numbers

Authors: Allan Meers1 Wright College, Shin Sait- CityColleges of Chicago, and Richard Neapolitan,Wright College

NO. we'll drew a rijht tI e who5eejleale %Idea Nath have lerth equal t5 I

t-4;,5,e5I,41 t

2

R4dhalul.tean2 ,k

,17

In

1 eec left. 2 f.blem5 d. rehetlt helpt -

aw I, the Li [au rul,t

If an Inteiev le het the c,onocn of onoth,th,-1 it, aware raat it ireatuDvel-

1, 4 ..1,Ar.7 .1 An Integer'

Td,4 .5nai1erihg the tole4tvve. a tte 5quave 4-554 5f 4 retlenala

6h a hal le5A`I u4leelv

515e a 1 the tr'4"0,7 at-aYe,

FPI-SS t T

,a-zio-ciL57.,17.;:q2Va ev-45,44445vPvel

NE. T f ! em

Objec iv :

1. To present a rationale for the existonce of irrational numbers.2. To present practice in recognizing irratima roots of whole numbers.

:

1. There are two sec '-ns:a. Introductionb. Drill

2. Section a demonstrates how tne need for more numbers gave rise tothe rational numbers; then further need gave rise to the irrationals.

3. Section b is a drill designed to teach tte student which roots ofwhole numbers are irrational. He must recognize four numbezs ctlyto complete the lesson.

Grade Level: High School and above Student 20 minutes

Subject_Area: Algebra ecs- 2595

Ll

File Name: algexIntroduction to Poilnomials

Author: B. F. Lathan, Kennedy-King College

°J2leS.PYS,To provide an introduction and practice exercises on operations with

monomials.

Description:1, Operation with monomials.2. Definitions of monomial, binomial, trinomial, and polynomial are

introduced.3. This introduction is followed by four drill se tions on:

a. Adding monomialsb. Combining like termsc. Multiplying monomialsd. Dividing monomials

4. The criterion for each section is to do five problems correctly n7

necessarily in a row).5. A short review can be accessed in each section by using the BACK key.

6. A lesson (file name: puzl) containing a crossword puzzle on algebraicvocabulary can be accessed from the index of this lesson.

GradeLevel: Elen_ntary algebra


6 9


ecs: 4331

L2

quFile Name. ad1-

Binomial Products: (x 2)(x - 3) etc.

Author: Louis V. DiSello, CERL

MAURY nit% Out;

.5 BUT a 75

With t raplacag by -i, sae thatIS kW MAIL TO .151,7ga

Man nn

Kw

ot.p_aincrgrr%

110T OWL TO

gain.

0-'ective:7o provide drill practi e in multiplying bincmial s

pescription:1. There are four sections:

a. A guideto these drillsb. Products like 3x(-2x 4- 5)c. Products like (x 2)(x 3)

d. Products like (-Sx +- 1) (2x - 4)2. In each of the drill sections the problems are generated at random,

and the student may work as many problems as he wants.3. Unacceptable answers are (1L,gnosed and saved on the screen for die

student; the correct answer is given after four mistakes.

Grade Level: Elementary A/gebra Student Time: 45 minutes


70

ecs: 3382

Pile Name:

L3

park2Binomial Products; (a b) b) etc.

Authors; Paul Thcmpson, Parkland College, and Robert Baillie,

CERL

Her. I5 a ste_eare.Each eid* 15 le..5)

orto f s t.s steeere (5e45) *(s tit) 0r tb)

Sotto loos. woo t o

15.t.12 166 62

Press NEWT te5 e,te kalif (a.a)2 ec51.515 tob

fief* ia s 5.-5,5,55,.115 51 o. 0.5) and 1.55)What 15 its aFra? )

Lech aide I. th tJ1 of she IrrIttros a and t,Nao lot's etvide the lama ta4uSia iatb fete the 1 Iffe ptecThe arra f the VOLE 55,4ere Iek the Wm of t he ahC45

the fh,e- attnkam pieceni

Sb

lhe ire.. of true lrge "ware i 6 Calib6hat is FOCITKilt Elepfasai n (sr 61,6)

a 2t2ab+b 2 ok

the.-.17ort,

(a+02 a242ab+b2

tREASal

Obiective:

To Provide ins_-uction and practice in binomial produots .

Descri ti1. There are five

a.

b.

C.

d.

se ions:

(a 4 b) 2

(a - b) 2

(a 4 b) (a b)

(a 4 b) (c 4 d)

Review Questions

2. In each of the first four sections, a geometric diagram is

justify the appropriate algebraic formula (e.g., (a 4 b)2 =

in section one). Then the student is given exercises of the

until he has answered four in a row on first ot secomd try.

five contains exercises of all four types.

Grade vel: Elementary algebra Student Time: 60 minutes


71

ecs: 4182

ed to2ab b2

same typeSection

L4

File Name: math95eMath Special Products I

Authors: Shin Saito, City Colleges of Chicago, andRichard Neapolitan, VrigItt

Freolv the rule:

FICC,5reitne to thecoef intent or

-HELP AW.1.1LE,

x.r

Apply the role)

oica.5rciloa to the eboye.coef(scient of y7

tgd

the

tpx 5y) to - 5y) - - 25y2

911 that 15 left to io ir to -etor to the orietrel4r,244 erre write the orvowe.

Ob3ective:To provide practice with help in special products.


a. Problem type: (ax + by) (ax by)

b. Squaring a binomialc. Multiplying two binomials

2. In each section the student is sho how to find tha type of productidicated on the index page. He must then find six ilcoducts of that

t/pe without HELP to complete the section. The HELP consists of asequence of questions which lead him to finding the product in steps.


Subject Area: Algebra eqs: 3478

72

L5

File Name_: Puz1CrosSvord Puzzle on Algebraic Vocabulary

Author; B. F. Lathan, Kennedy-King College

IN MIillaillIUM11111111111113g ria. ttrZ1111111pr

3wic, *2 r

11111111111111.111111111112111111111112! zi111111111.11MMI11111111

111111111111111111111111111111111101111111111

111111 II IMOMP.

2111111111firr r111111111111111111111111111111111111111111111111111111141111pionanimammguiminilimonniii

1111111111111EIn 111111M111111111111111111

MI _4F a 11111

4. 1.1v I. '1

tl.R.,.q

Ob'ectivc:To provide practice working with teriinclogy of polynomials.

Descri_ n:

1. The crossword puzzle to be completed is displayed on the screen. The

student chooses a Location (e.g., 3a for 3 across). He is then given

the clue for that word and can enter his answer Ln the puzzle.

2. The student can erase previous answers and by usIzq the HELP key, he

can get the correct answer for a location he selecte.Complete instructions can always be accessed by using the DACX key.

When the student has filled in the puzzle, he can have Is answ2rs

checked. He is required to correct any mistakes.


Subject Area: Algebra t,CS: 2631

M1

File Name: quad2Factoring Quadratic Polynomials

Author: Louis V. DiBello, CERL

Pkts.+:TIC[ FACJORING

iieffrTO- PIATC1-0

.30.41d

WWI for PLATO t o _It 101v votir ractorD

OR BACK to ch.ole po.r fogtorg.

VOLI1 WWW5

Objective:To provide dri practice in factoring quadratic polynomials.


a. A guide to these drillsb. Polynomials like 3x2 - 5xC. Polynomials like x2 x 2

d. Polynomials like -2x2 I- 5x 3

e. Polynomials like lox2 - 31x - 632. In each of the drill sections the problems are generated at random,

and the student can work as many problems as he wants.3. The student is required to factor each quadratic into a product of

two linear factors by providing the linear factors one at a time.Once the student has given two linear factors, his two factors aremultiplied out by PLATO to show him whether his factorization iscorrect or not. Incorrect factorizations are saved on the screen anddiagnosed for the student.

Grade Level: Intermediate algebra Student Time: 60 min tes

ERtipst ea: Algebra

74

ecs: 2495

M2

File Name: math95aFactoring Polynomials

Authors: Shin Saito, City Colleges of Chicago, andRichard Neapolitan, Wright College

Eider tl* few. st. 5Pra,, -tC-T- f ter

P/...e..1f,t,f., 1015: .1. Pi 155,5 1,0.1p.,1 11.

Fa ,air hi a p;f1 ,f1

Y

L A

!J1,5t -h fl 1

f

1-,fr5f.Ift f

r F. I la I

5 f .faf i r r. I ern

0h)ective:To present practice with help on factoring polynomials.

Description:1. There are six sections:

a. Problem type: ax b;z2

b. Problem type: ax4 bx2 cx

c. Problem type: ax2y bxy cxy2

d. Factoring the difference at two squarese. Factoring the trinomial squaref. Factoring the trinomial

2. In each section the student is first shown how to factor the polynomialtype listed for that section. He must then factor four polynomials ofthat type without HELP to complete the section. He may, however,request HELP at any time to receive assistance in factoring a givenpolynomial. The HELP consists of a sequence of questions and arrowswhich lead the student through the factoring process in steps.



75

ers: 4715

Ni

File_Name: solvelSolving Linear Equations

Author; Mitsuru Yamada, Malcolm X College

In order tifi get credit

mawat Ian. psi, suet ccaplete One PrOhles witteuthelp (ehmiCe 'A below). 55 finish the leseoni yeti

IMist get credit (or Sech alma of Ofpat ion Shown onthe previous page (eacept the optiohml eveCtioni-

problem

.32. -22 51

M515/ 5545h 1151p do W.5 55111 for the problem above.= a numher. ft le adVisable t6 start vich

PLATA will tell pou TA vill

5155 15 th5 5551pu15t1

tell PLAro what to .1o. PLATO vill do the

55.Put0116.hh 555

Y,A5 5,5.5 c&1 th5 next etep of the emNil

tut PLATO .All tell .iai chat to elko.

Ytu tv5.5 ,J, the ne.t etep of the elpat icrPLATO will help ,,,SOA Vf-u 45k.

prcblem

-3:. -Z: . 3

Atep 2

-32 -32

There IS 4 fra;tion en the left which can berecisc.S1 T55-5 ri an,1 pre5M NEM% PLATO will gall fractione en the left.

DATA for InfiornoetTS-Ss5 SHIFT-DATA tO S

_AMMMUMMW'

-1

his problen ever eig .n.

Objective:

The student will solve one equation of each type see the followingdescription) without help from PLATO.

1. One-step problems like 3x = 4.2. Two-step problem like 2x + 3 = 4.3. Equations where 'x' appeal's on both sides of the equal sign.4. Equations which have terms that can be combined.S. Equations with parentheses.6. Equations with fractions.7. Harder equations with fractions (op onal)

Grade Level: Intermediate algebra Student Time: 2 - 3 hours estimated

Subject Area: Algebra ecs: 7479

S ecial Notes:1. There are four levels of "help" available to the student on each problem.

At the highest level, PLATO tells the student what to do next and thendoes the arithmetic for the student. At the lowest level, the studentmust type in an equivalent equation.

2. There is cumulative data available to all non-student users of thislesson.

N2

File Name: wordlWord Problems Involving Linear Equations

Authors: Gary Peltz, Malcolm X College, and Mitsuru Yamada,Malcolm X College

Alrpl.rt n to s off 6X minutet aft OirOlaneA anki heads in the same Olrection. airplane Atravels wIth a constant vela.CitV or 735 ,60, 004ainplane B with a constant Velocity of I. m01,;n hew early hours will airplane el catch up 1,,;. air=Olarw R7

-PYos

s,!,1vs this 7-r,tlem7

5r1.1 -help- if

SJ' A ANSIIISKIMIIM

.;

0. 1

a I s P! I

P

.Plonsti

Objective:_

The student will be able to write equations for the word problemspresented in this lesson and solve the equations.

Desc- tion:Problems involving age, mixture, and rates are presented.


.2u.1,1jEt.Lk_rea: Algebra

7 7

ecs 4548

01

File Nam math95gReducing Algebraic Fractions

Author Richard Neapolitan, Wright College

Fir.t ctj 4.J.t diflldc tfl ,444.rhe th. bihst 4-4..t 4t.14.4 it?

Psnenter. ,qh.n .1-

-Ilt=f vh4. tt. r,jflsr,tit 4.A7Nfl/Wh 2: Srri 4W4t i it

Fins!! iv, 4h. ra,r4....t,,-.1 0,14h it.0.4 4,th

What is t

1±51 t;r;o.r.tt

-

cqtC__t i 6 pestletris_isithisit

th. tell ;1.4kr4 fh.4:t Rs ltsiest teems:

Wrist is the new nwn.r.t.t

sst:

erStit 4,4 tteiii f f.h5.i b.th

IS retiQe the evressi.mn tiv this ta;ts

I

h.5thF. t tt rviiiirta the r sesste

liieste the sumer Shiir in htsrest fermik% *01 (.*41

Write tre iies;Airist?ii in t4;tred

Press HELP again if vise el. n.t htsaai tIn snS..icr t.

miss or these n.to g.tett tpn..

Otjective:To present introduction and practice with help on reducing algebraicfractions.

Description:1. There are four ections:

a. Problems of the form 8x4 4x2b. Problems of the form 10x 5r4/2x4y7c. Problems of the form (6x5 - 4x4)/12x2d. Problems of the form (x2 5x 6)/(x2 +3x + 2)

2. In each section the student is shown how to reduce the fraction shownon the index. He must then reduce two fractionswithout HELP to completethe section. He may, however, request HELP for any given fraction toreceive a sequence of questions and arrows which will lead him throughthe reduction process in steps.

Grade Level: Intermediate algebra Student_Time: 35 minutes

Sub "ect Area: Algebra

78

ecs: 3471

02

File Name: math95hMultiplying Algebraic Fractions


loaw.;...]:=tirmlwatusemonnnow-,b.1±Ereet O tht he1 wernent is d

re,forel the IrKlica!ed ffultwIlcatton, rGIva FINFL ervar-)

what 15 the ntw ruograLr

F-ELP

DAM,

Ii roLtLA PF-IPER

5,1Y1r4 ;,151: 1,1i'l Phi,

;

_ALM_

.122a-1.1_,.ableedm 7

Ferrore the 4rrJiatei mwIt (G1V0 FINAL nftwerl

What 15 the new nufwel'at,A

4

liI er, fat,d- the app40,.1re In th5manerat.?1. thAt pr,f ir:4t 115 1"!11-;-..,1

1.11W I of p t t th roLfr,r,L,,

Prtz, ICLP ai, II W.,t.

thee rew

Ob'ective:To present practice with help on multiplica ion of algebraic fractions1


a. Problems of the form (x5 3y2) x (7x3/Y4)

b. Problems of the form (x4/3y5) x (5y2/x3)c. Problems of the form [(x2 + 7x + 12)/y7] x [5r6/(x + 4)]

2. In each section the student is first shown how to multiply the algebraicfractions shown on the index. He must then perform two multiplicationswithout HELP to complete the section. He may, however, request HELPfor any problem to receive a series of questions and arrows which willperform the multiplication for him.

Grade Level: Intermediate algebra Student Time minutes

Subject Algebra

7 9

ecs : 3101

CL3

File N e: math95iFinding the Least Common Multiple of AlgebraicExprssions


Find te !deist ccom

Ftictr tHh @Eq.,

Fat !r-f tthErt.tnHtrtE

Ft,f5. ft,: rtt

h t.f, -EHL,

,

Z. Ttot L.C.U. it tht tht,4t=ft ftftgrttErtt. .th eel H the HthItt ,ttntott.

Id e the htftheet eftr"-E

P I H t CLF t Ht tF 8

ind the Ist molt tF .L.C.11..I !.1

firtt

rett!reAeee 'AO .eprete,,e.

th,rd tint.' E H I inee,Ti-,..,-rtfrg, it pr ,f, h.! it tItt-th itft.fEtfti,

:tt,rttt.tt I ErH

ee..71, pr o're t.ttEtt- triftrt 'Eh! E fE

I tt r . TI. LIi It -tT. tht

Pr e D0.71 f

ph) e tive:

To present practice with help on finding the least common multiple ofalgebraic expressions.

Descr ption:1. There are five sections:

a. Two expressions of the form 6x3574b. Three expressions of the form 6x3574c. Three expressions of the form x2 + x -d. Two expressions of the form x3 -I- x2 - 6xe. Three expressions of the form x2 + x - 6

2, In each section the student is first shown tu.r-, the least comm nmultiple of expressions of the form indicatdd thd index. He mustthen find the least common multiple in three ptobiems without HELPto complete the section. He may, however, request HELP for any problemto receive a sequence of questions which will find the least commonmultiple in steps.

Grade ev InterMediate algebra

Subject ea- Algebra_ -

Student 11° utes

ecs: 4367

04

File Name: mLth95jAdding Algebraic Fractions


CMI f ,thit

1

li t-

F:, .I,

Objective:To present practice with help on addition of algebraic fractions.

Desc 4tion:1. There are seven sections;

a. Problem8 like 4x/3 + 5x/4b. Problems like 7x/2 + 2x2/3c. Problems like 3x/4 + 2y/5d, Problems like 2/5x + 5/3xe. Problems like 2/7x + 3/2xyf. Problems like (3x + 2)/4x + (2y + 5)/3yg. Problems like 3/(x2 - 4) + 2/(x2 -3x + 2)

2. In each section the student is shown how to add the algebraic fra tionshown on the index. He must then add algebraic fractions of that samevariety. He must do this three times without HELP to complete thesection. He may, however, request HELP at any time to receive a sequenceof questions which will lead him through the addition in steps.

Grade Level: Intermediate algebra Student ime 45 minutes

Sub'ect Area: Algebra ecs: 4123

05

File lim1

Solving Fractional Equations


t r0. I tl-0 e

VI*

Seivq the roll:5.41M otthetieh:

Pr000 0.0Pt° 00. NV_ I

WTYirn0741-

4

The L. C.D. a iZ

12 (60-Z) 1

3 (fia-27 (03

100=60360- la

300-20

06-

0 0 20 it

(40.2)

V 1.

Ob)ective:To provide practice with help on solving fractional equations.

Description:1. There are three sections

a. Problems like (x + 3)/2 + (x + 5)/6 = (x + 1)/9b. Problems like 3/4x + 6/5x - 13/20c. Problems like 2/(x - 1) - 3/(x + 3) = 6/(x + 2x - 3)

2. In each section the student is shown how to solve the equation listedon the index. He must then solve fractional equations of that typehimself. He may press HELP to receive a sequence of questions whichwill lead to the solution. However, he must solve two equations with-out help to complete the section.

Grade Leve Intermediate Algebra Student Time: 30 minutes

SatitELAEfsi: Algebra

8

ecs: 4705

P1

File N e: remtttHow to Plot Points

Author-: Donald Cohen and Jerry Glynn, Elementary Math Groups

CERLadapted by David Lassner, CERL

bj ective:To provide remediation in plotting points for stude

the checkup in cctttest several times.

s who have failL,

Descr tion:

1. The student is taught to move a cursor to a specified x,y location in

a grid.2. He is stepped through this process first, then he is asked to work

several similar problems until he can work them without error.

Grade Level: Intermediate algebra

Sub.ect Area= Aigebra

t Tim 30 minutes

ecs: 2679

P2

File Nam_ cctttTic-Tac-Toe

Authors: Donald Cohen and Jerry Glynn, Elementary Math Group,CEPS..

adapted by David Lassner, CERL

28111111SLInD ars.e.r,

Y fril PtftiC,

,

, -I

Ob'ective:To teach plotting points on a grid by using a tic-tac-toe game format.

Description:1. The student plays tic-tac-toe against PLATO on a 4 x 4 grid. The

markers are placed at the grid r-lints by giving the coordinates ofthe grid point.

2. Depending on the level of pla 7rid may include negatt

coordinates.



84

ecs: 3249

File Name: =battleBattleship

Author

P3

Donald Cohen and Jerry Glynn, Elementary Math Group1CERT.,

adapted by David Lassner, ERI,

Ob'ectivo:To provide remeiation on plotting points if student fails the checkup

in octttest.

Pg1SE12.117n:1. Similar to the commercial game "Battleship." The markers are placed

on grid points by typing their coordinates. The grid consists of all

four quadrants.2. The student plays agat PLATO.

Grade Level: Intermediate algebra Stt-d,nt Time: 30 minutes


85

ecs: 2340

P4

File Name: cotttestPlotting Poin: f-_-ckup

Authors: Donald Cohen ana ,ierry Glynn, 17

CERLadapted by David Lessner, CERL

tary Math Group,

0121!,ittive:

To provide a f:Itudent's ability to plot points.

De r ption:

1. The student swer two types of questions:

a, Give the coordinates of a given point a grd.

b. Move a cursor on a grid to a point whose coordinates are given2. To pass the checkup he must answer three out of four questions

correctly.

Grade Level: Tr:cermediate algebra Studen Time: 15 minutes

Subject -irea: Algebra

86

ers: 1560

File Name: linel

Graphing Straight Lines Table of Values

Author. Barbara Lederman, CERL

OWective:To provide instruction and practice in getting a table of valuessatisfying a given equation of the form y = mx b , am') using it

to graph the correspon.Ung -traight line.

Ra1aiaLiav1. There are three sections:

a. Getting the table (Y: varlues

b. What's my line (graph it using the tabie of values)c, What's my line (graph it by moving a cursor on a grid)

2 In the first two sections the student is given a linear equation ofthe form y = mx b and required to provide x and y values to makea table of values that satisfy the given equation. As each pair isentered in the ti&.0.0 it is automatically plotted on a grid.

3. in the third section the student moves a cursor to plot points on a(7-44 that satisfy a given linear equation of the form y = mx b .

In all three sections at least three correct points are required andall points are checked in the evation.

Grade Level: Intermedia aa

Sub'ect Area: Algebra


ecs: 4713

'Tau, lines:

92

File_Name: line2Intercept of Straight Lines

Author: Barbara Lede-_ an, CBRL

hie I I no:

In. goe5 thrfAlgh (0

5UT the I ne VO0 wAnt en thre.gh Ug

;;ZAIMMIAITT117X4.1:01M-Vir,TASIBEZZLITMEM.,,

To introduce the y-intercept and to provide instruction and practicein finding it from the graph of a linear equation.

Description:1. There are two sections:

a. What is the y-interceptb. What's my equation (fill in the y-intercept)

2. Section a starts by allowing the student to fill in the blank in an

equation of th. korm y = nx + and displaying the graph of that

eguation4 in soction b, he is taken through a se :Les of exercisesuntil he can determine the intercept by looking at the gr*ph.

Grade evel: Intermediate algebra

D2bi2s_tLALqA: Algebra

Student T4: 15 11.1A te

ecs: 2123

Name:

Author

line2aSlope of a Line

Ba ba a Lederman, CERL

1

o of th!, 1 Ifwf:

tho dirott ton.451RW

mal.WmPa,mmur.n.3171.71711girnWIMUUMY-ffAMIUM.,

Ob o_ive:To introdu e the slope and to provide instruction and practice inf2jiding it from the graph of a linear equation.

Description:1. In section a the student fills in the blank in equatics of the form

y x b and the graph of the resulting equation is displayed onthe grid.

2. Section b presents a trial-and-error drill where the student deL-t,mines the slope from a graph. If the student types in an incorrectslope, the graph of the line with that slope is displayed on the grid.

3. Section c presents the rise-over-run definition of slope.4. -,ection d develops the two-point formula for slope.

Grade Level: Intermediate gera Student Time: 30 minutes


8 9

ers: 44452

File Name: linelaPoint-Slope Form

Authors: LaVerne McFadden, Parkland College, Ceith Bailey,CERL, and Barbara Lederman, CERLprogrammed by David Lassner

-

MC PO -41--fC[C-C FORM

ttet the elope ard b.5th ,:.,,11h4tetk

t1,21 in

rdrvite

2) - II

oc,e =c=ordrr.tc

thjo .!1,

SO. MrTf:CFBEEZZA,Iz.

WrItg r. eqpdatIon rif the hoe

th,toth wth fla,c

a a fratlwr-I, er-N=loac it in ntrettt.d..--

FIII in the tAank[

[ St far. hatfe 0. 69[Y,E1 need te naawer I wit

1

EEIVESMOVIZ:Kirga":001#37=MZ;C:1:2=151WARL.WLMaj

Objective:Given two points or one point and the slope, the student will be ableto write an equation of the corresponding line.

Pes_LsLLL'LLD_aL1. There are two sections:

a. Given the slope and a point, write an equationb. Given two pojnts, write an equation.Each s2ctio.. contains instruction and practice exercises all of whichcan be accessed from an index.

3. In the practice exercises, the student can step through a problem bypressing the HETP key. He is required to do three problems withouthelp in each section to complete the lesson.

Grade Level; Inte=ediate algebra Stude Time: 30 nutes


9 0

ecs: 1976

File .tif e: line3Graphing Any Line in the Form y = mx ± b

Author: Barbara Lederman, CERT.,

YOUF !Ulan;

1.1 v..

in nd .tiOn 61 thin line;

Etb it tvtiittii,,

c!-gi ndd krni linen,

Arrablirn, rr-71=-77:MarliftW.'

Wh,t in th, ni,p,

tid,t

WIt,t th, in

[41

VerY en.od.

Rtet

3. 3

Alaatim:To provide prtice irt using the slope and intercept to find theequation of a given straight line or to graph a given linear equation.

1. There are four sections:a. Summary of intercept and slopeb. What's my equation (type it)c. Graphing hintsd. What's my line (graph it)

2. In the fir .iection, the student is given equation in t. formy mx h _cr which he must give the slope and the y-intercept.In the r tion, the student is given the graph of a straightline and L. : d2t type in a linear equation with that graph.

4. The third section helps the student step-by-step to graph a linearequation by using the y-intercept and the slope.

5. Tn the fourth se..7-tion he is given a linear equation and he must g_apil

it by plotting at least three correct points on a grid. The s',..,dent

is expected to make use of the concepts and techniques learned in theprevious line lessons.

Grade_Level: Into -ediate algebra Studer.t Time: 30 minutes

pubjeot Area: Algebra

91

PCs: `597

File

Q6

line4

The Lines y = b and x = c

Author: Barbara Lederman, CERL

pef4at

ITTUIPr000 tat to /nark A rtAt At

to AraAA a lApiAtt44t tA draw the 1 tee

Pio.; A ChAck

01a1M6r.INAZMIaintrrollerIlia..`;;;..'7"

YAur I ine,

ttv

thle Pine:

E - t

0r4e1":5-tirt.D.C&NKiatalan'tZ411M-, '

2121-ve:To introduce the lines y b and x = c and to drill the student ingraphing any such equation and in finding the equaLon of any horizon-tal or vertical line.

Desc iption:1. There are four sections:

a. Type the equation (horizontal lines)b. Graph the nquation (horizontal lines)c. Type the Auation (vertical lines)d. Graph the equation (vertical lines)

2. These sections introduce horizontal and verti.cal lines and presentdrills similar to those used in earlier lessons.

Grade Level: Intennediate algebra Student Time: 30 minutes

Subject Area Algebra ecs: 3634

9 4

Q7

File Name: line5

Graphing Lines in the FoLm ax + by + c . 0

Author: Barbara Lederman, CERL

- ISOM=-;:::-.:_i.,_7,--.:

-

Objective:

To enable the student to convert a linear equation in the forlpax + by + c . 0 to the form y = mx + b ar,d thereby identit: 4tsslope and intercept and be able to graph it.

E2E51-1214sa:1 There are five sections:

a. Find a, b, cb. Clange ax + by +c. What's my sloped. What's my intercepte. What's my l'ne (graph it)

2. In the first tv sections tho student isecuation from Le f7orm aX + = 0

3. In the last th,n- surtions the ,guationsand the drills ar- c-her-i e the same as

0 form y = mx + b

Grade Level: Intermedia algebra

taught to conve t a linearto y = mx + b.are given in the a, bl c, tomin earlier line lessons.


Subject_Axea: Algebra ecs:

EpeciaA

es:

his time a l lines presented in this lesson can be converted tothe form y = mx b . At some time in the future, vertical lines inthe form ax + by 4, c = 0 will be added to this lesson.

35:

Filo tlamo: 1

Authors:

More Execise s cn Linear Equa ions and Straight Lines

Donald Cohen and Jerry Glynn, Elementary Math Group, CERL

_L7.:7-..,7-7--,:lmwow=mmommmmummmimumwv-

1 faiMie I: 1 1:::::::MMilli:11111.1 MORMA MMMMM 1:4:11

111 11:1Mkiiiiiiiiii

:Mtn MM : MM :in::I:::8:::: :::::=:::::::::IS221111 11.1A mmmmmm maims!

lim:mml Imimmilmmulmmlemilill

111:::::::::421411:::::::11gw milmmilmilm Ow:BMW

rillmumnImMa mmm M m:VIIIiiiiiiwwirmlammurnONEKImi1 MIptiellimminOW I!

as i WO MunigliM F4 PSOMMI.L._

ailliiiiiiillime 11

Objective:To provide a series of problems which require the consolidation of allpreviously learned skills in graphing straight lines.

Desert tion:1. There are seven sections:

a. Give the equation of a line through a given polntb. Give the equation of a line ntter than a given linec. Give the equation of a iir th the same slope as a given lined. Give the equation of a lin(7! '±it meets a given line in a given

pointe. Give the equation of a li ugh twei g*'Ien pointsf. Give the equation of a lir dicular 7c a given lineg. Give the equation of a line Thrf ven points

2. In each section, the student wo-the given type of question.

Grale Level: Tntermediate algebra

ject Area: Algebra

9 4,

instancas of

Student Time: 60 itt_u_ s

ecs : 2054

File

tr.ln

IVa a aalutiOn ta a atattara. taath equ

-5x -

(,-

In m 5,711

R1

simequIntroduc ion to Systems of Equat ons

Barbara Lederman, CERL

21

Ob:lective:_

To provide an introduction to systems of linear equationsthe geometric meaning of the solution to a 2 x 2 system.

h emphasis

Description:Several large systems are shown. 2 x 2 systems are discussed.Solutions to a system are shown to be intersections of pairs of lines.


§-_41212_Lvrfft2 Algebra

9 5

eon: 3140

R2

File Name: simegulindependent Systems of Equations and Numbers ofSolutions

Author: Barbara Lederman,

If the boo linen don't1

pointin et-,

tv,At E111-V1 1

pftle 2@

I. ed-h ,4 the fo I

:f the tivn'fem im

-! intOnit t55 o0tee 15 dependent.

fbi

'77E= 1r7.

Objective:To familiarir the student with the geometry (graphs) of three dif-ferent types of systems: independent, inconsistent, and dependentas well as the number of solutions for each type.

Two sr'ries of drills are presented:

a. A graph (la equations) is presented. The student enters whichtype of system it represents and how many solutions it has.

b. Only the equatior5 are presented -nd ratios of coeffioints arediscussed. The students give system type and number of solutionsas before.



9 6

ecs: 3826

File Ncilm,

L(7-) Write C -1 U tC U I ysLe'Yls I itt

Author'

Objective:To provide directions and practice in typing itypes of systems,

1. There ere t e=e

a. Independentb. Tnconsiatent

c- DePendent2. A help seque0-2e

Grade Level= Int

_Sub-ect Area: Algebra

Solutions to the Wctens _ e given as follows:

a. Independent systems: an order pair

b. Inconsistent systems: the word "nouen

e. Dependent systems: first either equation is typed; then thxee

points on the "sal i" line must he given.

a

solutions to the three

-callable for the dependent sy -em se tion.

n, rine: 15 minutes

3072

e algebra

eds:

9 7

i e -111 e uSntri 2 2 5 p.r7tern:3 by C-17,11., I. Lnq

r

=

Objective:

To provide instruction an solving 2 x 2 li:1(ar sy:ltems by (Trap:7141g.

Descri'4t2on:

Thu student graphs one &Dation at a timc, and tnen estimat.-eE ho

_rEolation to ths system by reading t:le

C,rAde Le Intermediate Alqebra Student Time.: 30 minutes

Sub'ect Area: Algebra 261 1

1.1dme: :31,moq13

Introluc.1 to )1.1 _Tth liL Methods o Solvina2 A 2 ST-Aolon

: Bari)a- Leo, 1 cERL

Objectives:1. To provide motivation for learning algebraic methods for solving

systems of equations.To promote An understandicig of why the methods work through theuse of grapho.

Descri tions:1. Several systens axe presented which can almost be solved by inspection.

The student solves these with any requested help.2. The idea of egilivalent systems is presented using equations and graphs.3. The student is told that algebraic methods can be used to cbange

"ugly" systems into equivalent systems whose solutions are easy toread.

Grace Level: Intermediate Algebra Student Time: 30 minutes

jest Area: Alga)ra ers: 3459

iiiinq 2 x ms by Substion

crLT,

ch1ectivalTo provide instruction and exercises in solvinq 2 x 2 systems oflinear equations using the substitution methoe-

De- n:

The sabstitut-on method is presented step-by-step using flowcharts.The student then practices each step typimlin the resulting equations.Graphs are used to picture what is happening to the system.

2. Dependent and inconsistent systams are also solved.

Grade L vel: Intermediate Algebra Student Time: 45 minutes

Sub-ect Area- Algebra

100

ecs: 5560

1)7

-

Methoci

5y

LcclecnIp

_tact:Lon

Obje-tive:To provide instruction and exercises in solving 2 x 2 systems of linearequations using the addition-subtraction method (this method is alsoknown os the method of linear combinations).

12=11-L412EL:1. The addition-subtraction method is presented step-by-step using flow-

charts.2. The student then practices each step, typing in the resulting equations.

Graphs are used to picture what is happening to the system.

3. Independent, dependent, and inconsistent systems are presented.

Grade veL: Intermediate algebra Student Time: 45 minutes

Sub._ ea= Algebra ecs: 5344

R.8

File_ Name: simeg-u6

Exorcises on Snlviniq 2 2 Systems of Equati ls

Author: :bara Ledermnni1 CUL

ObjecTo provide practice in solving each type of 2 x 2 system of linearequations: independent, inconsistent, and dependent.

Descr tion:

This lesson is strictly a drill. No instruction is prov ded. A studentgives solutions to systems of equations.

Grade_Level; intermedlate algebra


102

Student Ime: 15 minutes, minimum

ecs: 2572

Vil_Name: sintestPosttest for Simultaneous Lquiti

Author : Barhara Ledo-man, CER1

Objective:To provide a posttest for the sequence ,2E PLATO lessons on simultaneousequations.

Desc iption:1. The test consi ts of twelve questions. There are two multiple choice

questions, six yes or no type questions, and four questions where thestudent must give the solution to a system.

2. The student can skip any question by pressing LAB and return to thatquestion later.

3. Within each problem type) Parameters for the exercises are randomlygenerated so that new questions will be presented to students whorepeat the test.

Grade Level: Intermediate algebra Student Time: 15 - 20 minutes

ISubject Area: Algebra

10

ecs: 2821

S1

Pile Namc: quadSolv atic -rs by FacLo

AothOr: Louis V. DiBello, CERL

Objc_ctive:To give drill practice in solving quadratic equations by fact ring.

Descri- tion:

1. There are five sections:a. A guide for thesedrillsb. Equations like 3x2 - 5x = 0e. Equations like x2 - x 4. 2 = 0

d. Equations like -2x2 Sx 3 0

e. Equations like 10x2 - 31x - 63 = 02. In each of the drill sections the problems are generated at random,

and the student may work as many problems as he wants.3. The student can choose to give the solutions right away or to factor

the equation first. Any solution he gives is checked by plugging itinto the equation and the student is shown this check.

4. If the student cannot give the solutions, he is required to factor theequation first. Incorrect factorizations are multiplied out for the

student and saved on the screen.5. After four incorrect factorizations, the correct factorization is given

and the student is required to solve the equation. After three incor-

rect attempts to give a solution, the factorization is analyzed tofind a solution from it.

Grade_Level: Intermediate algebra Student Time: 60 minutes

Sub'ect Area: Algebra ecs:

103370

Pilo Name: moth95mSalving Qu ldratic Equatio s by. (oinplettng the Squar

Author: Richa d -oapolitan, Wright Colic

Objectives1. To present an introduction and practice with help on completing the

square.To present practice with help in solving quadratic equat ons by com-pleting the square.

:

1. There are two sections:

Grade

a.

b.

In

Completing the SquareSolving by Completing the Square

section a the student is shown how to complete the square. He mustthen complete four squares himself without HELP to complete the section.He may, however, press HELP to receivewill complete the square in steps.In section b he is shown how to solve

a sequence of questions which

a quadratic equation by complethe square. Again he must solve four problems without HELP, but mayrequest HELP to selve any particular problem.

evel: Interwediate algebra Student Time: 30 minutes

Algeb a

105

ecs: 4668

ng

53

Fil_Name: solguadSolving- Quadratic Equntions by Pac-_:.--ing

Author; Richard Nedpoiitau, Wright College

Objective:To present pra tice excr-ises with help on solving quadratic equationsby factoring.

1. The student is first shown step-by-step, how to solve a quadraticequation by factoring. He must then solve quadratic equations himself.He can press LAB to see the.equation solved in steps, or HELP toreceive a sequence of questions and arrows which lead to the solution.

2. He muSt SOlVe tWo equations without any help to complete the lesson.

Grade Level: Intermediate Algebra Student Time. 30 nutes


l 0 u

ecs: 3080

Pile Name:

Author:

T1

,..scploU

FuncLion Plotter

Keith M ley, -

!-;0et _ur cJü

CERL-T

onuncd by Dan Sleator,

OLy'ective:To provide a function plotter for the -tuden s to use.

DeSc_riptiOn:1. There are four main sections.

a. y = f(x): y a function xb. r = f(t): polar functionsc. x = f(t), y = g(t): parametric equations

d. Implicit functions2. in each section the student can type in any function or equation of

the appropriate type and PLATO will graph it on a rid. The studentcan graph several functions on the same grid for purposes of com-parison, and he can choose the x and y scales.

2. A section containing instructions is available from the index or bypressing the HELP key.

Grade Level= High School and above

flIbigft Area: Function Plotting

Stude t Time: open-ended

COS: 2954

S ecial Notes:Previously entered formulas can be recalled and modified using the

COPY, EDIT, and ERASE keys. Use of this lesson has been Most effec-

tive when students were provided by their instructors with sequences

of equations to be graphed. 107

File Name: plot3Phe-Djrienmi-oni1 Function Plo

Author:

Obje ive:

To provide a threedrnerisionaL surface plotter.

Descriptio,n:

An expression in N and y, coordinates of dhe observation point, andsize can be entered. The corresponding surface is then plotted.

Grade evel: Commu ity College and above Student Time: open

Subject Area: Graphing functions

10

Cos: 951

U1

File Name: liter

Intxuction to the ?1etric System

p,titIner: Ratil Chabay, Department of Chemistry, University of

Illinois at UrbanaChampaign

h4-1,

fee=6-1 le

ide f

I

1,t,r Arn.'>.+1,1,,0F0",r,

Asi

t.t I

TO Present an 31 ntoducLj.on and practice on metric measures and conversions.

1. IristXuCtic)n and p-actice on netric neasures of diStance, weight, volume,

arld teinper'ature.

2. ccwezs corwerskons withi-n the metric system and conversion between

metrAc arid English- mite.

GZadeL6wel: Basic inatJerri&tics Student Tim

thineti c ecs: 5521

EPSJA1!11.1ItPa:CCMtaints em imlex froni wthich each topic can be accessed .

109

-tes

File Nan

vi

Introduction o Trigonometry

uithor Richard Neapolitan, Wright College

Objective:

To provide an introduction to the basic concepts of angles, triangles,and the terminology used in defining sine, cosine, and tangent ofangles in a right triangle.

Descri,ption:

There are four sections, each of which is available from an index.a. Az;le. The neaning of "angle" and measuring angles in degrees,

b.:..L.3d on dividing a circle into 360 equal parts, are presented.h. Triangle. The student is asked to select figures which are

triangles from a display of a variety of plane figures. Exercisesbased an the fact that the sum of the angles in a triangle is180 degrees are given.

c. Right triangles. The definition and examples are given.d. Basic trigonometric concapts. Instruction and exercises on

hypotenuse, side opposite an angle, and side adjacent to aal angleare given. Sine, cosine, and tangent of angles in a right triangleare defined and the student is asked to compute these values fortriangles with given sides and angles.

Grade Level: High School and ab_

Subject Area: Trigonometry

Student Time: 30 minu es

ecs! 4526

11 0

V2

File t1,7 r trigl

Similar Triangles and Pythagorean Theorem

Auth-- Thompson, Parkland College, and Robert Baillle, CERT,programed by Robert Baillie, CERL

X

t

To provide review of geonetric concepts prexequisite to trigonometry.

Description:1. Review of the concepts of acute, obtuse, and right triangles.2. Introduction to similar triangles and corxesponding parts in them.

The --udent Is asked tO rotate one triangle until it is in the saneposit. on as a similar triangle (see picture).

3. The student calculates ratios of sides ar4 finds missing sides bysimilarity.

4. The Pythagorean Theorem is presented -- along with the terminology:hypotenuse, opposite side, adjacent side, opposite angle, adjacentangle.

Grade Level: High School and a ove Stude_ Tine: 40 minutes

,§Aljec_t Area: Trigonometry

Special Notes:The student gets an index and can r_vie the sections in any order.

4024

V3

File Name: trig2

Spcial Right Triangle

Aut__ _7 Paul Thompson, Parkland College, and Robert Bil1ie CEB1programmed by Robert Baillie, CERL

Objective=To familiarize the student with facts about right triangles.

1. Instruction in typin_ the degree symbol (-), and a proof for "The sumof the angles of a triangle equals 180" are provided.

2. Properties of the 90°-45°--45° and 900-600_300 right triangleS aredeveloped. The student uses these and the Pythagorean Theorem tofind the unknown sides.

Grade Level= High School and above Student Ti - 30 minU -eS-Subject Area: Trigon etry ecs: 2110

The student gets an index and he can study the sections in any odx .

V4

FileName: tri

The Sine of an Angle

Authors. Paul Thompson, Parkland College, and Robert Bailiie1 CERLprogrammed by Robert Beillie, CERL

Objective:To provide instr tion in using the sine for finding missing sides Gr

angles of a right triangle.

Description:1. A definition of sinA is provided and used to find sinA when the Sides

are knoWn.2. The student firds missing parts of a right triangle when the sine of

an angle is given. Examples and practice are provided.

3. The student uses tables of sines to find sines or angles when one of

them is given.

Grade Level; High 2choo1 and above Student Time: 30 minu

Subject Trigonometry ecs: 31

V5

F le Name: trig4The Cosine and T-magent of an Angle

Auth s: Paul Thompson, Parkland College, and Robert -Baillie, CERLprogrammed by Robert Baillie, CERL

.5.657

53'53_1'53.3"

F. 011184.9911.553

53.1. 5.10SI_ 4'53.5' I 3949.3_5'

M S92S3.3' g .93653.1' A." 312SA. 5370

11i AMA2.5100,111

51 .br4ArRe ;0--A if rm tI tt,i- I > ,

> 2 21

9.1A=A H A.S. A Is BET F 3.1" 0A15..1 tA 11 ,5Art ,

ThIA --tAl I. IA, I- NOW 51[1E5.. ,

t WE% H I .I.1 'FF.,A1 rAALE151 ts, ;Itcj thA t-991;1_1.$.

AllaVISMIEMPFANIMILIMILWAIMIMMINIMIIMILMEMNIIIMMINAMINIPM

Objee _e:To provide instruction and practice on using the cosine and the tangentto find missing sides or angles of right triangles.

pescriptiorl:1. A definition of cos A is provided and used to find cosA when the sides

are given.2. The student uses tables of cosines to find cosines or angles when one

of them is given.Use of cosine to find missing parts of a right triangle.

4. Finding siaA by using cos(90-A) and vice versa Proof and practiceare provided.

5. Definition of tanA, and finding tanA when the sides are g ven.6. Uf.ing tables of tangents to find tanA or A when one is given.7. Use of tangent to find missing parts of a right triangle.

Grade Level: gigh School and above Student Time: 30 minutes

Subject_Area: T-riijonornetr; ecs:

114

4150

v6

File Name; trig5Solving Right 'riangles

Author: Robert Baillie, CERL

Objgctive:To provide a review for the sine, cosine, and tangent of a: angle and

applications to solving right triangles.

2S2alEt..12a:1. Right triangle probieriis are provided with the following par s given:

a. All three sidesb. Two sidesc. One side and one acute angle

2. The student is given help in finding the mIssing parts by breaking the

procedure into steps.

Grade Ie High School and above Student_Time: 30 minutes

ect_Area: igonometre ecs: 4150

S ecial Notes:An index is provided so that the student can review the sections in

any order.

115

V7

ile Name: trig6

Solving Oblique Trian les

Author: Robert Baillie, CERT..

[47 77. oh A- tat tt` attatt-. Vt a.

Gwt. FiT

ca nit Yr Fl ort the

_ar214Itt atAi.,er of a, b, atatO

t2.6) atk

n.B056 tt. 3i. tk

Ibe I a_-*n ,tt 1 h ts' 117

ta'tta.2a( acat ok

cZ b2),-Ua,).16- a, (2.24) ak

7,--trart ft a. 36. .k

I tatait 1Y: ahEle C-0t. I itftiici,2 6 lilt) pc, C

Ob ectiye:To introduce the laws of sines and cosines and provide examples andpractice in solving oblique triangles.

Description:1. The laws of sines and cosines are p esented without proofs but with

examples.2. Oblique triangle probl_ s are provided with the following parts given:

a. All three sidesb. Two sides and the included anglec. One side and two anglesThe student gets help wlth the algebraic manipulation of the laws asneeded in the problems. Answers are given in some places after severalmistakes are made.

Grade Level: High School and Above Student_Time: 30 minutes

Subjec Area: Trigonometry

116

ecs: 4720

Vs

Pile Name: trig7Sine of Angles _reate- than 90 Degrees

Author. Robert Baillie CERL

Soff15mtrww reel th tdrv4le 70. er0i It M..

Tttra.l.trtttr tir r ,"

the Arlie 0 _atle

Wrt,It tatIp 1,a1

it Ia hich Ia tr&a.ft-J

tate, iS 5 tat.I t or -51,tt-t frCan Or

Ltt 5 aa, fr a ow,e

51- artl ir. 1PP°. I 711. lI 0.1,36:11.. 411 zevlekl,16s. 211'

HIV or140. i

e' .1 le -1 5r P. 71,6dptit.

0,

.hr Can.it

1.0000100 0.0,44

V Mbb0

140'

V000

0.1_14e0

Ob ec-ive:To teach the student how to use tables to find values of the sine forangles greater than 90 degrees.

Description:This is a short lesson with ecerclses which develop the formulasnA sin(180 = A) from the pattern in a table of sine values.

Grade Level: High School and above Student Time: 5 minutes

Subject_Area: Trigonometry eos: 568

Special Notes:This lesson will be expanded to include a similar treatment for cosine.

117

V9

File Name: word2Word Problems with Trigonometry

Author: Gary Peitz, City Colleges of Chicago

Objective:To provide practice in solving word problems.

Description:tiven the angles of elevation from two observation points of a tr

on the opposite side of a river, the student is asked to generate anequation which can be solved for the width of the river. When he

has entered such an equation, he must then find its solution.2. Several types of help are available: see a general explanation of

the procedure to use, have the problem solved, or be stepped throughthe problem. In the step-through help sequence, the answers canalways be obtained by pressing the HELP key.

Grade Level: Kigh School and above Student Ti e: 20 minutes

Subject Area: Trigonometry andElementary Algebra

118

ecs: 4362

W1

File Name: scienotScientific Notation

Author: Barbara Lederman, CERT,programmed by David Lassner, CERL

Pr*ct.iqe

2

AINIMMIMENMENOMMNINERMENEMMEWIA

Objective:

To provide instruc; n and exercises on scientific no ation.

pescription:1. In the instructional section which precedes the practice exercises,

the relationship between the exponent in the power of 10 and movingthe decimal point is taught.

2. There are two types of practice exercises:a. Multiply out a number given in scientific no -_tion.b. Fill in the correct exponent in the power of tem so that the

number will be in scientific notation.

Grade Level: High school and above Student Time: 10 - 15 minutes

pa251 JILs1; Arithmetic

119

ec.S: 1873

X1

File Name: cclog

Introduction to Logarithms

Author: Donald Shirer, Valparaiso University

Objective:_

To provide an introduction to logarithms and loqarthm tables.

1. The lesson includes instruction and exercises on powers of 10 loga-

rithms, log tables, antilogs, use of logs, and a quiz.

2. There are also two optional topics: construction Of log tables,

and logarithmic relations between two quantities.

Grad Jevel: Elementary Algebra

Subject _Area: Algebra

Student T' 45 minutes

eCS: 5679

PPP.e."_17.11pte_S.:1. Use of on-line calculator is explained and made avai. able.

2. Topics are accessed from an index.

120

Y1

File Name: srl (jumpout to sr and scienot)Slide Rule

A -tor: Barbara Lederman, formerly of CERLprogrammed by David Lassner, CERL

Ohjec ive:

To provide instruction and practice J.multiplication and division problems.

the use of a slide rule for

Descri tion:1. There are five sections:

a. Review of scientific notationb. Reading a slide ruleC. Estimating answersd. Multiplicatione. Division

2. Each section has instruction and practice drills.3. A simulated slide rule is used for the instruction. The student

uses his own slide rule to work the exercises, with remediation pro-vided by the simulated slide rule.

Grade Level: Technical math or Student Time: 3.5 hoursphysical science courses

1.112.1ect Area: Slide Rule ecs sr: 3351

sr1; 5994scienot: 1873

S ecial Notes:The student needs his o- slide rule to work the exercises in sectionsfour and five.

121

File Name: crpro

Author:

271

tiom to Probability

Robert Baillie, CERL

A4T4 A LS

tAtI,Af.IAJOAOMN

41.97@ONO0

L th

TV-r, rt

417

Ct

I AI -Arrati t,rAt

t=tr't 1!1, ttt

LIMILUILMUM1111Wr

Wective:To acquaint the student with the meaning of randomness and probability.

Descrintion:1. Randomness experiment shows that

(the outcome of a coin tOse can not2. Formal definition of probability is

use the definition to calculate the

randonness involves unpredictabilityalways be predicted in advance).given, followed by examples whichvalues of various probabilities.

3. Example to show that impossible events have probabilities of 0, eventsthat are certainties have probabilities of 1, and all other eventshave probabilities between 0 and 1.

4. Coin and dice throwing ekperiments (see Special Notes).5. Explanation of the fact that, if 100 consecutive tosses of a balanced

coin come up "heads," the probability that the 101st toss will also be"heads" is still 1/2.

6. Examples show the difference between independent and dependent events,and the product law for independent events is obtained from examples.

Grade Level: Community College Studeiit Tim 60 ninutas

Sub'ect Area: Elementary probability eos::

Spe 'al Notes:Two sections simulate coin and dice throwing experiments. The studentcan see what is likely to happen when a large number (up to a billion)of coins or dice are tossed.

6200

122

AA1

File Name: mathccCommunity College Math Index

Contact: Louis V. DiBello CERL

Objective:To provide an on-line index of all community college math materialswhich are currently available for use, inspection, or criticism.

Desc.LLaan:This is an index allowing easy access to basic mathematics materials.It is periodically updated, and it contains the current status oflessons as "prellminary version," "under review, or "classroom tested."

Grade Level: Adult Education andCommunity College

Subject Are-. Mathematics

Student Time: not applicable

oCs: 2349

PR1

File Na_ studnotes

Author Tamar Abeliovich Weaver, CERLadapted from the Elementary M,th Group less 'kidnotes"

Objective:To let the student ite notes or comments on the lessons he hascompleted.

Description:1. The student is given a blank note space and a simple editor to write

notes or comments. His name, course, date and time are automaticallysaved along with the lesson the student has come from.

2 The note is stored in a dataset and these are readable by inst uctorsand authors through lesson "studnotesr".

Grade Level: not applicable Student Time: not applicable

Subject no__Area: pplicable ecs: 797

Special Notes:In order to make comments lesson available at the end of a lesson, theauthor must insert a short unit of code in the lesson. For moreinformation, contact Tamar Abeliovich Weaver.

124

Pile Name:

BB2

SLUdn0Le

TamAr Ahu tiovich Weave- , CENT,

adapted fram the Elementary rirth Group lesson "kidnc

Objective:To allow reading of student's comments about lessons that have beencollected via lesson "studnotes".

Description:Instructors and authors are able to read notes including the in or-mation about the student and which lesson he came from.

Grade Level: not applicable Student Time: not applicable

Subject Area: not applicable ecs: 1568

fpecial Notes:This file must be periodically emptied to allow for more notes. A fileof copies of student notes is kept for notes that have been deleted.For information, contact Tamar Abeliovich Weaver.

12

mH

1.jle Name: mathnoLe::

Note:;

ConLacL: Louis V. DiHelLo,

Objective:

To provide a communication file for authors, users, in5tructors, andother personnel intoze.lted in the commliniLy college math group.

Deseri-)tiop_:

Space is available for messages to be written to individuals orgroup:A. Messages will be maintained until they are no longer neededand then deleted.

Grade .Level: not applicable Student Time: not applicable

Subject Ar not applicable ecs: _.)830

126

Ermarmps - ERIC · · 2014-01-27Ermarmps. DOCUMENT RESUME. SE 020 947. DiBello, Louis V.; ......

Documents

Transcript of Ermarmps - ERIC · · 2014-01-27Ermarmps. DOCUMENT RESUME. SE 020 947. DiBello, Louis V.; ......