Ermarmps - ERIC · · 2014-01-27Ermarmps. DOCUMENT RESUME. SE 020 947. DiBello, Louis V.; ......
Transcript of Ermarmps - ERIC · · 2014-01-27Ermarmps. DOCUMENT RESUME. SE 020 947. DiBello, Louis V.; ......
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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Documents acquired by ERIC include many informal unpublished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
Subject Area: Arithmetic
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
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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
Author: Tamar Abeliovich Weaver, CERL
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.
Grade Level: Basic mathematics
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
Subject Area: Arithmetic
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
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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
Author: Tamar Abeliovich Weaver, CERL
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.
Grade Level: Basic mathematics Student Time: 10 minutes
Subject Area: Arithmetic
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.
Grade Level: Basic mathematics Student Time: 60 minutes
Sub'ect Area: Arithmetic
2 8
ecs: bank 3481
bank2 1990
B13
File Name: werdpSigned Number Word Problems on Tempe ature andSea Level
Author: Tamar Abeliovich Weaver, CERL
-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.
Grade Level: Basic mathematics
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.
Grade Level: Basic mathematics Student Time: 60 minutes
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
Grade Level: Basic mathematics
Subject Area: Arithmetic 37
Student Time: 40 minutes
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.
Grade Level: Basic mathematics
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
Grade Level: Basic mathematics Student Time: 15 minutes
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.
Grade Level: Basic mathematics Student Time: 30 minutes
Subject Area: Arithmetic
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.
Grade Level: Basic mathematics Student Time: 40 minutes
$ 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
Subject Area: Arithmetic
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.
Grade Level: Basic mathematics Student Time: 10 minutes
Subject Area: Arithmetic ecs- 2800
4 4
El
File Name: decDecimal Skills: Introduction
Author: Errol Magidson, Kennedy-King College
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
Grade Level: Basic mathematics Student Time: 10 minutes
Subject Area: Arithmetic eos: 1500
4 5
E2
File Name: dealReading and Writing Decimals
Author: Errol Magidson, Kennedy-King College
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.
Grade Level: Basic mathematics Student Time: 60 minutes
Subject Area- Arithmetic
4 6
ecs: 5712
E3
File Name: dec2Adding and Subtracting Decimals
Author: Errol Magidson, Kennedy-King College
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.
Grade Level: Basic mathematics Student Time: 60 minutes
Subject Area: Arithmetic ecs: 5278
4 7
E4
File Name: dec3Multiplying and Dividing Decimals
Author: Errol Magidson, Kennedy-King College
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.
Grade Level: Basic mathematics Student Time: 60 minutes
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.
Grade Level: Basic mathematics Student Time: 60 minutes
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.
Grade Level: Basic mathematics Student Time: 60 minutes
Subject Area: Arithmetic ecs: 3567
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
Grade Level: Basic mathematics
Sub'ect Area: Arithmetic
S uden Time: 10 mintes
ecs 1500
F2
Ft
File Name: perlPercent-Decimal-Frac on Conversions
Author: Errol Magidson, Kennedy-King College
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
Subject Area: Arithmetic ecs: 4146
F 3
File Name: per2 (jumps out to per3 and per4)Word Problems with Percent
Author: Errol Magidson, Kennedy-King College
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.
Grade Level: Basic mathematics Student Time: 90 minutes
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
Subject Area: Arithmetic
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.
Grade Level: Basic mathematics Student Time: 35 minutes
Subject Area: Arithmetic ecs: 2451
Hi
File_Meme: sqrtFindina the Square Root
Author: Tamar Abeli v.ich Weaver, CERL
,
I
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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
Subject Area: Arithmetic
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
Description:1. There are five sections:
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
Subject Area: Arithmetic
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
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1010
141g
19
10
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iff
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11.14.1,1 4.4.11114
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, 4 313r. 14
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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
Student Time: 40 minutes
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
Subject Area: Algebra
6 9
Student Time: 40 minutes
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
Subject Area: Algebra
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
Subject Area: Algebra
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.
Description:1. There are three sections:
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.
Grade Level: Intermediate algebra Student Time: 25 minutes
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.
Grade Level: Intermediate algebra Student Time: 20 minutes
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.
Description:1. There are five sections:
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.
Grade Level: Intermediate algebra Student Time: 40 minutes
Subject Area: Algebra
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.
Grade Level: Intermediate algebra Student Time: 60 minutes
.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
Author: Richard Neapolitan, Wright College
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
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Ob'ective:To present practice with help on multiplica ion of algebraic fractions1
Description:1. There are three sections:
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
Author: Richard Neapolitan, Wright College
Find te !deist ccom
Ftictr tHh @Eq.,
Fat !r-f tthErt.tnHtrtE
Ft,f5. ft,: rtt
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Z. Ttot L.C.U. it tht tht,4t=ft ftftgrttErtt. .th eel H the HthItt ,ttntott.
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ind the Ist molt tF .L.C.11..I !.1
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th,rd tint.' E H I inee,Ti-,..,-rtfrg, it pr ,f, h.! it tItt-th itft.fEtfti,
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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
Author: Richard Neapolitan, Wright College
CMI f ,thit
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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
Author: Richard Neapolitan, Wright College
t r0. I tl-0 e
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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.
Grade Level: Intermediate algebra Student Time: 30 minutes
Subject Area: Algebra
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
Subject Area: Algebra
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
Student Time: 30 minutes
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
Subject Area: Algebra
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
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thjo .!1,
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th,toth wth fla,c
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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
Subject Area: Algebra
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.
Student Time: 60 minutes
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.
Grade Level: Intermediate algebra Student Time: 15 minutes
§-_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.
Grade Level: Intermediate algebra Student Time: 30 minutes
Sub'ect Area: Algebra
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
Subject Area: 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
Sub'ect Area: Algebra
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
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File Name: liter
Intxuction to the ?1etric System
p,titIner: Ratil Chabay, Department of Chemistry, University of
Illinois at UrbanaChampaign
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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 .
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File Nan
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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
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File t1,7 r trigl
Similar Triangles and Pythagorean Theorem
Auth-- Thompson, Parkland College, and Robert Baillle, CERT,programed by Robert Baillie, CERL
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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
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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..
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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
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Pile Name: trig7Sine of Angles _reate- than 90 Degrees
Author. Robert Baillie CERL
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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
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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
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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:
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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
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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