,,APH^R ,NUMB] ,L9E ,DEVICE ,GUIDEBOOK ,COPY"R ^C #BJAA ,AM]ICAN ,PR9T+ ,H\SE =! ,BL1 ,9C4 ,L\ISVILLE1 ,,KY #DJBJF-JJHE ,9 #A ,VOLUME ,BRL PAGES P#A-P#E & #A-BH ,PR9T PAGES #A-A#BJ ,"P ,NUMB] #FA-BFG-JCD = USE 9 ,CATALOG ,NUMB] #A-JCDHJ-JA P#A ,A REVI.N ( ..,GUIDE 6! ,,APH ,NUMB] ,L9E .,DEVICE 0,EL1NOR ,PE/] PRODUC$ 0,,APH4 ,ALL "RS RES]V$4 ,PR9T$ 9 ! ,UNIT$ ,/ATES ( ,AM]ICA4 ,? PUBLIC,N IS PROTECT$ 0,COPY"R & P]MIS.N M/ 2 OBTA9$ F ! PUBLI%] PRIOR 6ANY REPRODUC;N1 /ORAGE 9 A RETRIEVAL SY/EM1 OR TRANSMIS.N 9 ANY =M OR 0ANY M1NS1 ELECTRONIC1 ME*ANICAL1 PHOTOCOPY+1 RECORD+ OR O!RWISE4 ,= 9=M,N REG>D+ P]MIS.N1 WRITE TO3 ,AM]ICAN ,PR9T+ ,H\SE =! ,BL1 ,9C4 ,RES\RCE ,S]VICES #1839 ,FRANK=T ,AV5UE ,L\ISVILLE1 ,,KY #40206-0085 ,"P ,NUMB] #61-267-034 ,= USE 9 ,CATALOG ,NUMB] #1-03480-01 ,PROJECT ,L1D]3 ,J1NETTE ,WICK] ,3SULTANT3 ,SUSAN ,O/]HAUS ,3TRIBUTORS3 ,D>L5E ,DONH(F ,FRANK ,HAYD5 ,TOM ,POPPE ,EL1NOR ,PE/] ,]ICA ,RUCK] P#C ,,SPECIAL ,,SYMBOLS ,,US$ ,,9 ,,? ,,VOLUME ,-PUT] ,BRL ,CODE _+ 2G9 ,-PUT] ,BRL ,CODE _: 5D ,-PUT] ,BRL ,CODE / SLA% . (46) P]IOD : COLON - (36) HYPH5 @ (4) AT SIGN _& 3T9U,N 9DICATOR ,O!R ,SYMBOLS ^R REGI/]$ TRADEM>K SYMBOL ^C COPY"R SYMBOL _/ SLA% 2T ^WS ,,TRANSCRIB]'S ,,NOTES ,? GUIDEBOOK HAS BE5 TRANSCRIB$ AC 6..,THE ,NEME? ,BRL ,CODE = ,MA!MATICS & ,SCI;E .,NOT,N #1972 ,REVI.N1 #2007-2011 ,UPDATES4 P#E ,,NUMB] ,,L9E #A ,,DEVICE ,! NUMB] L9E IS A BASIC TOOL = T1*+ NUMB] 3CEPTS1 NUMB] SEQU;E1 C.T+1 A4I;N1 SUBTRAC;N1 MULTIPLIC,N1 DIVI.N1 R.D+1 E/IMAT+ :OLE NUMB]S1 -MON FRAC;NS1 & DECIMALS4 ..,! ,PR9CIPLES & ,/&>DS = ,S*OOL .,MA!MATICS /ATES T /UD5TS ;,K-#12 %D 8,"U/& NUMB]S1 WAYS ( REPRES5T+ NUMB]S1 REL,N%IPS AM;G NUMB]S1 & NUMB] SY/EMS0 (,N,NAL ,C\NCIL ( ,T1*]S ( ,MA!MATICS1 #2000, P4 #32)_4 ,NUMB] ,L9ES C 2 A USE;L TOOL 9 MEET+ ! /&>DS Z /UD5TS DET]M9E ! RELATIVE MAGNITUDE ( :OLE NUMB]S1 ! E6ECTS ( A4I;N & SUBTRAC;N ( :OLE NUMB]S1 -P>E & ORD] FRAC;NS1 EXPLORE NUMB]S LESS ?AN Z]O1 & GRAPH ALGEBRAIC EQU,NS4 ..,! ,-MON ,CORE ,/ATE ,/&>D = .,MA!MATICS (2010) DIRECTLY REF];ES ! USE ( NUMB] L9ES 6T1* MA!MATICAL 3CEPTS4 ,! /&>DS RANGE F REPRES5T+ :OLE NUMB] SUMS ON A NUMB] L9E AT #A ! ELE;T>Y LEVEL1 6REPRES5T+ A#A FRAC;NS ON A NUMB] L9E AT ! 9T]M$IATE LEVEL1 & LOCAT+ IRR,NAL NUMB]S ON A NUMB] L9E AT ! MI4LE S*OOL LEVEL4 ------------------------------------#B ,NUMB] L9ES >E A VALUA# TOOL = /UD5TS ) VISUAL IMPAIR;TS4 ,KAPP]MAN (1997) NOTES3 ,! ,NUMB] ,L9E C 2 US$ = "W+ ON OP],NS1 REL,N%IPS1 FRAC;NS1 & DECIMALS4 ,NUMB] L9ES >E ESPECI,Y USE;L :5 !Y >E /RET*$ ACR ! TOP (! /UD5T'S DESK4 ,/UD5TS C F9D ! L>G] NUMB]1 C.T =W>D = A4I;N & C.T BACKW>D = SUBTRAC;N4 ,/UD5TS C USE NUMB] L9ES = "W+ ON POSITIVE & NEGATIVE NUMB]S Z WELL4 (P4 #23) ,! ,NUMB] ,L9E ,DEVICE IS DESIGN$ = USE 0/UD5TS :O USE L>GE PR9T & BRL4 ,! DEVICE C 2 US$ 6SUPPLE;T ANY MA? PROGRAM & 6SUPPORT MA? 3CEPTS TAUS 6HELP ! /UD5T A#B DEVELOP ! FOLL[+ 3CEPTS AB NUMB] L9ES 9TUITIVELY3 #1_4 ,NUMB] L9ES USU,Y H EQU,Y SPAC$ M>KS ) NUM]ALS "U EA* M>K (BESIDE EA* M>K IF ! NUMB] L9E IS PRES5T$ V]TIC,Y)_4 #2_4 ,! Z]O M>K IS USU,Y ! 2G9N+ M>K B MAY 2 POSI;N$ AT ANY 3V5I5T PLACE ON ! L9E4 #3_4 ,! NUM]AL "U EA* M>K TELLS H[ F> X IS F ! 2G9N+ M>K (BESIDE EA* M>K IF ! NUMB] L9E IS PRES5T$ V]TIC,Y)_4 ------------------------------------#C #4_4 ,! NUMB]S "ND AL;G A NUMB] L9E 2COME GRT] F LEFT 6"R & BOTTOM 6TOP4 #5_4 ,! NUMB] L9E GOES ON & ON (INFINITELY) AT BO? 5DS & IS REPRES5T$ 0ONLY A SMALL SEG;T4 #6_4 ,! NUMB] L9E IS USU,Y HORIZONTAL1 B C AL 2 V]TICAL OR EV5 R.D4 #7_4 ,"S -MONLY US$ NUMB] L9E SEG;TS >E RUL]S1 Y>D/ICKS1 !RMOMET]S1 & CLOCKS4 #C ,,DESCRIP;N ,,( A#C ,,! ,,DEVICE ,! NUMB] L9E DEVICE 3SI/S ( ?REE "PS3 A BLUE PLA/IC BASE1 FIFTE5 9T]*ANGEA# V9YL L9E SEG;TS1 & =TY PLA/IC CYL9D]S1 : S]VE Z PEGS AND_/OR 9T]LOCK+ B>S4 ,"! >E T5 A4I;NAL PLA/IC CYLINDERS_/PEGS ) AN >R[ =M,N ON "O 5D T MAY 2 US$ 0OLD] MA? /UD5TS Z !Y GRAPH L9ES & RAYS4 ,! PLA/IC BASE H\SES "O OR TWO (! V9YL L9E SEG;TS AT A "T4 ,! SEG;TS >E FA/5$ SECURELY 6! BASE OV] A PEG LOCAT$ AT EA* 5D (! BASE4 ,ON ! BASE 2H EA* L9E SEG;T IS A HORIZONTAL GROOVE ) HOLES AT 9T]VALS4 ,? HORIZONTAL GROOVE CORRESPONDS 6! L9E ON ! SEG;T :ILE ! HOLES REPRES5T ! COORD9ATE SCALE M>KS4 ------------------------------------#D ,! PLA/IC BASE AL 3TA9S TWO WORK_/STORAGE >1S4 ,! L>GE WORK_/STORAGE >EA AT ! BOTTOM (! BASE C 2 US$ 6/ORE ! NUMB] /RIPS OR Z A "W SPACE DUR+ 9/RUC;N4 ,! SMALL] A#D WORK_/STORAGE >EA ON ! "R (! BASE C S]VE Z A /ORAGE >EA =! PEGS OR Z A "W SPACE DUR+ 9/RUC;N4 ,EA* V9YL L9E SEG;T IS :ITE )A BLACK RAIS$ L9E RUNN+ ! L5G? (! /RIP4 ,L>GE RAIS$ BLACK DOTS >E LOCAT$ AT 9T]VALS ON ! RAIS$ L9E & 9DICATE ! POSI;N (! BRL & PR9T NUM]ALS ON ! SEG;T4 (,BRL NUM]IC 9DICATORS H BE5 ELIM9AT$ ON ALL SEG;TS 6FACILITATE R1D+ & PLACE;T (! NUMB]S ON ! /RIP)_4 ,! FOLL[+ L9E SEG;TS M>K$ HORIZONT,Y >E 9CLUD$3 #1_4 #0--#20 0"OS #2_4 #0--#200 0T5S #3_4 #0--#100 0FIVES #4_4 -#10--+10 0"OS #5_4 ,HALVES #6_4 ,?IRDS #7_4 ,F\R?S #8_4 ,FIF?S #9_4 ,SIX?S #10_4 ,EIKS #14_4 ,UNNUMB]$ ) #20 COORD9ATE SCALE M>KS #15_4 ,UNNUMB]$ ) NO COORD9ATE SCALE M>KS ------------------------------------#E ,! UNNUMB]$ L9E SEG;TS H BE5 9CLUD$ 9 ! KIT 6PROVIDE ! T1*] FLEXIBIL;Y 9 DESIGN+ PRO#MS4 ,:5 US+ ! UNNUMB]$ L9E SEG;TS USE ,,APH ,FEEL 'N ,PEEL ,NEME? ,BRAILLE_/,PRINT ,NUMB] ,/ICK]S 6M>K ! NUMB] L9E )! APPROPRIATE NUMB]S4 ,Y MAY USE GRAPHIC >T TAPE 6MAKE ! COORD9ATE SCALE M>KS ON ! 8BLANK0 NUMB] L9ES4 ,"S SU7ES;NS = US+ ! UNNUMB]$ L9ES >E Z FOLL[S3 #1_4 #0--#1000 0HUNDR$S #2_4 ,SKIP C.T+ 0TWO1 ?REE1 F\R1 OR ANY NUMB] #3_4 #20--#40 0"OS HORIZONT,Y 6EXT5D ! 2G9N+ NUMB] L9E SEG;T 3CEPTS Z NE$$ #4_4 -#60--+130^.* 0T5S V]TIC,Y A#E 6SIMULATE ! M>K+S ON A -MON M]CURY !RMOMET] #5_4 ,GRAPH+ SIMPLE ALGEBRAIC EXPRES.NS ,! =TY :ITE PLA/IC CYL9D]S >E US$ 6%[ NUM]ICAL REL,N%IPS ON ! NUMB] L9E SEG;TS4 ,!Y >E HOLL[ ON "O 5D )A CORRESPOND+ PROJECT$ TIP ON ! O!R 5D4 ,! TIP & OP5+ 5A# ! CYL9D]S 6BE 9T]LOCK$4 ,:5 !Y >E 9T]LOCK$ & PLAC$ HORIZONT,Y 9 ! BASE GROOVE1 ! CYL9D]S >E CALL$ B>S4 ,B>S REPRES5T ! SEG;TS ON ! NUMB] L9ES4 ,:5 ! CYL9D]S >E PLAC$ 9DIVIDU,Y & V]TIC,Y 9 ! BASE HOLES1 !Y ------------------------------------#F >E CALL$ PEGS4 ,! PEGS REPRES5T ! COORD9ATE SCALE M>KS ON ! NUMB] L9ES4 ,T5 PEGS H BE5 9CLUD$ T H 8>R[S0 AT ! TIP 6REPRES5T RAYS OR L9ES4 ,OLD] /UD5TS MAY F9D ^! USE;L :5 GRAPH+ 9EQUALITIES4 #G ,,"W+ ,,) A#F ,,! ,,NUMB] ,,L9E #1_4 ,PLACE ! BASE ON A TA# OR DESK DIRECTLY 9 FRONT (! /UD5T4 ,:5 US+ HORIZONT,Y M>K$ L9E SEG;TS1 ! L>GE WORK_/STORAGE >EA =! L9E SEG;TS ON ! BASE %D 2 NE>E/ 6& P>ALLEL 6! /UD5T'S BODY4 ,:5 US+ V]TIC,Y M>K$ L9E SEG;TS1 ! BASE %D 2 P]P5DICUL> 6! /UD5T'S BODY )! L>GE WORK_/STORAGE >EA 6! "R IF ! /UD5T IS "R-H&$ OR 6! LEFT IF ! /UD5T IS LEFT-H&$4 #2_4 ,PLACE ! DESIR$ L9E SEG;T(S) OV] ! 5D PEGS PROTRUD+ F ! PLA/IC BASE4 ,A HOLE AT EA* 5D ( EA* SEG;T ALIGNS )! PEGS 9 ! BASE 6HOLD ! SEG;T SECURELY4 ,:5 US+ ONLY "O SEG;T ON ! DEVICE1 PLACE X ON ! L[] LEVEL NE>E/ ! L>GE WORK_/STORAGE >EA = 3V5I;E4 #3_4 ,PUT A SUITA# NUMB] ( PEGS_/BARS (A FEW M ?AN W 2 REQUIR$ =! PRO#MS 2+ D"O) 9 ! SMALL] WORK_/STORAGE >EA4 #4_4 ,US+ A PRO#M GIV5 0! T1*] OR #G "O TAK5 F ! MA!MATICS TEXTBOOK1 C.T ! DESIGNAT$ NUMB] ( PEGS_/BARS =! F/ "P (! PRO#M 96! WORK_/STORAGE >EA4 #5_4 ,DECIDE :E!R 6USE PEGS OR B>S 6"W ! PRO#M4 ,PEGS EMPHASIZE PO9TS & C.T+1 B 2W>E ( 8SKIPP+ ]RORS0--]RORS CAUS$ 0SKIPP+ HOLES 9 ! BASE4 ,B>S EMPHASIZE L9E SEG;TS & L5G?S4 ,:5 "W+ ) FRAC;NS1 USE B>S 6%[ "PS ( "O :OLE4 ,USE PEGS 6%[ "PS (A SET4 ,IF DESIR$1 USE BO? PEGS & B>S 6%[ 3TRA/4 ,= EXAMPLE1 USE PEGS 6ILLU/RATE "OS & B>S 6ILLU/RATE T5S4 #6_4 ,AF C.T+ ! PEGS_/BARS 96! "W >EA1 NEXT PLACE !M 9 ! GROOVE OR HOLES ON ! BASE CORRESPOND+ 6! L9E SEG;T OR PO9T DESIR$4 ,! NUMB] 6! "R OR ABV Z]O IS USU,Y US$ Z ! />T+ PO9T4 ,:5 US+ PEGS1 PLACE ! TIP (! PEG 9 ! GROOVE & SLIDE X 6! "R =A HORIZONT,Y M>K$ SEG;T1 OR PLACE ! PEG ABV ! LA/ PEG 9S]T$ =A V]TIC,Y M>K$ SEG;T4 ,SLIDE ! PEG AL;G UNTIL ! NEXT HOLE IS LOCAT$ 0BO? S.D #I & FEEL4 ,!N 9S]T ! PEG V]TIC,Y A#G 96! HOLE4 ,3T9UE 9 A SIMIL> MANN]1 TAK+ ! PEGS F ! "W >EA & PLAC+ !M 9 ! DESIR$ HOLES ON ! BASE4 ------------------------------------#H ,:5 US+ B>S1 ! B>S MAY 2 JO9$ TGR 9 ! "W >EA OR ! /UD5T'S DESKTOP OR :]"E X SEEMS 6BE 3V5I5T =! /UD5T4 ,!N PLACE ! 9T]LOCK$ B>S 9 ! GROOVE HORIZONT,Y1 )! TIP 6! LEFT1 =A HORIZONT,Y M>K$ SEG;T OR )! TIP D[N =A V]TIC,Y M>K$ SEG;T4 ,!N SLIDE ! 9T]LOCK$ B> 9 ! DIREC;N ! TIP IS PO9T+ UNTIL X GOES 96A SMALL HOLE 9 ! 5D (! BASE4 #7_4 ,R1D ! NUM]AL ON ! L9E SEG;T CORRESPOND+ 6! LA/ PEG OR B> ON ! "R OR TOP 5D (! BASE4 (,BRL R1D]S %D TAKE C>E 6MOVE _! F+]S P]P5DICUL>LY 9 A /RAI 6! CORRESPOND+ NUM]AL ON ! L9E SEG;T4) #8_4 ,6C.T ! PEGS ALR PLAC$ 9 ! BASE1 />T AT EI 5D & SAY ! CORRESPOND+ NUM]AL = EA* "O Z X IS T\*$ :ILE MOV+ AL;G ! GROOVE T[>D ! OPPOSITE 5D (! R[ ( PEGS4 ,6C.T ! B>S A#H ALR PLAC$ 9 ! BASE1 />T AT EI 5D & SAY ! CORRESPOND+ NUM]AL = EA* "O UNTIL ! OPPOSITE 5D IS R1*$4 (,IF DI6ICULTY IS EXP]I;ED 9 P]CVG ! JO9+ (! B>S1 !Y MAY 2 PULL$ A"P SLI+ 6ANO!R NUMB]1 ETC4)_4 ------------------------------------#I #10_4 ,US+ ! SAME SCALE OR ANO!R "O1 P]=M ! NEC OP],NS AND_/OR PROC$URES Z \TL9$ ABV 9 /EPS "O "? SEV5 OR 9 ! FOLL[+ SU7ES;NS = -PLET+ ! PRO#M4 ,,SU7ES;NS ,,= ,,US+ ,,! ,,DEVICE ,,= ,,T1*+ ,,MA!MATICS ,? DEVICE HAS BE5 DESIGN$ S T X C 2 US$ 6AUG;T ANY MA!MATICS TEXTBOOK S]IES4 ,USE YR [N ID1S &! FOLL[+ SU7ES;NS 6GET />T$ US+ ! DEVICE4 #AA ,,! ,,NUMB] ,,SY/EM A#I ,,& ,,PLACE ,,VALUE ,USE SEG;T .##1 (0--#20 0"OS) OR AN UNNUMB]$ SEG;T SUITABLY M>K$ & EI PEGS OR B>S 69TRODUCE C>D9AL NUMB]S1 C.T+1 & R1D+ NUM]ALS4 ,USE SEG;T .##1 (0--#20 0"OS) ) PEGS OR B>S 6T1* ! M1N+ ( Z]O4 ,"! IS NO HOLE =A PEG CORRESPOND+ 6Z]O %[+ T Z]O HAS NO VALUE4 ,IF A B> IS PLAC$ 9 ! GROOVE ) Z]O ON ! LEFT1 ! NUM]AL ON ! "R IS CORRECTLY R1D Z 8"O04 ,USE SEG;TS .##1 (0--#20 0"OS) & .##2 (0--#200 0T5S) ) PEGS OR B>S 6T1* ! M1N+ ( T54 ,PLACE SEG;T .##1 ON ! BOTTOM (! BASE & .##2 ON -----------------------------------#AJ ! TOP4 ,H ! /UD5T PLACE T5 PEGS OR B>S ON SEG;T .##1, NOT+ T ! LA/ CORRESPOND+ NUM]AL IS T5 & HAS TWO DIGITS4 ,H ! /UD5T %[ ! SAME NUMB] T5 ON SEG;T .##2 US+ ONLY "O PEG OR B>4 ,NOTICE H[ ? CORRESPONDS 6! DIGIT 8#1_0 9 ! T5S PLACE3 #10_4 ,USE SEG;TS .##1 (0--#20 A#AJ 0"OS) & .##2 (0--#200 0T5S) ) PEGS OR B>S 6ILLU/RATE EXP&$ NOT,N = TWO DIGIT NUMB]S &! IDEA ( REGR\P+4 ,PLACE SEG;T .##1 ON ! BOTTOM (! BASE & .##2 ON ! TOP4 ,%[ T5S ON TOP & "OS ON ! BOTTOM4 ,EXAMPLE3 #27 .K #20 ON ! TOP +7 ON ! BOTTOM4 ,USE SEG;T .##1 (0--#20 0"OS) ) PEGS 6%[ ! REL,N%IP 2T ODD & EV5 NUMB]S4 ,PLACE A PEG 9 EA* HOLE 9 ! BASE CORRESPOND+ 6AN EV5 NUMB] #2, #4, #6, ETC4 ,NOTICE ! NUMB] ( HOLES SKIPP$ (1) 2T ! EV5 NUMB]S AND_/OR ! NUMB] A4$ (2) 6R1* ! NEXT PEG4 ,FOLL[ ! SAME PATT]N = PLAC+ ! PEGS />T+ ) 8#1_04 ,NOTE ! REL,N%IP 2T ! ODD & EV5 NUMB]S--ODD NUMB]S >E ^? SKIPP$ 2T ! EV5 NUMB]S & !Y FOLL[ ! SAME PATT]N Z SE5 9 ! F/ EXAMPLE4 ,! NUMB] ( HOLES SKIPP$ 2T ! ODD NUMB]S IS "O &! NUMB] A4$ 6R1* ! NEXT PEG IS TWO4 ,PRACTICE C.T+ BY #2_'S_4 ,USE SEG;T .##2 (0--#200 0T5S) ) PEGS OR B>S 62COME FAMILI> )! #AC REL,N%IP AM;G ! DECADES4 ,SEG;T B#AJ .##1 (0--#20 0"OS) MAY AL 2 US$ 6HELP 4COV] ! NUMB] : HAS BE5 A4$ (10) -----------------------------------#AA 6GET 6! NEXT DECADE ON ! NUMB] L9E4 ,PRACTICE C.T+ BY #10_'S_4 ,USE SEG;T .##3 (0--#100 0FIVES) ) PEGS OR B>S 62COME FAMILI> )! REL,N%IP AM;G ! FIVES4 ,SEG;T .##1 (0--#20 0"OS) MAY AL 2 US$ 6HELP 4COV] ! NUMB] : HAS BE5 A4$ (5) 6GET 6! NEXT 9T]VAL ON ! NUMB] L9E4 ,PRACTICE C.T+ BY #5_'S_4 ,USE SEG;T .##4 (-#10--+10 0"OS) ) PEGS OR B>S 69TRODUCE ! IDEA ( POSITIVE & NEGATIVE 9TEG]S4 ,EXP& ! ID1S ( 8GRT] ?AN0 MOV+ 6! "R & A4+ OR 8LESS ?AN0 MOV+ 6! LEFT & SUBTRACT+4 ,= EXAMPLE1 9 ! PRO#M #2-5 .K -#3_2 />T ON #2, MOVE LEFT #5, & 5D ON -#3, %[+ ? 6BE J AN EXT5.N (! FAMILI> SEG;TS : H Z]O ON ! LEFT 5D4 ,9 A4I;N1 Y MAY USE AN UNNUMB]$ SEG;T M>K$ L A !RMOMET] & TEMP]ATURES ABV & 2L Z]O 6%[ ! USE ( POSITIVE & NEGATIVE 9TEG]S4 A#AA ,,SET ,,!ORY ,USE SEG;T .##1 (0--#20 0"OS) ) EI PEGS OR B>S 6T1* T A SET IS A COLLEC;N ( OBJECTS2 6-P>E SETS 0"O-TO-"O CORRESPOND;E ( SET MEMB]S EMPHASIZ+ ! CORRESPOND+ NUM]ALS ON ! SEG;T2 & 64COV] EQUIVAL5T SETS (2+3 IS ANO!R "N = #5), EMPTY SETS (SETS ) NO MEMB]S), OR SUBSETS ("PS (A GIV5 SET--#2 IS "P OR SUBSET ( #5)_4 -----------------------------------#AB ,USE SEG;T .##1 (0--#20 0"OS) OR A SEG;T V]TIC,Y M>K$ ) EI PEGS OR B>S 69TRODUCE ! 3CEPTS ( 8GRT] ?AN0 (MOV+ 6! "R OR UP) & 8LESS ?AN0 (MOV+ 6! LEFT OR D[N) ON ! NUMB] L9E4 ,,A4I;N ,,& ,,SUBTRAC;N ,USE SEG;T .##1 (0--#20 0"OS) ) PEGS OR B>S 6ILLU/RATE & %[ ! REL,N%IP ( A4I;N & SUBTRAC;N FACTS ) SUMS #AE UP TO #20_4 ,A SUBSET ( #2 PLUS A#AB A SUBSET ( #3 EQUALS A SET ( #5 OR 2G9N+ )A SET ( #5 REMOVE (SUBTRACT) A SUBSET ( #3 L1V+ A SUBSET ( #2_4 ,USE SEG;T .##1 (0--#20 0"OS) ) PEGS OR B>S 6DEMON/RATE ! -MUTATIVE (ORD]) PR9CIPLE &! ASSOCIATIVE (GR\P+) PR9CIPLE = A4I;N4 ,= EXAMPLE1 9 ! PRO#M #2+3+1, ADD A SUBSET ( #2 &A SUBSET ( #3 ON ! NUMB] L9E 6MAKE A SUBSET ( #5 & !N ADD ANO!R SUBSET ( #1 6MAKE A SET ( #6 ON ! NUMB] L9E4 ,US+ ! SAME NUMB]S1 ADD A SUBSET ( #1 &A SUBSET ( #3 ON ! NUMB] L9E 6MAKE A SUBSET ( #4 & !N ADD ANO!R SUBSET ( #2 6MAKE A SIMIL> SET ( #6 ON ! NUMB] L9E4 ,USE SEG;TS .##1 (0--#20 0"OS) & .##2 (0--#200 0T5S) ) PEGS OR B>S 6ILLU/RATE A4I;N & SUBTRAC;N ( TWO DIGIT NUMB]S )\T REGR\P+ &) REGR\P+4 ,PLACE SEG;T .##1 ON ! BOTTOM (! BASE & SEG;T .##2 ON ! TOP4 ,%[ T5S ON TOP & "OS ON ! BOTTOM4 ,EXAMPLE3 #15+12 .K #27 #AC ,6%[ #15, PLACE FIVE PEGS ON ! BOTTOM /RIP 6REPRES5T ! #5 "OS & "O PEG ON ! TOP /RIP 6REPRES5T #10_4 ,ADD #12 0PLAC+ TWO PEGS ON ! BOTTOM /RIP & "O PEG ON ! TOP /RIP 6REPRES5T #10_4 ,! NUMB] L9E N[ %[S TWO PEGS ON ! TOP /RIP REPRES5T+ #20 & SEV5 PEGS ON ! BOTTOM /RIP OR #27_4 ,EXAMPLE3 #27+14 .K #41 ,6%[ #27, PLACE SEV5 PEGS ON ! BOTTOM /RIP & TWO PEGS ON ! TOP /RIP 6REPRES5T #20_4 ,ADD #14 0PLAC+ F\R PEGS ON ! BOTTOM /RIP & "O PEG ON ! TOP /RIP 6REPRES5T #10_4 ,REGR\P ! #11 "OS ON ! BOTTOM /RIP 6MAKE "O #10 ON ! TOP /RIP =A TOTAL ( #4 PEGS OR #40 & L1V+ "O PEG ON ! BOTTOM OR #41_4 ,REGR\P 96T5S & "OS :5 ! SUM (! "OS IS T5 OR GRT]4 (,6HELP ! /RU7L+ /UD5T "U/& :5 6REGR\P Y MAY PLACE A TACTILE /ICK] OR GRAPHIC >T TAPE AF ! #9 ON SEG;T .##1_4) #AG ,USE SEG;T .##2 (0--#200 A#AC 0T5S) ) PEGS OR B>S 6ILLU/RATE R.D+ (F NUMB]S4 ,= EXAMPLE1 9 ! PRO#M #17+34, R.D (F #17 TO #20 (THE NE>E/ T5) & PLACE #2 PEGS OR B>S ON ! F/ TWO T5S ON ! NUMB] L9E4 ,NEXT R.D (F ! #34 TO #30 (THE NE>E/ T5) & ADD #3 M PEGS OR B>S 6! F/ #2 T5S 6REPRES5T ! NEXT #3 T5S ON ! NUMB] L9E4 ,!N F9,Y R1D ! E/IMAT$ ANSW] =! PRO#M #17+34 ON ! NUMB] L9E3 #50_4 -----------------------------------#AD ,,MULTIPLIC,N ,,& ,,DIVI.N ,USE SEG;T .##1 (0--#20 0"OS) ) PEGS OR B>S 6DEMON/RATE T MULTIPLIC,N IS REP1T$ A4I;N & T DIVI.N IS REP1T$ SUBTRAC;N4 ,USE SEG;T .##1 (0--#20 0"OS) ) PEGS OR B>S 6ILLU/RATE & %[ ! MULTIPLIC,N FACTS ) PRODUCTS UP TO #20_4 (,IF ! UNNUMB]$ SEG;T ) #20 COORD9ATE SCALE M>KS IS US$1 ? C 2 EXT5D$4) ,6ILLU/RATE ! PRO#M #3@*6 .K #18, PUT SIX SUBSETS ( ?REE TGR ON ! NUMB] L9E 6MAKE EIS ON ! NUMB] L9E1 REMOVE SUBSETS ( #6 UNTIL "! >E LESS ?AN #6 LEFT & C.T ! NUMB] ( SUBSETS (3) T 7 REMOV$4 ,USE SEG;T .##1 (0--#20 0"OS) ) PEGS OR B>S 6DEMON/RATE ! -MUTATIVE (ORD]) PR9CIPLE &! ASSOCIATIVE (GR\P+) PR9CIPLE = MULTIPLIC,N4 ,= EXAMPLE1 9 ! PRO#M #2@*3@*1, PUT ?REE SETS ( TWO PEGS ON ! NUMB] L9E #1 "T 6MAKE A PRODUCT ( #6 ON ! NUMB] L9E4 ,US+ ! SAME NUMB]S1 PUT "O SET ( #3 ON ! NUMB] L9E TWO "TS 6MAKE ANO!R SIMIL> PRODUCT ( #6 ON ! NUMB] L9E4 -----------------------------------#AE ,,FRAC;NS ,USE SEG;TS .##5 (,HALVES), .##6 (,?IRDS), .##7 (,F\R?S), & .##9 (,SIX?S) ) B>S 6ILLU/RATE ! M1N+ ( ?1/2#, ?1/3#, ?1/4#, & ?1/6# (A :OLE4 (,USE A #1-FOOT RUL] 6REPRES5T "O :OLE4) ,-P>E ! B>S 6! :OLE & #AI 6EA* O!R US+ ! SU7E/$ SEG;TS ON A#AE ! BASE TWO AT A "T4 ,NOTE3 ,D N USE SEG;TS .##8 (,FIF?S), .##10 (,EIE ?1/2# & ?1/3#, PLACE SEG;T .##5 (,HALVES) ON ! BOTTOM & SEG;T .##6 (,?IRDS) ON ! TOP (! BASE4 ,HOLD ! #1-FOOT RUL] NEXT 6EA* (! SEG;TS 9 TURN NOT+ T ! RUL] R1*ES J 6! 8#1_0 M>K4 ,PUT TGR ON ! BASE 5 B>S (6) 6R1* ! ?1/2# M>K ON ! BOTTOM SEG;T4 ,REMOVE ? SEG;T ( B>S F ! BASE & -P>E XS L5G? 6T (! RUL]4 (,IT IS N ! PURPOSE (! RUL] 6M1SURE1 J 6REPRES5T "O :OLE S R1D+ (! RUL] M>K+S IS N NEC OR EV5 DESIRA# AT ? "T4) ,NEXT1 PUT TGR ON ! BASE 5 B>S (4) 6R1* ! ?1/3# M>K ON ! TOP SEG;T4 ,REMOVE ? SEG;T ( B>S F ! BASE & -P>E XS L5G? 6T (! RUL]4 ,!N -P>E ! B> SEG;T REPRES5T+ ?1/2# 6! "O REPRES5T+ ?1/3# AWAY F ! BASE4 ,F9,Y1 B#AE PLACE BO? B> SEG;TS BACK ON ! BASE NEXT -----------------------------------#AF 6! SEG;TS !Y REPRES5T1 R1D1 & -P>E ?1/2# & ?1/3# ON ^! SEG;TS4 ,USE SEG;TS .##5 (,HALVES), .##6 (,?IRDS), .##7 (,F\R?S), & .##9 (,SIX?S) ) PEGS 6ILLU/RATE ! M1N+ ( ?1/2#, ?1/3#, ?1/4#, & ?1/6# (A SET HAV+ #12 MEMB]S4 ,-P>E ! PEGS 6! SET ( #12 & 6EA* O!R US+ ! SU7E/$ SEG;TS ON ! BASE TWO AT A "T4 ,= EXAMPLE1 6-P>E ?1/2# & ?1/3# (! SET ( #12 PLACE SEG;T .##5 (,HALVES) ON ! BOTTOM & SEG;T .##6 (,?IRDS) ON ! TOP (! BASE4 ,F9D ! 8#1_0 M>K ON EA* SEG;T & C.T ! NUMB] ( HOLES 9 ! BASE NE$$ 6R1* ? M>K (12)_4 ,PUT 5 PEGS (6) 9 ! BASE 6R1* ! ?1/2# M>K ON ! BOTTOM SEG;T4 ,C.T ! PEGS 9 ! BASE & -P>E ? NUMB] TO #12_4 ,NEXT1 PUT 5 PEGS (4) 9 ! BASE 6R1* ! ?1/3# M>K ON ! TOP SEG;T4 ,C.T ! PEGS 9 ! BASE & -P>E ? NUMB] TO #12_4 ,!N -P>E ! PEGS 9 ?1/2# (A SET ( #12 (6) #BA 6! PEGS 9 ?1/3# (4) (A SET ( A#AF #12_4 ,R1D & -P>E ?1/2# & ?1/3# ON ^! SEG;TS 0SLID+ ! F+]S AL;G IMAG9>Y P]P5DICUL>S 2T ! TWO SEG;TS4 ,USE SEG;TS .##5 (,HALVES), .##6 (,?IRDS), .##7 (,F\R?S), & .##9 (,SIX?S) ) B>S & PEGS 6ILLU/RATE & -P>E ! M1N+ ( ?1/2#, ?2/4#, ?3/6#, ?4/6#, FRAC;NS REPRES5T+ "O1 EQUIVAL5T FRAC;NS1 MIX$ NUMB]S1 & FRAC;NS GRT] ?AN "O :OLE OR "O SET4 ,USE SEG;TS .##11 (,FRAC;NAL ,T5?S) & .##12 (,DECIMAL ,T5?S) ) B>S OR PEGS 69TRODUCE ! IDEA ( T5?S &! USE ( DECIMALS Z AN ALT]NATE WAY ( -----------------------------------#AG WRIT+ T5?S4 ,PUT SEG;T .##11 (,FRAC;NAL ,T5?S) ON ! BOTTOM (! BASE & .##12 (,DECIMAL ,T5?S) ON ! TOP (! BASE4 ,F9D ?1/10# ON ! BOTTOM SEG;T & M>K X )A PEG OR A B>4 ,FOLL[+ AN IMAG9>Y P]P5DICUL>1 SLIDE YR F+]S 6AN EQUIVAL5T PLACE ON ! TOP SEG;T & NOTE ! M>K+1 8#.1_04 ,USE ! SAME PROC$URE = ?2/10# & #.2, ?3/10# & #.3, ETC4 ,3CLUDE T ?1/10# IS ! SAME Z A#AG #.1_2 ?2/10# ! SAME Z #.2_2 ETC4 ,USE SEG;TS .##8 (,FIF?S) & .##11 (,FRAC;NAL ,T5?S) ) B>S & PEGS 6ILLU/RATE & -P>E ! M1N+ ( ?1/5#, ?2/10#, ?3/5#, ?6/10#, ?5/5#, ?10/10#, FRAC;NS REPRES5T+ "O1 EQUIVAL5T FRAC;NS1 MIX$ NUMB]S1 & FRAC;NS GRT] ?AN "O :OLE OR "O SET4 ,USE SEG;TS .##8 (,FIF?S) & .##10 (,EIS & PEGS 6ILLU/RATE ! A4I;N & SUBTRAC;N ( FRAC;NS1 FRAC;NS REPRES5T+ "O1 MIX$ NUMB]S1 & FRAC;NS GRT] ?AN "O :OLE4 ,USE SEG;TS .##7 (,F\R?S) & .##10 (,EIE N EQUIVAL5T4 ,PLACE SEG;T .##7 ON ! TOP & SEG;T .##10 ON ! BOTTOM (! BASE4 ,H ! /UD5T F9D 8#1_0 ON EA* SEG;T4 ,:ILE ?1/4# %D 2 EQUIVAL5T TO ?2/8#, DEMON/RATE T ?2/8# IS ACTU,Y L>G] ?AN ?1/4# 9 ? EXAMPLE4 #BC ,,M"OY #AH ,USE SEG;TS .##11 (,FRAC;NAL T5?S) & .##12 (,DECIMAL T5?S) ) B>S OR PEGS & DOLL>S1 DIMES1 & P5NIES 6ILLU/RATE _! M1N+S & -P>E ! USE (! DOLL> SIGN &! DECIMAL PO9T )! USE ( FRAC;NS & DECIMALS4 ,US+ R1L M"OY %[ ! /UD5T T #10 PENNIES .K #1 DIME & #10 DIMES .K #1 DOLL>4 ,-P>E ! VALUE (A P5NY (@S.01) )A DIME (@S.10) &A DIME (@S.10) )A DOLL> (@S1.00)_4 ,%[ ^! AM.TS (?1/10# & #.1) ON BO? (! SU7E/$ SEG;TS US+ EI ! PEGS OR ! B>S4 ,NOTE ESPECI,Y ! DECIMAL M>K+ ON ! SEG;T4 ,WRITE OR BRL ^! SAME AM.TS US+ ! DOLL> SIGN & DECIMAL PO9T4 ,NOTE ! SIMIL>ITIES & DI6];ES 9 WRIT+ DECIMALS (US+ ! NUM]IC 9DICATOR &! DECIMAL PO9T) & WRIT+ M"OY (US+ ! DOLL> SIGN &! DECIMAL PO9T)_4 ,,L9E> ,,M1SURE;T ,USE SEG;T .##1 (0--#20 0"OS) ) PEGS OR B>S &A #1-FOOT RUL] A#AH 6DEMON/RATE M1SUR+ 0AN 9*4 ,S9CE EA* :ITE PLA/IC CYL9D] IS #1-9* L;G1 ! IDEA ( AN 9* %D ALR 2 FAMILI> 6! /UD5T F PREVI\S EXP]I;E )! MAT]IALS4 ,^! :ITE PLA/IC CYL9D]S C 2 MADE 96V>I\S L5G?S ( B>S = M1SUR+ PRACTICE4 ,PLACE A PEG AT A "PICUL> PO9T DICTAT$ 0! 9/RUCTOR4 ,F9D & PO9T 6A SIMIL> MARKING_/POINT ON ! #1-FOOT RUL]4 ,? W PROVIDE PRACTICE 9 R1D+ A RUL]4 -----------------------------------#AI ,USE SEG;TS .##5 (,HALVES) & .##7 (,F\R?S) ) PEGS OR B>S &A #1-FOOT RUL] ) HALF-9* & QU>T]-9* M>K+S 6DEMON/RATE M1SUR+ & R1D+ A RUL] 6! NE>E/ HALF 9* & QU>T] 9*4 ,USE ^! SEG;TS 6PROVIDE AN 5L>G$ V].N (! M>K+S ON ! RUL] = R1D+ PRACTICE Z DESCRIB$ ABV4 ,,CLOCKS ,USE SEG;TS .##1 (0--#20 0"OS) & .##3 (0--#100 0FIVES) ) PEGS OR B>S 6FAMILI>IZE ! /UD5T ) "OS & #BE FIVES & -P>E ! "OS 6H\RS ON ! A#AI CLOCKS &! FIVES 6M9UTES4 ,! CLOCK IS RE,Y TWO CIRCUL> NUMB] L9E SEG;TS--"O ) VISI# NUMB]S #1--#12 & OBVI\S 9T]VALS ( #1 H\R EA*1 & ANO!R ": ! SAME NUMB]S #1--#12 RE,Y /& =! NUMB]S #5--#60 & EA* 9T]VAL REPRES5TS #5 M9UTES4 ,,TEMP]ATURE ,USE A SEG;T M>K$ V]TIC,Y 6A3U/OM ! /UD5T 6R1D+ A V]TICAL NUMB] L9E4 ,USE SEG;T .##4 (-#10--+10) 6A3U/OM ! /UD5T 6US+ NEGATIVE NUMB]S4 ,USE AN UNNUMB]$ SEG;T & M>K -#60^.*"--+130^.* 0T5S V]TIC,Y 6RESEM# A !RMOMET] ) B>S 6REPRES5T ! M]CURY ADJU/$ 6V>I\S TEMP]ATURES4 ,,REF];ES #BJ ..,-MON ,CORE ,/ATE ,/&>DS .,9ITIATIVE4 (2010, ,JUNE)_4 ,RETRIEV$ ,DECEMB] #16, #2010, F ,PREP>+ ,AM]ICA'S ,/UD5TS = ,COLLEGE & ,C>E] ,ONL9E3 _+HTTP://WWW.CORESTANDARDS.ORG/_& ABOUT-THE-STAND_: ,KAPP]MAN1 ,G4 ,H4 (1997)_4 ..,/RATEGIES = ,DEVELOP+ ,MA!MATICS ,SKILLS 9 ,/UD5TS ,:O ,USE .,BRL4 ,SYCAMORE1 ,,IL3 ,RESE>* & ,DEVELOP;T ,9/ITUTE4 ,N,NAL ,C\NCIL ( ,T1*]S ( ,MA!MATICS4 (2000)_4 ..,PR9CIPLES & ,/&>DS = ,S*OOL .,MA!MATICS4 ,RE/ON1 ,,VA3 ,N,NAL ,C\NCIL ( ,T1*]S ( ,MA!MATICS4 #BG ,,APH^R A#BJ ,AM]ICAN ,PR9T+ ,H\SE =! ,BL1 ,9C4 #1839 ,FRANK=T ,AV5UE--,P4,O4 ,BOX #6085 ,L\ISVILLE1 ,K5TUCKY #40206-0085 ,PH"O3 #502-895-2405 ,TOLL ,FREE3 #800-223-1839 ,FAX3 #502-899-2274 ,EMAIL3 _+INFO@APH.ORG_: _+WWW.APH.ORG_: ,"P ,NUMB] #61-267-034 = USE 9 ,CATALOG ,NUMB] #1-03480-01 ,,! ,,5D