,provi.nal ,guid.e on        #a
              ,transcrib+
          ,ma!matics 9 ,,ueb
               ,may #bjai

      @.<,,bana logo@.>

                 ,3t5ts

#a4 ,9troduc;n """""""""""""""""""""" #b
#b4 ,spac+ ( signs """""""""""""""""" #b
#c4 ,g5]al =mat """"""""""""""""""""" #c
#d4 ,divid+ ma!matics expres.ns
  ov] brl l9es """""""""""""""""""""" #c
#e4 ,*oice ( grade #a 9dicators
  ) ma!matics expres.ns """"""""""""" #d
#f4 ,addi;nal 9=ma;n relat$ to
  grade #a 9dicators """""""""""""""" #g
#g4 ,numb]$ ,equa;ns """""""""""""""" #h
#h4 ,ellipses """"""""""""""""""""""" #h
#i4 ,spatial problems """"""""""""""" #h



                                      #a
    #a4 ,9troduc;n                    #b
  ,! foll[+ guidel9es1 9t5d$ = use 9 !
,,us & ,canada1 supple;t ! rules &
guid.e pres5t$ 9 ! 9t]na;nal publica;ns
.7,rules ( ,unifi$ ,5gli% ,brl1 #bjac.'
"<,,rueb"> & .7,unifi$ ,5gli% ,brl
,guidel9es = ,te*nical ,mat]ial.'
"<,,gtm"> au?oriz$ by ! ,9t]na;nal
,c\ncil on ,5gli% ,brl "<,,iceb">4 ,!
purpose ( ? docu;t is to provide
addi;nal cl>ifica;n & practical su7es;ns
= ! transcrip;n ( 8te*nical0 "<t is1
ma!matics & sci;e"> texts transcrib$ us+
,unifi$ ,5gli% ,brl1 s z to a*ieve a
r1sonable level ( /&>d transcrip;n4 ,!
examples & "s ( ! language us$ 9 ?
docu;t >e f ! ,,uk ,associa;n =
,a3essible ,=mats "<,,ukaaf"> docu;t1
8,addi;nal ,guid.e = ,,ueb ,ma!matics0 &
>e us$ ) p]mis.n4
  ,^! guidel9es prim>ily apply to ,,ueb
ma? brl transcrip;ns1 "picul>ly =
mat]ials t wd b5efit f 3si/5t practice
s* z /&>diz$ te/s or transcrip;ns cr1t$
)\t 9=ma;n ab ! classroom or /ud5t4   #b
,di6]5t approa*es may 2 ne$$ 9       a#b
classroom practice1 "<e4g41 9 reg>d to !
spac+ ( signs = 2g9n+ le>n]s1 z not$ 9
,,gtm #a4a4b">1 & ! pres5ta;n ( spatial
problems = 9/ruc;nal purposes4
,simil>ly1 ! guidel9es /at$ "h1 s* z !
spac+ ( signs or ! *oice ( grade #a
9dicators1 wd n necess>ily 2 appli$ 9
non-ma!matical 3texts4 "<,see1 =
example1 ,,rueb #aa4b4a4"> ,z is
,,bana's practice1 \tl9$ 9 ! ,,bana
.1,=mats guidel9es1 a transcrib]'s note
may 2 ne$$ to let ! r1d] "k :5 pr9t
=mats >e n foll[$2 g5]al r1dabil;y &
cl>;y ( pres5ta;n take prec$;e4
  ,9 ? docu;t ! ^w 8expres.n0 signifies
any gr\p ( ma!matical symbols4 ,x may 2
a s+le t]m or a l;g] gr\p ( ma!matical
symbols1 s* z an equa;n1 : is n brok5 by
ord9>y text4

    #b4 ,spac+ ( signs "<,,rueb #aa4b4b2
    ,,gtm #a4a">
  ,foll[ ! g5]al rule to l1ve a space on
ei side ( comp>ison or rela;n signs   #c
& place op]a;n signs unspac$ f _!    b#b
adjac5t t]ms4 ,h["e1 ! ,,gtm all[s
spaces >.d signs ( op]a;n = 2g9n+ r1d]s1
s foll[ ag5cy deci.n ab h[ signs >e
pres5t$4
--------------------------------------#c

      ,example3
  #f "7 #a"8#b"8#c "7 #a"6#b"6#c
    8six equals "o "ts two "ts ?ree
    equals "o plus two plus ?ree0

    #c4 ,g5]al =mat "<,,gtm #a4d4a">
  ,= te*nical mat]ials1 use m>g9s #c-#a2
d n use block$ p>agraphs4 ,if ! 5tire
textbook is 9 block$ p>agraphs1 note !
*ange to 9d5t$ p>agraphs 9 a ;,,tn4
  ,foll[ .7,brl ,=mats3 ,pr9ciples (
,pr9t-to-,brl ,transcrip;n1 #bjaf.' = !
=mat ( 4play$ lit]>y text except =
p>agraph =mat1 : is n"e block$4 ,=
4play$ ma!matical expres.ns1 use blank
l9es prec$+ & foll[+2 & 9d5t #b cells f
! runov] posi;n ( ! mat]ial to : !y
apply4                                #d
  ,use ( ! full brl l9e = a 4play$   a#c
te*nical expres.n "<) runov]s 9 cell
#c">1 is appropriate = hi<] ma? ":
expres.ns >e l5g?y & m complicat$4 ,!
spaces us$ to 9d5t 2y ! runov] 9 e6ect c
make ! di6];e 2t divid+ or keep+ a
ma!matical unit tgr4
  ,= direc;ns prec$+ itemiz$ mat]ials1
use m>g9s #e-#e4 ,if "! >e addi;nal
p>agraphs1 use m>g9s #g-#e4 ,= directive
s5t;es t prec$e mat]ial t is n itemiz$
use m>g9s #c-#a4
  ,tr1t an ex]cise ) sub5tries z a ne/$
li/ & ! 9d5ta;n patt]n is det]m9$ by !
complete set1 n 9dividually4 ,= example1
if two levels3 #a-#e1 #c-#e2 if ?ree
levels3 #a-#g1 #c-#g1 #e-#g1 & s =?4
  ,keep a2revia;ns on a brl l9e ) !
numb]s to : !y apply4

    #d4 ,divid+ ma!matics expres.ns ov]
    brl l9es "<,,gtm #a4d4a-#c">
  ,z /at$ 9 ! ,,gtm1 :5 a ma!matical
expres.n _c 2 kept on "o brl l9e1 !
*oice ( a l9e br1k site %d foll[      #e
ma!matical /ructure3                 b#c

_4 2f comp>ison signs 
--------------------------------------#d
_4 2f op]a;n signs "<un.s !y >e )9 "o (
    ! ma!matical units 2l"> 
_4 2f a ma!matical unit s* z3 
  ,- frac;ns "<& )9 ! frac;n 3sid] !
    num]ator & d5om9ator z units"> 
  ,- func;ns 
  ,- radicals 
  ,- items ) modifi]s s* z sup]scripts
    or b>s 
  ,- %apes or >r[s 
  ,- any?+ 5clos$ 9 pr9t or brl gr\p+
    symbols 
  ,- a numb] & xs a2revia;n or
    coord9ates 
  ,usually ! be/ place to divide an
expres.n is 2f a comp>ison sign or
op]a;n sign4 ,br1k+ an expres.n 2t brl
pages %d 2 avoid$4 
  ,if y make r1sonable divi.ns foll[+ !
abv guid.e1 ! dot #e 3t9ua;n 9dicator
m5;n$ 9 ,,gtm #a4d w n (t5 2 ne$$2    #f
! m1n+ or =mat %d make x cle> 5 t    a#d
! expres.n on ! new l9e is a 3t9ua;n ( t
on ! previ\s l9e1 e4g4 x w typically />t
) a comp>ison or op]a;n sign4

    #e4 ,guid.e on grade #a 9dicators )
    ma!matics expres.ns "<,,rueb #e4i2
    ,,gtm #a4g">
  ,2c ! num]ic 9dicator al 2g9s ,grade
#a mode1 "! w (t5 2 cases ": no grade #a
9dicators >e requir$ 9 a ma? or sci;e
expres.n4 ,9 addi;n1 ! ,,ueb rules all[
di6]5t approa*es = ! use ( grade #a
9dicators1 & s s"eal approa*es c 2
equally correct4
  ,z expla9$ 9 ! 9troduc;n1 ! purpose (
! foll[+ guidel9e is to pres5t a /&>diz$
me?od1 ?\< x does n 9validate o!r
approa*es4
  ,if grade #a 9dicators >e requir$1 !
basic pr9ciple to foll[ is3
^7,un.s a ma? expres.n c 2 correctly
repres5t$ ) only a grade #a symbol
9dicator 9 ! f/ ?ree cells or 2f a s+le
lr /&+ al"o any": 9 ! expres.n1 2g9   #g
! expres.n ) a grade #a ^w 9dicator   #e
"<or a passage 9dicator if ! expres.n
9cludes spaces">4^'
  ,! result ( ? pr9ciple is t grade #a
symbol 9dicators )9 ! ma? expres.ns >e
l>gely avoid$4 ,( c\rse1 "! >e cases ":
a grade #a 9dicator is ess5tial at a
"picul> po9t1 notably ": a lr a-;j immly
foll[s a numb]4 ,? prev5ts x f 2+ r1d z
a digit4 ,! abv rule does n apply to s*
cases ": "! is no op;n to avoid ! use (
! grade #a 9dicator4
  ,note t1 9 ! case ( an expres.n t is
divid$ ov] m ?an "o l9e1 ! 5d ( a brl
l9e c.ts z a brl space un.s ! dot #e
3t9ua;n 9dicator is us$4 ,rememb] t1
8/&+ al"o0 is us$ ac to ! /&>d ,,ueb
def9i;n 9 ,,rueb #b4f & 9cludes v>i\s
cases ": a lr adjo9s brackets or
punctua;n4

      ,examples3
  x"6y "7 #f
    8;x plus ;y equals six0
  "<,no grade #a 9dicators ne$$4">    #h
                                     a#e
  x;9#b"6y9#b "7 ;,c
    8;x sup]script two plus ;y
    sup]script two equals ;,c0
  "<,grade #a 9dicator is 9 f/ #c cells
& 2f a lr /&+ al"o4">

  ;;(a./b)"6(c./d)
    8a ov] ;b plus ;c ov] ;d0
  "<,unspac$ expres.n2 grade #a ^w
9dicator ne$$ 2c o!rwise ! expres.n wd 2
9t]rupt$ ) a grade #a 9dicator 2f ! ?ree
rema9+ g5]al frac;n 9dicators4">

  ;;;a9n"8a9m "7 a9<n"6m>;'
    8a sup]script ;n "ts a sup]script ;m
    equals a sup]script ,8;m plus ;n,00
  "<,spac$ expres.n2 grade #a passage
9dicator ne$$4">
--------------------------------------#f
  ;;log5x ;y
    8log subscript ;x ;y0
  "<,grade #a ^w 9dicator ne$$ 2c !
grade #a symbol 9dicator 2f ! subscript
is 9 ! #dth cell2 x is al ne$$ 2f a   #i
lr /&+ al"o4">                       a#f
  ,9 addi;n1 note ! foll[+3

"<a"> ,units3 ,": a m1sure;t unit is "p
  ( a l;g] expres.n1 tr1t ! unit z 2l;g+
  to ! l;g] expres.n 9 ! applica;n ( !
  abv rule4 ,h["e1 ": a unit is /&+ al"o
  or j a3ompanies a numb]1 tr1t ea*
  spac$ ele;t ( ! unit z a sep>ate
  expres.n1 ea* foll[+ ! abv rule4

      ,examples3
  #ajj^j,f
    8"o hundr$ degrees ,fahr5heit0

  #be km;9#b
    8#be km squ>$0
  #f ;m ;;s9<"-#a>
    8six ;m ;s sup]script ,8"-#a,00

"<;b"> ,": a ma? expres.n 9volves ^ws1 x
  may 2 be/ to use a grade #a symbol or
  ^w 9dicator ": ne$$ )9 ! expres.n1 r
  ?an grade #a passage mode = ! :ole
  expres.n4 ,? approa* all[s ! use   #aj
  ( 3trac;ns 9 ! ^ws4                b#f
--------------------------------------#g

      ,example3
  ;,c "7 _<9teg]s less ?an ,n;9#b_>
    8;,c equals _<9teg]s less ?an ;,n
    sup]script two_>0

"<;c"> ,2c matrices (t5 take up a lot (
  space 9 brl1 "! w 2 o3a.ns ": us+ a
  grade #a symbol 9dicator )9 s* an
  expres.n w 2 pref]able to us+ grade #a
  passage 9dicators4

  ,note t examples 9 ,,gtm d n
necess>ily illu/rate ! same *oice (
grade #a 9dicators z pres5t$ "h1 b !
m1n+ ( ! brl is ! same4 ,ag1 ! guidel9es
pres5t$ 9 ? docu;t >e 9t5d$ to su7e/ a m
3si/5t approa* to transcrip;n & improve
! r1dabil;y ( ma!matics expres.ns4

    #f4 ,addi;nal guid.e on grade #a
    9dicators
  ,": grade #a passage 9dicators     #aa
>e us$ >.d a ma? expres.n1           a#g
punctua;n at ! 5d ( ! expres.n "<e4g4 a
p]iod at ! 5d ( a s5t;e"> %d normally 2
9clud$ 2f ! grade #a t]m9ator1 ev5 ?\< n
"p ( ! expres.n xf4

      ,example3
  ;;;x"6y "7 z "7 t9#b4;'
    8;x plus ;y equals ;z equals ;t
    sup]script two0

  ,if "! is m ?an "o sep>ate ma?
expres.n "<e4g4 s"eal equa;ns">1 foll[+
"o af ! o!r1 ! grade #a passage
9dicators c 2 us$4 ,9 t case1 ! :ole
gr\p c 2 5clos$ 9 passage 9dicators r
?an us+ sep>ate 9dicators = ea* item4
,9t]v5+ punctua;n wd 2 9clud$ )9 !
passage 9dicators4 ,h["e1 text wd n
ord9>ily 2 9clud$ 2c ! ^ws wd 2
uncontract$4 ,g5]ally1 ! num]ic passage
wd 2 t]m9at$ 2f ! ^ws & a new passage
mode wd 2 add$ at ! 2g9n+ ( ! next set (
ma? expres.ns4
,note t a grade #a passage 3t9ues    #ab
onto a new brl page until !          b#g
passage t]m9ator2 if an expres.n is
split ov] brl pages y d n ne$ to re/>t !
passage 9dicator on ! new page4
--------------------------------------#h

    #g4 ,numb]$ ,equa;ns
  ,equa;n numb]s %d 2 plac$ 2f ! equa;n
9 brl1 & 2 sep>at$ f x by a s+le space1
ev5 if !y appe> on ! "r 9 pr9t4 ,a
transcrib]'s note %d 2 9clud$ to expla9
? *ange f pr9t4

    #h4 ,ellipses
  ,": pr9t uses f\r or m dots = an
ellipsis )\t special r1son1 z 9
expres.ns = s]ies or sets1 = 3si/5cy use
only #c unspac$ p]iods "<dots #bef">4

    #i4 ,spatial problems
  ,s"eal 4play op;ns >e all[$ 9 ,,ueb =
spatial ma? problems4 "<,see ,,gtm #d4">
,"s ( ^! op;ns d n mat* ! pr9t %[n 9
textbooks b may provide easi] "u/&+ (
ma!matical proc$ures & 3cepts = "y   #ac
brl r1d]s4 ,^! me?ods >e suitable    a#h
= 9/ruc;nal purposes4 ,h["e1 = ! sake (
3si/5cy 9 /&>diz$ te/ situa;ns1 foll[
pr9t =matt+ ( spatial problems4
  ,an excep;n to ? guidel9e c 2 made if
! transcrib+ ag5cy is reque/$ to use a
specific =mat by ! /ate's $uca;nal sy/em
to mat* a /ate m&at$ ma? curriculum1
especially = "y] le>n]s :o may h limit$
exp]i;e ) v>i\s pres5ta;n /yles4














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