The Hitchhikers Guide to UEB

Mathematics

UEB Curricula Support Writing Group

First published 2008
Revised 2013
 Contents - Mathematics
Quick Reference .. 1
Introduction . 3
KISS Principles 10 Simple Rules . 4
What on Earth is That? 5
Braille Indicators . 6
o Number Sign
o Grade 1 Indicators
Signs of 7
o Operations
o Comparison
o Grouping
Fractions .. 8
Decimals .. 9
Superscripts and Subscripts . 9
Square Roots 9
Greek Letters .. 10
Print Symbols . 10
Formatting .. 10
List of Common Symbols .. 11

Acknowledgements
Thanks go to the Ministry of Education for their support in the
development of this resource which is licensed under the Creative
Commons Attribution-Noncommercial-Sharealike licence. To view a
copy of this licence, visit http://creativecommons.org/licenses/by-nc-
sa/3.0/nz/
The members of the 2008 UEB Curricula Support Writing Group were
Elaine Gilmour, Jenny McFadden, Catherine West, Diane Glynan, Janet
Reynolds, Isobel Dinning and Steve Bellamy.
 1

UEB MATHS QUICK REFERENCE

Print UEB Print UEB Print UEB
1 #a plus + "6 round bracket ( "<
2 #b minus - "- round bracket ) ">
comma 1 multiply x "8 equilateral triangle $#c
decimal point 4 divide "/ square $#d
numeric space " plus or minus _6 circle $=
@c multiplication dot . "4
$ @s ratio : 3 arrow indicator \
% .0 = "7 right-pointing arrow \o
degree ~j < @<
square root % + > @> parallel // #l
fraction line / / less than or equal to _@< perpendicular #-
infinity #= greater than or equal to _@> general omission +
angle indicator _[ not equal to "7@: tally mark _
pi .p superscript change level up 9
Examples
32+26 = 58 #cb"6#bf "7 #eh #c/d 5 #e#c/d
52 = 25 #e9#b "7 #be 4 ;%#d+ -3 "-#c
Revised October 2013
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Revised October 2013

 3

Introduction
The Hitchhikers Guide to UEB first edition was written in 2008 by a group of dedicated
Resource Teachers Vision from the Blind and Low Vision Network New Zealand together with
support from staff at the Royal New Zealand Foundation of the Blind, Accessible Format
Production.

The team members gifted their time, knowledge and passion for braille, to produce a resource to
support staff, learners and producers with Unified English Braille (UEB) production, as New
Zealands adoption of UEB became a reality in the education and braille worlds.

The Hitchhikers Guide to UEB was developed to serve as a quick memory jogger. It is not a
comprehensive braille instruction guide. This edition, updated in 2013, reinforces the use of the
guide as a reference tool to be used by Resource Teachers Vision (RTVs), teachers, teacher
aides, Whnau and parents, who find themselves needing to braille texts quickly for student use.

For more in-depth braille rules please refer to the Braille Authority of New Zealand Aotearoa
Trust BANZAT website at www.banzat.org.nz from which the current editions of the manuals
listed below can be downloaded.

Unified English Braille Manual: New Zealand Edition

Unified English Braille Guidelines for Technical Material
The Rules of Unified English Braille

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 4

KISS Principles
(Keeping it so simple!)

For UEB
10 Very Simplified Rules

1. + - x = all take dot 5

2. money symbols take dot 4 and are followed by number sign
3. operation signs are unspaced both sides
4. comparison signs are spaced before and after
5. greater than and less than signs take dot 4
6. simple fraction line /
7. mixed numerals repeat number sign
8. superscript change level up (9)

9. subscript change level down (5)

10. square root has to open and close (% +)

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U.E.B.
What on Earth is That?
Dots 4, 5
Dot 4 symbols Dots 4, 5, 6 symbols Dots 4, 6 Dot 5
symbols
@s $ ~j _6 plus or minus .0 % "6 +
Money symbols

plus

@c "-

Operation signs
~9 minus

@e _@> greater than or equal to ./ general fraction line "8 multiply

@a @ _@< less than or equal to "4 multiplication
dot
@< < _/ / .p "/ divide
@>

Greek letters
>
.a "7 = equals

Comparisons
Signs of
.b "7@:
@.< open _9 approximately equal to ,.s capital Sigma not equal to
transcribers note (tilde over horizontal line)
@.> close .< [ square brackets "9 * asterisk
transcribers note
_[ .> ]
@: line through ",- ____
previous item long dash, typically used to indicate
(cancellation, "not") missing answer

e.g. "7@:
Dot 5 is used as the numeric space symbol to indicate when a space has been used instead of a comma e.g. 1 000 000 #a"jjj"jjj

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The Hitchhikers Guide to UEB

Mathematics

In UEB each print symbol has one and only one braille equivalent.

UEB Maths is not a separate code. All the symbols you would meet in UEB literary
material are the same when met in a maths setting.

Braille Indicators
The limitations of the 6-dot cell make it impossible to represent in braille, without
duplication, the many arbitrary signs used in print mathematics. A system of braille
indicators is therefore used. These indicators have no corresponding ink print signs
but impart particular meanings to the braille symbols which precede or follow them.

Number Sign (dots 3 4 5 6)

The most common braille indicator is the number sign which signals that the
following cell (or cells) forms a number. The digits one to nine and zero are shown
by the letters a to j preceded by the number sign.
e.g. 1 #a 500 #ejj

Grade 1 Indicators (dots 5 6)

If a braille symbol also has a Grade 2 meaning then the Grade 1 Indicator must be
used unless Grade 1 mode is already in force.

; indicates the following symbol is in Grade 1

;; indicates the following word is in Grade 1
;;; indicates the following passage is in Grade 1
;' (dots 56, 3) terminates the Grade 1 passage.

Any algebra expression may need a Grade 1 Word Indicator or, if it includes
spaces, a Grade 1 Passage Indicator. A simple arithmetic equation will not.

The Number Sign acts as a Grade 1 indicator.

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Signs of Operation
The basic mathematical operations are addition, subtraction, multiplication and
division. These are 2-cell signs.

plus + "6 (dot 5, dots 2 3 5)

minus - "- (dot 5, dots 3 6)
multiply "8 (dot 5, dots 2 3 6)
divide "/ (dot 5, dots 3 4)
plus or minus _6 (dots 4 5 6, dots 2 3 5)
multiplication dot . "4 (dot 5, dots 2 5 6)

The signs of operation are unspaced.

e.g 6+3, 4-2, 89

#f"6#c1 #d"-#b1 #h"8#i

Signs of Comparison
In braille these are at least 2-cell signs and must be preceded and followed by a space.
The most common is the equals sign. Others include the symbols for greater than >,
less than <, etc.

equals = "7 (dot 5, dots 2 3 5 6)

greater than > @> (dot 4, dots 3 4 5)
less than < @< (dot 4, dots 1 2 6)
not equal to "7@: (dot 5, dots 2 3 5 6, dot 4, dots 1 5 6)

e.g. 6+3 = 9 #f"6#c "7 #i

Signs of Grouping
The basic brackets are
Round brackets ( ) "< ">
(opening: dot 5, dots 1 2 6; closing: dot 5, dots 3 4 5)
Square brackets [ ] .< .>
(opening: dots 4 6, dots 1 2 6; closing: dots 4 6, dots 3 4 5)
Curly brackets { } _< _>
(opening: dots 4 5 6, dots 1 2 6; closing: dots 4 5 6, dots 3 4 5)

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Braille Enclosure Indicators

Braille grouping indicators are used when there are no print brackets but the symbols
still need treating as an item. See the last examples in the Superscripts and Subscripts
Section on the next page.
opening < (dots 1 2 6)
closing > (dots 3 4 5)

Simple Fractions
In braille, fractions are a little different from the print forms because they are written
across the line. We do not talk about the top and bottom parts of a fraction; we refer
to them by their correct names numerator and denominator.

In print, simple fractions may be written either as 3 or as 3/4 and in both cases we
4
would say either three quarters or three over four. Be consistent and use the same
form for each case.

3 #c/d 5 #e#a/b
4

Complex Fractions
When you have fractions with more complex numerators or denominators you will
need to indicate that it is a fraction by using the General Fraction Open and Close
Indicators.

Opening ( (dots 1 2 3 5 6)
closing ) (dots 2 3 4 5 6)

Since the General Fraction Open Indicator has a Grade 2 meaning the following
examples use a Grade 1 Indicator.

3+6 ;(#c"6#f./#d)
4

x ;(x./#b)
2

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Decimal Point
The symbol used for the decimal point is dots 2 5 6 4 the same as the full stop
because a decimal point looks like a full stop.

Superscripts and Subscripts (Level Indicators)

Superscripts have changed level up and are indicated by 9
2
3 #c9#b
If letters are involved then the level indicator could be a contraction so a Grade 1
indicator is needed.
2
y y;9#b
A level indicator only refers to the next item. If a superscript contains more than one
symbol e.g. y-2 , x4+5 the items -2 and 4+5 must be enclosed in braille grouping
symbols.
y-2 ;;y9<"-#b>

x4+5 ;;x9<#d"6#e>
Notice that the Grade 1 word indicator covers all the possible contractions in this
expression.

Subscripts have changed level down. They are indicated by 5 and the rules are the
same.

Square Roots and other Radicals

The expression inside the square root sign in print (the radicand) should be preceded
by the open radical sign and followed by the close radical sign.

opening % (dots 1 4 6)
closing + (dots 3 4 6)

4 ;%#d+

Both the opening and closing radical signs have alternative grade 2
meanings so we need the Grade 1 Indicator.

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Greek Letters
Greek letters are used quite a lot in maths, for various reasons. The most famous is,
of course, pi or as the Greeks write it, . The Greek letters usually correspond to
print letters e.g. alpha is a, but some have no single letter equivalent e.g. theta.

The symbol used to indicate that the next letter is a Greek letter is dots 4 6.
e.g. (alpha) .a
(beta) .b
(theta) .?
(pi) .p
(sigma) .s
(sigma upper case) ,.s

Note that the capital sign comes before the Greek letter symbol.

Print Symbols
If the print character looks like a letter of some kind then the braille often uses that
letter, preceded by the prefix dot 4.
e.g. $ @s (dot 4, s)
@ @a (dot 4, a)

See the UEB Symbols list, or Guidelines for Technical Materials, for a full set of
Maths symbols.

Formatting
The normal braille line has space for 40 cells. Make sure the brailler is set at this
length.

Begin at the very first cell of the line. If the equation or the problem has to extend on
to subsequent lines these are called run-overs. Run-overs go in cell 3 of the second
and following lines.

In 2- or 3-step equations which overrun make sure that the equals sign stays with the
answer. Normally this means that the run-over line would start with the equals sign.
This makes it easy for the student to review and for the teacher to mark.

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Common Symbols
Date
Print UEB
28-5-2014 #bh-#e-#bjad
19/1/2014 #ai_/#a_/#bjad
Numbers, money, measurement
Print UEB Name Examples
1 #a digit one 12 0 300
#ab #j #cjj

1st #ast first #ast

5th #eth fifth #eth
. 4 decimal point 0.56 (decimal) #j4ef .7 #4g
, 1 comma 1,000,000 #a1jjj1jjj
" numeric space 1 000 000 #a"jjj"jjj
@c cent 99 #ii@c

$ @s dollar $44.99 @s#dd4ii

% .0 percent 50% of $2.50 #ej.0 ( @s#b4ej

~j degree 3 C #c~j ;,c

cm cm centimetre 0.45 cm #j4de cm

m ;m metre 0.45 m #j4de ;m
km kilometre
Km 45 km #de km
g ;g gram 500 g #ejj ;g
kg kg kilogram 5 kg #e km
mL M,l millilitre 250 mL #bej M,l
L ;,l litre 5 L #e ;,L

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Operation signs
Print UEB Name Example
+ "6 plus 9+3 #i"6#c
- "- minus 7-2 #g"-#b
x "8 multiplied by 12 x12 #ab"8#ab
. "4 multiplication dot 3.a #c"4a
"/ divided by 3913 #ci"/#ac
: 3 ratio 3 : 4 #c3#d
_6 plus or minus x 3 x_6#c
% + square root 4 ;%#d+
N.B. the square root symbols enclose the number
! 6 factorial sign 6! #f6
Comparison signs
Print UEB Name Example
= "7 Equals 4+5 = 9 #d"6#e "7 #i
> @> greater than 6>5 #f @> #e
< @< less than 4<5 #d @< #e
_@> greater than or equal to 4d #d _@> ;d
_@< less than or equal to 6 x #f _@< ;x
"7@: not equal to 4 8 #d "7@: #h

Time
Print UEB Example
5:30 pm #e3#cj pm
5.30 am #e4cj am
1300 hrs #acjj hrs
80 km/h #hj Km_/h

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Fractions
Print UEB Name Example
/ / simple numeric fraction line 3 3
or #c/d
4 4

5 #e#a/b
./ general fraction line a+6 ;(a"6#f./#d)
( general fraction open indicator 4
NB Number sign must be repeated after
) general fraction close indicator the general fraction line.

Superscripts and Subscripts

UEB Name Example
9 superscript change level up. 32 #c9#b
y2 y;9#b
y-2
;;y9<"-#b>
x 4+5
;;x9<#d"6#e>
5 subscript change level down. P1 ,P;5#a
1002 #ajj5#b

Miscellaneous mathematical symbols

Print UEB Name
#= Infinity
_[ angle sign
// #l parallel to
#- perpendicular to
,* therefore
@/ since
+ general omission symbol

Shapes
Print UEB Name
$ shape indicator
$#c regular (equilateral) triangle
$#d square
$#e regular pentagon (5-sided figure)
$= circle

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Arrows
UEB Name
\ arrow indicator
\o simple right pointing arrow (east)
\[ simple left pointing arrow (west)
\+ simple up pointing arrow (north)
\% simple down pointing arrow (south)

And just because

Bullets, Barbs and Daggers!
UEB Name
_4 bullet
r regular barb, full, in line of direction
;\33rro double-barbed arrow
@,? dagger

Revised October 2013