UEB Math: What’s Different from the Nemeth Code

Arizona AER Sunggye Hong

BANA Resolution

Therefore, it is moved that the Braille Authority of North America (BANA) adopts Unified English Braille to replace the current English Braille American Edition in the United States while maintaining the Nemeth Code for Mathematics and Science Notation, 1972 Revision; the Music Braille Code 1997; and the IPA Braille Code, 2008. The official braille codes for the United States will be Unified English Braille, Nemeth Code for Mathematics and Science Notation, 1972 Revision and published updates; Music Braille Code, 1997; and The IPA Braille Code, 2008.

Numbers

Numeric mode indicator –is unique to braille and lets you know that you are reading a number. “Sets” numeric mode. It is dots 3-4-5-6 ⠼

The numbers 1-9 and 0 are the first 10 letters of the alphabet. Here are some examples:⠼⠛ ⠼⠃ ⠼⠋⠑ ⠼⠁⠚ ⠼⠉⠊

Signs of Operation and Comparison

⠐⠖ + (plus) ⠐⠤ - (minus)

⠐⠦ x (multiplication sign)

⠐⠲ (multiplication dot)

⠐⠌ ÷ (division sign)⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤

⠐⠶ = (equals) ⠈⠣ < (less than) ⠈⠜ > (greater than)

Try To Figure These Out

⠼⠁⠃⠐⠖⠼⠉⠑ ⠐⠶ ⠼⠙⠛

⠼⠑⠚⠐⠌⠼⠑ ⠐⠶ ⠼⠁⠚

⠼⠓⠐⠲⠼⠉ ⠐⠶ ⠼⠃⠙

⠼⠊⠃ ⠈⠜ ⠼⠓⠉

Try To Figure These Out

⠼⠁⠃⠐⠖⠼⠉⠑ ⠐⠶ ⠼⠙⠛

12+35 = 47⠼⠑⠚⠐⠌⠼⠑ ⠐⠶ ⠼⠁⠚

50÷5 = 10⠼⠓⠐⠲⠼⠉ ⠐⠶ ⠼⠃⠙

83 = 24⠼⠊⠃ ⠈⠜ ⠼⠓⠉

92 > 83

Unification of Literary and Mathematical TextsUEB is designed to unify signs across literary

and mathematical contexts. Numbers, signs of operation and

comparison are the same in literary and mathematic textbooks.

⠠⠚⠥⠁⠝ ⠐⠖ ⠠⠇⠥⠏⠊⠞⠁ ⠐⠶ ⠠⠠⠞⠗⠥⠑

⠠⠠⠇⠕⠧⠑⠲

Juan + Lupita = TRUE LOVE.

Spacing of Math Problems

There is some flexibility in spacing. In general, spacing conforms to print. There is a preference to not have a space on

either side of a sign of operation and a space on both sides of a sign of comparison.

Spatial Equations

Linear

⠼⠙⠋ ⠐⠖ ⠼⠙⠁ ⠐⠶

⠼⠓⠛

Spatial

⠼⠙⠋

⠐⠖⠼⠙⠁

⠐⠒⠒⠒⠒

⠼⠓⠛

Spatial Equations: Following the Print

Align the numeric indicators on the left Align the numbers in columns Include a horizontal bar line that is at least as wide as

the problem ⠐⠒⠒⠒⠒⠒ Young children may need a wider horizontal bar line.

⠼⠁⠃

⠐⠤⠼ ⠙

⠐⠒⠒⠒⠒

⠼ ⠛

Spatial Equations: Use of Numeric Passage Indicator

Numeric passage indicator ⠼⠼Numeric passage termination sign ⠼⠄With this method, the numeric indicator is not

needed before each number.

Spatial Equations: Use of Numeric Passage Indicator Examples

⠼⠼

⠑⠊⠙ ⠐⠖

⠋⠉⠁

⠃⠉

⠐⠒⠒⠒

⠁⠃⠙⠓

⠼⠄

Simple Fractions and Mixed Numbers

⠌

Simple Numeric Fraction Line

⠸⠌

Forward Slash

Examples

2 1213

⠼⠁⠌⠉ ⠼⠃⠼⠁⠌⠃ ⠼⠃⠲⠑⠌⠉⠲⠑

2.53.5

Fractions

Most are written using the simple Numeric Fraction Line.

In fractions with numerals, there is no need to repeat the numeric indicator after the fraction line.

Decimal points and/or commas do not negate the numeric indicator.

Forward Slash and Fractions

Used when the print fraction is written with the numerator and denominator written horizontally or linearly instead of vertically.

5/6 of the class can go. ⠼⠑⠸⠌⠋ ⠷ ⠮ ⠉⠇⠁⠎⠎ ⠉ ⠛⠲

Numbers Used with Letters and Punctuation Marks

The numeric code indicator is TERMINATED by a space, hyphen, dash, apostrophe and colon.

The numeric indicator SETS GRADE 1. th and sh CANNOT be used for ordinal numbers. Use the grade 1 mode indicator when letters a-j

follow a number. 3.b ⠼⠉⠲⠰⠃ 3.m ⠼⠉⠲⠍report3.doc ⠗⠑⠏⠕⠗⠞⠼⠉⠲⠰⠙⠕⠉

Currency and Measurement

⠿⠈⠉ ⠈⠎⠿

cent sign ¢ dollar sign $

⠿⠈⠑ ⠿⠈⠇

euro symbol € British pound £

⠿⠶ ⠿⠶⠶

feet ‘ inches “

Examples

$11.50 ⠈⠎⠼⠁⠁⠲⠑⠚ 5’4” ⠼⠑⠶⠼⠙⠶⠶£100 ⠈⠇⠼⠁⠚⠚

£ and € credited ⠈⠇ ⠯ ⠈⠑ ⠉⠗⠫⠊⠞⠫

Special Symbols

⠿⠨⠴ ⠿⠘⠚ ⠿⠸⠪

percent % degrees o angle ⠠⠭ ⠊⠎ ⠼⠊⠛⠘⠚ ⠳⠞⠎⠊⠙⠑ ⠞⠙⠖

It is 97o outside today!⠸⠪⠠⠠⠁⠃⠉ ⠐⠶ ⠼⠙⠑⠨⠴

ABC = 45o

⠠⠊ ⠁⠍ ⠼⠊⠊⠲⠊⠨⠴ ⠎⠥⠗⠑⠲

I am 99.9% sure.

Parallel, Perpendicular and Basic Shapes

⠼⠇ parallel to ∥⠼⠤ perpendicular to⠫ shape indicator⠱ shape terminator⠫⠼⠉ regular (equilateral) triangle △⠫⠼⠙ square

⠫⠿ circle

Rules for Shape Indicators

Use the Grade 1 indicator before a shape indicator unless numeric mode is already set.

Do not use a shape termination sign if the shape is followed by a space.

Use a shape termination sign when the shape is followed by a punctuation mark or other symbols.

Examples

△ ABC ⠰⠫⠼⠉ ⠠⠠⠁⠃⠉

△ABC ⠰⠫⠼⠉⠱⠠⠠⠁⠃⠉

Notice how the second example is unspaced.

Superscripts and Subscripts (Level Indicators)

Superscripts have changed level up and are indicated by ⠔

3 ⠼⠉⠔⠼⠃

If letters are involved then the level indicator could be a contraction so a Grade 1 indicator is needed.

⠽⠰⠔⠼⠃

continue 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.

⠰⠰⠽⠔⠣⠐⠤⠼⠃⠜

⠰⠰⠭⠔⠣⠼⠙⠐⠖⠼⠑⠜

Notice that the Grade 1 word indicator covers all the possible contractions in this expression.

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

Provisional Guide in the Use of the Nemeth Code within UEB Context1. Any mathematical or chemical formula should be done in Nemeth Code. 2. All other text, including punctuation that is logically associated with surrounding sentences, should be done in UEB.3a. A mere mention of a number or a letter variable within an otherwise UEB context should be done in UEB.3b. When a comma or semicolon occurs between items that are to be transcribed in Nemeth Code, even if they could logically be regarded as belonging to the sentence structure, the comma or semicolon should be transcribed in Nemeth Code.

One word switch indicator To avoid use of switch indicators when a single word standing

alone occurs between two math expressions, a one-word switch indicator (6, 3 ,' ) may be used in Nemeth mode to indicate that the following word is in UEB.

(ax + by)(cx +dy), where ac = 12, bd = −10, and ad + bc = 7

(ax+by)(cx+dy), ,'":

ac .k #12, bd .k -#10, ,'&

ad+bc .k #7

Opening and Closing Nemeth Code Indicators Place the opening Nemeth Code indicator followed by a

space before the sequence to which it applies.

Opening Nemeth Code Indicator _% Closing Nemeth Code Indicator _:

Example

The result will be in the form (ax + by)(cx +dy), where ac = 12, bd = −10, and ad + bc = 7.

⠠⠮ ⠗⠑⠎⠥⠇⠞ ⠺ ⠆ ⠔ ⠮ ⠿⠍ ⠸⠩

⠷⠁⠭⠬⠃⠽⠾⠷⠉⠭⠬⠙⠽⠾ ⠸⠱⠂ ⠐⠱ ⠸⠩

⠁⠉ ⠨⠅ ⠼⠂⠆⠠ ⠃⠙ ⠨⠅ ⠤⠼⠂⠴ ⠸⠱⠂ ⠯ ⠸⠩

⠁⠙⠬⠃⠉ ⠨⠅ ⠼⠶ ⠸⠱⠲

He said, "4x+3y is the numerator." ⠠⠓⠑ ⠎⠙⠂ ⠦⠸⠩ ⠼⠲⠭⠬⠒⠽ ⠸⠱ ⠊⠎ ⠮

⠝⠥⠍⠻⠁⠞⠕⠗⠲⠴

Expressions on Multiple LinesWhen the Nemeth Code text is displayed on one or

more lines separate from the UEB text, the opening Nemeth Code indicator and the Nemeth Code terminator may each be placed on a line by itself or at the end of the previous line of text.

Example Solution. Again we group the first two terms and the last two terms.

4x3 − 12x2 − x + 3 = 4x2(x − 3) − (x − 3)= (x − 3)(4x2 − 1)= (x − 3)(2x + 1)(2x − 1)

⠨⠂⠠⠎⠕⠇⠥⠰⠝⠲ ⠠⠁⠛ ⠺⠑ ⠛⠗⠳⠏ ⠮ ⠋⠌ ⠞⠺⠕ ⠞⠻⠍⠎ ⠯ ⠮ ⠇⠁⠌

⠞⠺⠕ ⠞⠻⠍⠎⠲

⠸⠩

⠼⠲⠭⠘⠒⠐⠤⠂⠆⠭⠘⠆⠐⠤⠭⠬⠒

⠨⠅ ⠼⠲⠭⠘⠆⠐⠷⠭⠤⠒⠾⠤⠷⠭⠤⠒⠾

⠨⠅ ⠷⠭⠤⠒⠾⠷⠲⠭⠘⠆⠐⠤⠂⠾

⠨⠅ ⠷⠭⠤⠒⠾⠷⠆⠭⠬⠂⠾⠷⠼⠆⠭⠤⠂⠾

⠸⠱

Maybe, more questions than answers!

What are your questions?