Unified English Braille For Math
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1 Unified English Braille For Math For Sighted Learners By Heather Harland & Cheryl Roberts 1
2 UEB Braille for Math Previously braille readers used the Nemeth code for math and literary braille code numbers for most other things. With the implementation of UEB, numbers will remain the same regardless of subject and are positioned in the upper section of the braille cell. Braille numbers are written by putting a number sign in front of the first 10 letters of the alphabet. # a b c d e f g h i j # Examples: #cei #adgb #i1hjd ,804 Math Symbols "6 "- "8 "/ "7 + - = dots 5, dots 5,3-6 dots 5, dots 5, 3-4 dots 5, Note: The number sign must appear before each number. The number sign no longer carries through a hyphen or equation. The addition, subtraction, multiplication, division and equal sign are two cells each. For young students, there is a space before and after each of these math symbols (Manitoba Variation). Examples: #ej "6 #aj "7 #fj = 60 #c "8 #h "7 #bd 3 8=24 #ag "6 #ab "7 #bi = 29 2
3 #ib "- #fh "7 #bd = 24 #ea "/ #c "7 #ag 51 3=17 #be "8 #d "7 #ajj 25 x 4 = 100 PRACTICE 1 Interline the following. #e "/ #a "7 #e #f "- #c "7 #c #ae "/ #c "7 #e #c "8 #d "7 #ab #a1bjj "6 #de "7 #a1bde #af "6 #f "7 #bb #d "- #d "7 #j #e "8 #c "7 #ae PRACTICE 2 - Braille the following. 2-1 = 1 7, =7, =2 24 6=4 3 x 7 = 21 2x9 = = =14 3
4 Decimals The Decimal is now represented with dots 2-5-6, the same as a period #a4be I need cups of flour.,i ne$ #b-#c4e cups ( fl\r4.8 is a decimal between 0-1. #4h is a decimal 2t #j-#a4 Dollar Sign The Dollar Sign is represented with dots 4, $3.45 4
5 Spatial Addition Decimals (dots 2-5-6) must be lined up. #dbc " # e 5 "333 # 4cd.34 #g4h 7.8 "6#c4jd "3333 Numbers are always lined up to the right unless there is a decimal; number signs are lined up on the left. Operations symbols (+ - x etc) can appear to the immediate left of the last listed number, or at the top right or left of the top number with one empty cell between. When you are brailling for your student, choose the placement they prefer, and use it consistently. Separator lines extend the length of the numbers, dots 5, 2-5. "6 #dg + 47 #dd 44 A "33 #Ia 91 1 carry over A line is often left as room to indicate carry over between the question and the answer. When you braille math for your student, you only need to braille the basic question, without the separation line. Your student will add the separation line, additional lines and answer as they work through the question. i.e "6 #ce #ab 5
6 Spatial Subtraction with Cancellations/Borrowing "- #hbef On the braille page, the question appears like #bcdg this: A a "3333 "- #hbef #eiji #bcdg The student adds the borrowing indicators, separation line and answer In UEB, a note is made below the question, above the answer to indicate borrowing. As the user advances to each place value, they will need to check for a borrowing indicator and subtract, if required. 6
7 Spatial Multiplication Should it not be practical to place number signs in front of every number in a spatial layout, numeric passage indicators may be used to show that the following selection is entirely numbers. Spatial multiplication and division will often use numeric passage indicators. ## Numeric Passage Indicator #' Numeric Passage Indicator Terminator ## A line or more is left between the question and the answer as room to indicate carry over as a result of multiplying. bgjd " x ab 12 a line for carryover when multiplying the 2 line for carryover when multiplying the 1 "333 edjh 5408 bgjd 2704 a 1 carry over from addition "33333 cbddh #' 7
8 ## "8 bcab Fe A a a a "33333 aaefj achgb aa "33333 aejbhj x carryover when multiplying the carryover when multiplying the carryover when adding #' 8
9 Spatial Division Method 1 ## ic " e _ dfe de 45 " ae 15 ae #' 0 Method 2 ## e _ dfe _i de 45 " ae _c 15 3 ae ans3 #ic Ans : 93 #' 9
10 PRACTICE 3 Interline the following. "6 #bb,- #ea "8 #bc #ah #ce # f a a aa "33 " #dj #af #ach ## ee "3333 e _ bde be "33 ae ae "3 j #' (Yes, the student got the answer wrong! Our job here is only to interline for the teacher.) PRACTICE 4 Braille the following. Braille the operation signs at the top left of the question x
11 Omitted Numbers An Omission mark shown as an underscore is represented by dots 4-6, The underscore will be the most common form of omission you will likely see in classroom materials. PRACTICE 5 - Braille using the underscore = 10 x = 50-5 = = 8 + = 15 x 6 = 24 PRACTICE 6 - Interline the following. #c.- #g "7 #aj #e "6 #aa "7.- #df "- #be "7.- #ef "/.- "7 #h.- "8 #h "7 #gb 11
12 Fractions The Simple Fraction Line is represented with dots 3-4. / _5_ 8 of the class are boys. #e/h (! class >e boys #aa/b #b/f #e/h #i/d A mixed number is considered like two numbers for use of the number sign. I need 2½ cups of flour.,i ne$ #b#a/b cups ( fl\r4 3 ½ 4 ¼ #c#a/b #d#a/d When a fraction is written in a linear fashion, an ordinary slash mark (an oblique stroke) is used, dots 4-5-6, 3-4, _/ and a second number sign is added after the oblique stroke. 3/8 of the class are girls. #c_/#h (! class >e girls4 12
13 ;; Two Grade 1 Indicators means the whole word should be read as uncontracted braille. ; One Grade 1 Indicators means only the next cell should be read as uncontracted braille. Any fraction more complicated than the previous examples or which includes letters or words requires the use of a General Fraction Line instead of a simple fraction line and General Fraction Opening and Closing Indicators. General Fraction Indicators can be confused with the contractions for of or with so as you braille for your student, consider whether you will need one or more grade 1 indicator at the beginning of a fraction containing letters../ General Fraction Line, dots 4-6, 3-4. ( General Fraction Open indicator, dots ) General Fraction Close indicator, dots x 1 3 y x b ;;(x./y) ;(#a./x) ;(#c./b) distance time ; (4t.e./ "t;) If a number sign immediately follows the General Fraction Open Indicator only one Grade 1 Indicator is needed at the beginning to designate that this passage is dealing with numbers and uncontracted braille. 13
14 Spatial Fractions "8 #aa/ab x 11/12 # b/d 2/4 These are examples of fractions aligned spatially. "6 #aa/b + 11/2 # c/h 3/8 ## #' a a b c e "3 "6 "3 "7 "3 "6 "3 "7 "3 3 b f f f = + = This is a spatial fraction. This format can be very useful when a student is first learning. 14
15 PRACTICE 7 Interline the following. #a/c #c/e #a#a/b ;;(x./y)"8#b #b_/#aj ;(#b./c) ;(m"oy./ "t;) PRACTICE 8 Braille the following. 2 x 8 fun /16 3 b x work z
16 Exponents/Superscripts An exponent or superscript has a special symbol in front of it so the braille reader knows that it is "up in the air." That symbol is written using dots 3-5 followed by the number. 9 If the symbol is following a letter, a grade 1 indicator is needed to ensure that the letter and indicator are not read as a word. e.g. read as bin2 instead of b x 2 #e9#b x;9#b Subscript Subscript is represented with dots As with superscripts, if the subscript symbol follows a letter, a grade 1 indicator is needed to ensure the letter and indicator are not read as a word. e.g. read as Hen2O instead of H 2 O H 2 O CO 2,h;5#b,o,,co;5#b 16
17 Algebra Parenthesis Opening ( "< "> ) Closing a(1+3) = 8 a"<#a"6#c"> "7 #h Grade 1 Indicators are used to specify letters instead of numbers or contractions when a letter stands alone or when the letters a-j follow a number. y = x+4c ;y "7 x"6#d;c x 2 + 2x 1 + x 2 =1 ;;;(x9#b"6#bx./#a"6x9#b) "7 #a;' The Grade 1 Passage Indicator (dots 5-6, 5-6, 5-6) can be used to indicate that a passage should be read entirely as uncontracted braille, that is, letter for letter. The specified passage ends when the reader encounters dots 5-6, 3. This symbol represents the Grade 1 passage terminator. ;;; The Grade 1 Passage Indicator means the whole passage should be read as uncontracted braille. ;' This symbol is used to end the effect of the grade 1 passage indicator. The passage is finished. 17
18 Algebra - Putting it all together Example: EXAMPLE 6. Factor 12x 2 + 7xy 10y 2. The plus, minus, and equals signs are shown in red. The superscript indicator is shown in green.,,example #f4,factor #abx;9#b"6#gxy"-#ajy;9#b4 Grade 1 passage indicator is used in this example: 3x-4y+y 2 = x 2 ;;;#cx"-#dy"6y9#b "7 x9#b;' 18
19 UEB Braille Notes Addition + dot 5, "6 Subtraction - dot 5, 3-6 "- Division Linear: dot 5, 3-4 "/ Multiplication x dot 5, "8 Equals = dot 5, "7 Separation line dot 5, 2-5 " Vertical line segment for spatial work dot Decimal. dot _ Spatial: "33333 _ Used to separate spatial math questions from work and answers. Omission Underscore dots 4-6, Fraction lines Simple dots 3-4 / General./ General Fraction Opening ( indicators Closing ) Grade 1 Indicator Symbol ; dots 5-6 Word ;; Parenthesis Opening ( dots 5, "< Superscripts, Exponents & Subscripts Superscript & 9 Exponents Greater than > dot 4, Less than < dot 4, Passage ;;; ;' Terminator Closing ) dots 5, "> Subscript 5 19
20 ANSWERS PRACTICE 1 Interline the following. 5 1 = = 3 #e "/ #a "7 #e #f "- #c "7 #c 15 3= 5 3x4=12 #ae "/ #c "7 #e #c "8 #d "7 #ab 1, = 1,245 #a1bjj "6 #de "7 #a1bde 16+6 = =0 #af "6 #f "7 #bb #d "- #d "7 #j 5x3 = 15 #e "8 #c "7 #ae PRACTICE 2 - Braille the following. 2-1 = 1 #b "- #a "7 #a 7, =7,000 #g1ejj "- #ejj "7 #g1jjj 6 3=2 24 6=4 #f "/ #c "7 #b #bd "/ #f "7 #d 3 x 7 = 21 2x9 = 18 #c "8 #g "7 #ba #b "8 #i "7 #ah 25+9= =14 #be "6 #i "7 #cd #d "6 #aj "7 #ad 20
21 PRACTICE 3 Interline the following. "6 #bb + 22,- #ea - 51 "8 #bc #ah 18 #ce 35 # f 1 a a aa "33 " #dj #af #ach x ## ee "3333 e _ bde be "33 ae ae "3 j #'
22 PRACTICE 4 Braille the following x "8 #bf "6 #dc "- #ih "3333 #ae #he #fd #D _ #ab PRACTICE 5 - Braille using the underscore = 10 x = 50 #e "6 #h "7.- #aj "8.- "7 #ej -5 = =.- "- #e "7 #ib #ab "- #b " = 15 x 6 = 24 #h "6.- "7 #ae.- "8 #f "7 #bd PRACTICE 6 - Interline the following. 3 7 = = #c.- #g "7 #aj #e "6 #aa " = 26 = 8 #df "- #be "7.- #ef "/.- "7 #h x 8=72.- "8 #h "7 #gb 22
23 PRACTICE 7 Interline the following ½ x 3 5 y x2 #a/c #c/e #a#a/b ;;(x./y)"8#b 2/10 2 money c time #b_/#aj ;(#b./c) ;(m"oy./"t;) Practice 8 Braille the following. 2 x 8 3 b x #b/c ;;(x./b) ;(#h./x) or ;(x./b;) fun 1 23 work z 100 ;(fun./"w;) or ;(#a./z) #bc/ajj ;;(fun./work) 9/16 #i_/#af 23
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