Teaching and Learning of the Nemeth Braille Code

Teaching and Learning of the Nemeth Braille Code n Superscripts n Subscripts

Definition of Terms 3 Level Indicators n The normal level of writing is called the “base line” dot 5 " n Superscript – above baseline, raised dot 4 -5 ^ n Subscript – below baseline, lowered dot 5 -6 ;

Examples x 3+7 n yf n x-5 n x 2+1 n n n (x 2+y 2) x^3"+7 y; f x^-5 x^2"+1 ? 1/x^2"# (x^2"+y^2")

Left Superscripts and Subscripts Use level indicator first, then subscript or superscript symbol, then base line indicator, and finally the symbol on the baseline. n Not used very often. n

Examples n –x b a n cd n left superscripts and subscripts ^-"x ; a"b ^c"d

Hierarchy of Superscripts and Subscripts First Order – one level from base line n Second Order – two levels from base line n Etc. n

Examples n n hierarchy of scripts x; 2; ; r y^n^^2 a; x; ^y b^x^; y

Numeric Subscripts n Do not use a subscript indicator if the subscript n Is Numeric n Is First Order n n n Is associated with an abbreviated function name or a letter which has a separate identity Doesn’t have its own subscript or superscript Note: A prime (’) is not considered a superscript

Examples x 5 n y’ 3 n a’’ 4 n n 10, 000 n log 3 x n log 28 n of numeric subscripts x 5 y'3 a''4 n 10, 000 log 3 x log 2 #8

Numeric Subscripts and the Base Line Indicator n The baseline indicator is not needed after a numeric subscript (x 2 – x 1)2 + (y 2 – y 1)2 n (x 2 -x 1)^2"+(y 2 -y 1)^2 n n n M. k ? y 2 -y 1/x 2 -x 1#

Why Do These Need Subscript Indicators? n 3 x 127 n x 2’ n x 2+k n seven 3 n ; 3"x #12; 7 x; 2' x; 2+k seven; 3

Use of the Multipurpose Indicator with Subscripts n The Multipurpose Indicator, dot 5, must be used between a numeric subscript and a numeral which follows it on the baseline. n C 0102 + C 110 + C 2 n , c 0"10^2"+, C 1"10+, c 2

Changes of Level n #1 No base line indicator is needed if the PI follows the superscript or subscript Find the value of x 3. n , f 9 d ! Value ( x^3_4 2 n x ’s n x^2_'s n

Changes of Level n No base line indicator is needed if a comma follows the superscript or subscript n n #2 x 2 , x 3 x^2, x^3 A comma within a long numeral does not have the same effect. Why? n X 16, 000 + ? X^16, 000"+=

Changes of Level n #3 No base line indicator is needed if a space or transition to a new line comes after the superscript or subscript and is followed by literary text, unrelated mathematical material, or a comparison symbol #2 p^2 is alw ev 54 #2^x "k #3^x n 2 p 2 is always even. n 2 x < 3 x n Conversion of a base 5 numeral to a base 10 numeral: 2341 5 = 2∙ 53 + 3∙ 52 + 4∙ 51 + 1∙ 50 , 3 v]. n (a base #5 num]al 6 a base #10 num]al 3 #2341; 5. k #2*5^3"+3*5^2"+4*5^1 "+1*5^0_4

Changes of Level n #4 A space after a symbol of shape or an abbreviated function name preserves the level already in effect, but if these items carry a superscript or subscript, the space following it reinstates the level that was in effect before 2 n cos x cos^2 x n A∆ABC , A; $t , a, b, c

Changes of Level n #5 Contractions may not be used in a word or abbreviation in contact with a level indicator. n 13 seven n #13; seven 2 n inch-pound n 9*-pound^2

Degree Symbol n The small hollow dot used in print as the sign for “degrees” is a superscript. n Hollow Dot . * 90 + 90 = ? n #90^. *"+90^. *. k =^. * n

Assignment n p. 74 all