Where's that Margin Again?
Displayed Material in UEB Math/Science
Jonathan Carson
Unlike Nemeth transcriptions, in which a displayed technical expression is presented on the next line indented 2 cells to the right of the previous line's runover position (and with its own runovers two cells to the right of that), UEB displayed material (whether it is technical material or literary material) follows the guidelines issued in Braille Formats: Principles of Print-to-Braille Transcription, 2016. For a basic, single displayed expression following a 3-1 or 1-1 paragraph, the formatting for a UEB technical expression is very similar to that of one in Nemeth, excepting that blank lines are needed both before and after the expression. So, for a print layout like the one shown here:
An equation is defined as a mathematical statement demonstrating that two expressions are equal.
2x+7 = 23
the braille would be presented as a 3-1 paragraph, followed by a blank line, followed by the 1-3 expression being presented with an adjusted margin of 2 cells from cell 1, making it 3-5:
,an equa;n is def9$ z a ma!matical /ate;t demon/rat+ t two expres.ns >e equal4
#bx"6#g "7 #bc
Keeping with basic paragraphs, when the displayed material contains subentries, the adjusted left margin would be based upon a 1-5, 3-5 basic layout. As such, when material is displayed following a 3-1 or 1-1 paragraph, the adjusted left margin would be 2 cells to the right of the paragraph's runover position (cell 1). Thus, the margins would now be 3-7, 5-7 for the print example shown below, and could look like this:
An equation with a single variable can be solved by isolating the variable on one side of the equation using inverse operations.
2x+7 =23 = 16 Isolate the term using ASPE. Subtract 7 from both sides. = 8 Isolate the variable using MDPE. Divide both sides by 2.
and the braille could be presented as:
,an equa;n ) a s+le v>iable c 2 solv$ by isolat+ ! v>iable on "o side ( ! equa;n us+ 9v]se op]a;ns4 #bx"6#g "7 #bc "7 #af ,isolate ! t]m us+ ,,aspe4 ,subtract #g f bo? sides4 "7 #h ,isolate ! v>iable us+ ,,mdpe4 ,divide bo? sides by #b4
However, as our endgame as transcribers always should be to best reflect the structure of the mathematics for the braille reader (regardless of print’s visual layout), with regard to linked expressions as in the example above, it might be best practice to follow Nemeth's formatting requirements and consider them as a displayed nested list with the anchor in 1-5 and its links in 3-5. Once the adjusted margin is taken into account, the layout would follow the same 3-7, 5-7 layout, albeit with an additional line break before that first equals sign and might be presented thusly:
,an equa;n ) a s+le v>iable c 2 solv$ by isolat+ ! v>iable on "o side ( ! equa;n us+ 9v]se op]a;ns4 #bx"6#g "7 #bc "7 #af ,isolate ! t]m us+ ,,aspe4 ,subtract #g f bo? sides4 "7 #h ,isolate ! v>iable us+ ,,mdpe4 ,divide bo? sides by #b4
Moving on to itemized material, when there are no subentries, the runover position of the itemized material would be cell 3, and thus, the adjusted left margin would begin in cell 5.
1. Solve the following equation.
2x+7 = 23
Following the itemized directive, the braille for the displayed equation would begin in cell 5, preceded by a blank line:
#a4 ,solve ! foll[+ equa;n4 #bx"6#g "7 #bc
However, if the displayed material to a 1-3 itemized problem is not a single expression but, say, a word problem, the adjusted left margin would remain the same (cell 5) but the beginning of the displayed material would be determined by the indent level of the paragraph. Thus, if the displayed paragraph is blocked, then the adjusted margin to a 1-3 itemized question would be 5-5. However, if the displayed text is indented, as in the example below, the displayed text must be presented in 7-5.
1. Solve the following word problem.
Sam likes fruit. He has seven apples. He also has some oranges. Marta gives him the same amount of oranges. Sam now has 23 fruit in all. How many oranges did Sam have at the beginning?
#a4 ,solve ! foll[+ ^w problem4 ,sam likes fruit4 ,he has sev5 apples4 ,he al has "s oranges4 ,m>ta gives hm ! same am.t ( oranges4 ,sam n[ has #bc fruit 9 all4 ,h[ _m oranges did ,sam h at ! 2g9n+8
Oftentimes, an itemized question with no subentries will consist of the itemized material, followed by displayed text or technical material, followed by a continuation of (or an additional paragraph to) the original material, as shown here:
1. Read the following word problem.
Sam likes fruit. He has seven apples. He also has some oranges. Marta gives him the same amount of oranges. Sam now has 23 fruit in all. How many oranges did Sam have at the beginning?
Jonathan did not solve the word problem correctly. What did Jonathan do wrong?
½x + 7 = 23
½x = 16
½x × 2x = 16 × 2x
x=32
Show how to solve the word problem correctly.
Breaking this down piece-by-piece, as it has no subentries, the initial line will be transcribed as 1-3. The adjusted margin for the displayed paragraph will be 7-5, the additional paragraph to the initial itemized material will be 5-3, followed by the displayed equations in 5-7, followed by the continuation of the additional paragraph in cell 3. Both the displayed paragraph and the displayed equations will need blank lines both before and after them.
#a4 ,r1d ! foll[+ ^w problem4 ,sam likes fruit4 ,he has sev5 apples4 ,he al has "s oranges4 ,m>ta gives hm ! same am.t ( oranges4 ,sam n[ has #bc fruit 9 all4 ,h[ _m oranges did ,sam h at ! 2g9n+8 ,jona?an did n solve ! ^w problem correctly4 ,:at did ,jona?an d wr;g8 #a/bx"6#g "7 #bc #a/bx "7 #af #a/bx"8#bx "7 #af"8#bx ;x "7 #cb ,%[ h[ to solve ! ^w problem correctly4
Taking this same problem and modifying it slightly, when itemized material has subentries, the adjusted margin for any displayed material remains two cells to the right of the itemized material's runover position. Thus, in a 1-5, 3-5 nested problem as below, the adjusted margin would begin in cell 7. Consequently, a displayed paragraph's margins would now be 9-7, while a displayed series of equations would be 7-9, as shown in the following example:
1. Read the following word problem.
Sam likes fruit. He has seven apples. He also has some oranges. Marta gives him the same amount of oranges. Sam now has 23 fruit in all. How many oranges did Sam have at the beginning?
a. Jonathan did not solve the word problem correctly. What did Jonathan do wrong?
½x + 7 = 23
½x = 16
½x × 2x = 16 × 2x
x=32
b. Show how to solve the word problem correctly.
#a4 ,r1d ! foll[+ ^w problem4 ,sam likes fruit4 ,he has sev5 apples4 ,he al has "s oranges4 ,m>ta gives hm ! same am.t ( oranges4 ,sam n[ has #bc fruit 9 all4 ,h[ _m oranges did ,sam h at ! 2g9n+8 a4 ,jona?an did n solve ! ^w problem correctly4 ,:at did ,jona?an d wr;g8 #a/bx"6#g "7 #bc #a/bx "7 #af #a/bx"8#bx "7 #af"8#bx ;x "7 #cb ;b4 ,%[ h[ to solve ! ^w problem correctly4
Whew. And that is it for today's rundown of the increasingly complex layout of modern mathematical textbook materials in print and how they might be transcribed into braille. May your braille be perfect and may your margins always be correctly adjusted.
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