[Fred Van Ackeren]

Hello Kyle,

Attached is a print page and my braille for spatial calculations that have comments following equations, all within a numerical passage.

Q: Is everything within a numerical passage in grade 1?

1) In this book there are several examples that have math comments like 300 X 32, would these be brailled w/o the numeric indicators?

2) can text comments be brailled contracted with a TN explaining that these comments are not in grade 1?

3) I used a key for the comments and to explain the down arrows showing numbers in the dividend moving.

Please review my braille to see if correct. In the GTM, there are no examples in spatial math for operation signs in division, so I used best judgement.

Thanks, Fred

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[Fred Van Ackeren]

Kyle,

I reupped the braille file.

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[kdejute]

Thank you for your question, Fred.

Though I do not doubt our braille-using friends, students, and neighbors would make sense of contracted comments within a numeric passage, I cannot recommend it.

A numeric passage indicator sets grade 1 mode until the numeric terminator ends that grade 1 mode (RUEB2024 §6.9.1). If we use contracted braille within a numeric passage, then we use symbols that have a grade 1 meaning in an environment that says their grade 1 meaning is what’s important.

In responses to your questions:

Q: Yes, everything within a numeric passage is in grade 1.

1) A math comment like 300×32, would be brailled without the numeric indicators within a numeric passage.

2) No. For the sake of clarity, translatability, and consistency, we should not braille text comments contracted within a numeric passage.

Regarding your key for comments: I really like your placements of the key letters (i.e., each following the quotient piece to which it applies). However, remember what RUEB2024 § says: “… any lowercase letter a-j is preceded by a grade 1 indicator.” Since you’ll have to use a grade 1 symbol indicator for each of those letters, I think you should get rid of the periods. Also, in your key listing, please check the formation (and grade 1 indicating) of your letters (especially the b). One more note: you do not need a blank line before the braille line that contains only a numeric terminator (GTM §4.1, last paragraph before 4.1.1).

In other words, regarding your #3, it is a good choice to use a key for the comments, and it seems practical to use a TN to explain the printed down arrows showing numbers in the dividend moving.

Last, but not least, I agree, spatial division with operation signs is challenging; I think you’ve done a very good job of aligning by place value and placing the symbols of operation where they apply.

Braille on!
–Kyle

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