Number Line Question

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    Lucas Timpe


    We're transcribing an algebra book and ran into an issue. We have a number line with a, zero, and negative a on it. The positive a requires a grade 1 symbol indicator on it but how would I let the student know that the negative a is not a negative one? Would you put a grade 1 word indicator before the negative sign? Let us know what you would recommend please. I have attachments below.


    Thank you for your time.

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    Great question. Thank you, Lucas.

    Personally, I would put a grade 1 symbol indicator between the minus symbol and the letter. But I have cross-posted this question in NBA's tactile graphics forum so we can get further input. In that forum, the question is titled Number Line Question, negative lowercase letter below number line.


    Donald Winiecki

    The TG Skills Group agrees with Kyle's assessment that the grade 1 indicator should be placed between the minus sign and the letter "a." This is consistent with section 4.1 of the Guidelines for Technical Material (GTM) indicating "...any lowercase letter a to j is preceded by a grade 1 indicator." (The context of your TG is different from the specifics of GTM 4.1, but maintaining consistency throughout our use of UEB is definitely a good thing for braille readers!)

    In addition, we would like to offer some advice on your draft TG of this number line. There are a number of issues we want to comment on. All of these come from a comparison of the original print number line (Figure 1) and the draft TG (Figure 2) provided as pictures in the original Ask an Expert (AaE) question that was posted in the "UEB Technical" AaE forum.

    We close with some additional information that may be useful with other TGs in the algebra book you are transcribing.

    Four figures are referenced throughout our response. Those figures are attached to this post.


    1. First, the original print number line (Figure 1) shows that the line segment between the hollow circles at "-a" and "a" is bolded.

    In the draft TG (figure 2), (a) the desired segment of the line is not bolded, and instead (b) the bolded line segments are placed "outside" of the hollow circles toward the arrow heads.

    Please change the TG so that the bolded line segment is placed between the hollow circles.


    2. Second, in the original print graphic (Figure 1), the dashed scale lines drawn upwards from the number line at "-a" and "a" are centered at the hollow circles.

    However, in the draft TG (Figure 2), the hollow circles are drawn <i>inside</i> the scale lines.

    Please change the TG so that the hollow circles are centered at the scale lines.


    3. Third, in the interest of adding a little bit of information that may be helpful when preparing other TGs for this book, in the language of mathematics, when all or part of a number line (including termination points) is bolded it means that the number line values associated with those bolded items are included in the solution set. In the print graphic (Figure 1) the number line is bolded, but the"hollow circles indicate that the plotted points are not included in the solution set. (In the print graphic (Figure 1), the scale marks are the vertical dashed lines extending upward from the number line.) See GSTG for more details on this.

    NOTE: In the vocabulary of GSTG, the number line is "bolded" or not, as noted above. The circles that denote the ends of a line segment are "solid" or "hollow" and these are analogous to a line being bolded or not-bolded in order to indicate if those points are included in the solution set or not. Examples shown in GSTG illustrate this.


    4. Fourth, more additional information related to the placement of labels on a number line. See GSTG 6.5 and examples provided in GSTG for illustrations of the following.

    According to GSTG, "Variables (usually lowercase letters) representing omitted numbers or any real number should be placed below the number line." The draft TG (Figure 2) shows the proper placement below the number line.

    However, also indicates that the first numeral or first alphabetic symbol of a label should be aligned with the scale line. The draft TG (Figure 2) shows misalignment of these labels.

    NOTE: In contrast, if a label or sign of omission represents a plotted point on a number line (i.e., with a solid circle), the label should be moved above the number line regardless of placement in print. See the examples provided at GSTG 6.5 for specifics. While this doesn’t apply to the current examples or question, it probably occurs elsewhere in the textbook being transcribed.

    Please change the TG so that the labels are properly aligned under the scale lines.


    5. Finally, included here (Figure 3) is an example showing how we recommend the whole TG should be represented, if a raised line drawing is used.

    Because this is an algebra book, we are pretty confident that students using this book are older than grade 3. GSTG requires use of raised line graphics for grades 3 and below, and allows braille line mode for higher grades. If braille line mode is used for the number line, Figure 4 shows our recommendations.

    Following GSTG, line mode symbols should be included on the special symbols page if they occur frequently in the book. If the symbols are used only infrequently, place them in a TN directly before the TG.

    See GSTG 5.13.2 for considerations when categorizing symbols on the Special Symbols Page. In this case, categorization is required.

    Both Figure 3 and Figure 4 include all of the details identified above.

    NOTES: For Figure 4.

    When using UEB-Technical:

    a. the braille "y" is used for hollow dots and placed above the number line. If solid dots are shown in the print version, use the full braille cell (dots 123456) and place it above the number line. See GTM 4.4.1, p. 28.

    b. the braille "w" is used for tick marks along a number line. See GTM 4.4.1, p. 28, and Rules of UEB 16.2.

    c. line mode arrowheads are as shown in Figure 4. See GTM 13.1.


    We hope this answers your questions and adds information that will help in the future!

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