base-10 blocks in place-value tables

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    Chris Clemens

    This inquiry is also posted in Tactile Graphics.

    I have several math books to asses, and I wanted to get some feedback regarding treatment of base-10 blocks as presented in these texts.

    Images of these blocks are shown stacked, offset, and in the columns of a place-value chart. (a representative sample is attached)

    As you can see, the steps of subtraction, including regrouping, are illustrated by groups of blocks being moved from one column to the next and "dismantled."

    In the example, 500 is shown as four 100-piece blocks stacked offset, and one 100-piece block circled, with an arrow pointing to the tens' column of the place-value chart. Then, the whole chart is repeated, with only the offset stack of four, 100-piece blocks in the hundreds' column, and ten new 10-piece blocks in the tens' column. Then the whole arrangement is printed again, but this time the appropriate amount 10-piece blocks appear with a red X showing that these can now be subtracted. (It should be noted here that this print page is the the end of Step 2: which started on the previous print page.)

    While I realize that for this grade level, these images should be reproduced as a tactile drawing, help me understand how spreading this across dozens of pages of Braille enhances communicating this relatively simple concept.

    Has anyone come up with a compact Braille representation, tactile or otherwise, that can communicate the intent of these images while also keeping related information on the same Braille page?

    I appreciate any and all input, even if it is not "officially sanctioned" by NBA.


    Dave R

    Chris Clemens

    I recently transcribed a book with these types of base-10 blocks showing borrowing and carrying. I did them as tactiles so obviously I don't have a better suggestion for you. I can't advocate for anything other than the sanctioned way. Perhaps someone else can offer a suggestion?


    Thanks for the response, Ms Worthington. As well as the call for Community replies. I hope I'm not being perceived as some sort of Braille rebel, refusing to comply with accepted norms.

    I've considered using shape indicators.


    [simbraille]$hn $tn $on[/simbraille]
    [simbraille]$hn $tn[/simbraille]
    [simbraille]$hn $tn[/simbraille]

    for 431. OR, possibly using numbers, which I considered inferior because [simbraille]$100[/simbraille] implies a 100-gon.

    Nemeth code allows for creating shapes for "Moon" and "Church," why not base-10 shapes?

    My contention: Even though print shows 100 individual blocks that potentially could be counted by a sighted reader, with a microscope and a sharp pencil, I'll wager the vast majority of readers encounter the shape and translate it to "100" as readily as I translate "100". Further, the accepted method requires a student to "carry" across the boundaries of a braille page, whenever tactile representation in base-10 blocks wont fit on one page, which is often.

    I would introduce the format via TNote, after showing the NBA method: one page for 400, and one page for 31. I can easily adapt this method to the cubes used to represent 1000 as well. I feel this would be more effective than showing top/front/side views of the identical 10-by-10 faces of the 3-dimensional 10-by-10-by-10 cube that are required to represent it in the approved method.

    I am hoping for some feedback from any braillist willing to attack my thinking here.

    I realize that I don't have experience teaching VI students, so my thinking process likely missed many pedagogic considerations, so I'd especially appreciate feedback from educators.

    Thanks, in advance, for any feedback.

    Lindy Walton

    Dave, I absolutely approve of your idea. Teachers are instructed to provide students with the actual interlocking cubes when learning this concept. I do not understand the need for the braille reader to transfer that 3-dimensional tactile experience with a tactile graphic on the page. Sighted students look at those diagrams and think "100" or "10" or "1," they are not counting each block. We are slowing down our students' ability to enjoy this same experience by creating unwieldy graphics out of these -- some of which can take up several pages.

    However, the warning must be understood that, once we have a BANA rule or guideline for specific items, this is how they will be produced on the standardized tests. We do our students a disfavor when we do not follow those guidelines in their daily work. I do think this topic of grouped counting cubes needs to be reassessed.

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