The Brannan Cubarithm slate and cubes comprise a system that allows the user to enter and manipulate numeric symbols. The slate consists of a 16 by 16 grid of square cups. Plastic cubes with braille markings are placed in these cups. Each cube has six faces. Five of these faces have raised dot characters from which selections can be made to produce the digits 0 through 9. The sixth face of each cube has three raised dots. Depending on the orientation of this face, these dots can be thought of as the braille letter "o" (dots 1, 3 and 5) or the braille "ow" sign, (dots 2, 4 and 6). This sixth face also can be oriented so that its three dots can resemble an up-arrow or a down-arrow.
The use to which this slate is put depends on the needs and abilities of the user. While one can use it to set down numbers during a calculation, it may be of greater value as the means of displaying the format of a problem. At best, the process of entering numerals is slow. First, One must pick up a cube. Then, the face appropriate to the task at hand must be positioned so it is facing upward. Then, the dot pattern on that face must be rotated horizontally so that its pattern of dots represents the desired digit. For example, one face of the cube has a three dot pattern. Once this pattern is facing up, rotating the cube horizontally can orient the pattern to produce the digit 6, 8, 4 or 0.
The three-dot pattern already mentioned (braille letter "o" or "ow") can be used by a student or teacher to represent a special symbol (plus, minus, times or divided by). This can be a matter of agreement among those concerned with the processes being performed or studied.
As an example of problem layout, consider a short exercise in addition. First, we need to orient ourselves to the slate. Since it is square, it can be set down with any of its four sides as the upper edge. However this is done, let us call the vertical rows letter rows and the horizontal spaces along each row number spaces. Thus, The upper left square is row A column 1. The lower left square is P1. The upper and lower right squares A16 and P16 respectively.
The problem we will consider is 123+456+789.
On A7, A8 and A9, set 123. On B7, B8 and B9 set 456. On C7, C8 and C9 set 789. For the present, skip D7, D8 and D9. On E6, E7, E8 and E9 set 1368.
Now, return to row D and on D5, D6, D7, D8 and D9 set five cubes oriented so their two-dot patterns represent dashes. Once this is done, you have the layout of the problem, a line of separation between terms to be added and the result.
In the study of fractions, spatial orientation is important. in the case of a pure fraction, the numerator can be shown on a line while the denominator is shown two lines below with a blank line between. In the case of a mixed fraction, the whole number is shown on one line while the numerator is one line above and one space to the rightof the last digit of the whole number. The denominator is one line below and one space to the right of the last digit of the whole number.
Consider the mixed fraction 22-5/7. On spaces G7 and G8 set 22. On F9 set 5 and on H9 set 7.
The Cubarithm Slate is a device that permits students and teachers to make maximum use of imagination.
Brannan Cubarithm Slate, APH catalog number 1-00320-00. Cubes for Brannan Cubarithm Slate, catalog number 1-00330-00.
Contributor: Fred Gissoni