Project Math Access

Teaching Mathematical Concepts

Basic Number Facts and Operations

Collaborative and Inclusive Strategies

The Personal Perspective of Abraham Nemeth

The procedures involved in multiplication will be presented using two different types of problems. The first involves a two-digit multiplicand and a one-digit multiplier. The second involves a two-digit multiplicand and a two-digit multiplier. The methods for multiplying larger numbers can be extrapolated from these two examples.

In the multiplication of a two-digit multiplicand and a one-digit multiplier, the item identifier is brailled. On the same line, the multiplicand is brailled, leaving two blank spaces between the end of the identifier and the first digit of the multiplicand. No numeric indicator is used anywhere in the problem.

The paper advance is tapped once. The carriage is positioned in the column containing the units digit of the multiplicand; the one-digit multiplier is written in that location. No multiplication sign is written preceding the multiplier. The paper advance is tapped twice, leaving a blank line under the main portion of the problem. The carriage is positioned so that it is "pointing" to the units column. The student can use his or her finger to easily determine whether the carriage is positioned correctly.

The next step is to multiply the multiplier times the units digit of the multiplicand. The result of that operation is brailled. The backspace key is struck twice to position the carriage correctly for the next step. If the result of the previous multiplication is a two-digit number, the tens portion of that number is held in memory by the student. As suggested earlier, if the student experiences difficulty holding the number in his or her memory, an abacus can be used to temporarily store it.

Once the student has multiplied the multiplier times the tens digit of the multiplicand, if a number were held in the student's memory or if it were stored on an abacus, it is added to the result; the units digit of that number is written. If a tens digit exists in this number, the backspace key is struck twice and that number is written. Once again, if the teacher deems it necessary, the student should advance the paper two lines, move the carriage to the far left and write: ans. = followed by the answer, with a numeric indicator preceding it.

#5. 267182ans. = 182

The following is a description of the procedure which should be used for a two-digit multiplicand and a two-digit multiplier. The multiplicand is brailled following the problem identifier. The paper is advanced once. The carriage is positioned in the units column. The two-digit multiplier is brailled immediately under the two-digit multiplicand. The paper is advanced two lines, leaving a blank line under the multiplier.

The carriage is positioned in the units column. The multiplication is carried out by multiplying the units digit of the multiplier times the units digit of the multiplicand. The units digit of the answer is brailled. The backspace key is tapped twice. If a tens digit exists in the answer, it is remembered by the student.

The units digit of the multiplier is multiplied times the tens digit of the multiplicand. If a tens digit exists in the previous multiplication, it is added to the answer and the units digit is written. If a tens digit exists in this result, the backspace key is tapped twice and the tens digit is written. The paper advance key is tapped once. The carriage is positioned in the tens column of the problem.

The tens digit of the multiplier is multiplied times the units digit of the multiplicand. The units digit of the resultant number is brailled. The backspace key is tapped twice. If a tens digit exists, it is remembered.

The tens digit of the multiplier is multiplied times the tens digit of the multiplicand. If a tens digit had existed from the previous multiplication, it is added to the result and the units digit of that result is written.

If a tens digit exists in the resultant number, the backspace key is tapped twice and it is written. The paper advance is tapped twice, leaving a blank line under the partial products. The carriage is positioned in the units column.

The single digit in the units column is written, and the backspace key is tapped twice. The numbers in the tens column are added, and the units digit of that result is written. The backspace key is tapped twice and the next column is added appropriately. This is done until all columns have been added. Once again, the paper advance key is tapped twice and the carriage is moved to the far left where ans. = followed by the answer, with a numeric indicator preceding it, is written. This procedure can be used with numbers of any size. The number of digits in the multiplier determines the number of partial products.

#6. 36472521441692ans. = 1692