When children learn about properties of individual numbers, it is convenient to have a counter which has such number as its value. So, besides standard two-color counters with the values 1 for the white and -1 for the red side, at least two or three other kinds of counters should be available. The teacher should assign letter names to these, such as a, k, p, x, or z. These names should be written as lower case letters.
All kinds of numbers can be assigned as values (for example, negative numbers, fractions, and irrational numbers). Counters with assigned values should be called "variable counters", because their values depend on the task in which they are used. On a counting board, the value of a variable counter is its current value multiplied by the location-value of the square it occupies. Let the counter t have value 5, the counter d have value -8, and the counter h have value 11. (5 * 11) + (6 * -8) + (6 * -8) + 2 = -39 (1 * 5) + (1/2 * -8) + (1/6 * 11) + (1/6 * 11) + (1/5 * -1) + (1/15 * 5) + 1/60 + 1/60 = 29/6 2t + 5t + d + -10 + -1 = 7t + d - 11. If t = 7 and d = -1/2, then the value of the board is (7 * 7) - 1/2 - 11 = 37 1/2. 6t + 6t + 12d + 5d + 12h + -2 + 1 + 30 = 12t + 17d + 12h - 2 + 31. If t = 2, d = 3/2, and h = -3, then the value of the board is (12 * 2) + (17 * 3/2) + (12 * -3) - 2 + 31 = 42 1/2. Number Board index |