Using different counting boards can be confusing because two rules of regrouping, 5 = 4 + 1 and 3 = 2 + 1, are used together on both of the 3 by 4 boards.
Working with these boards is not essential for learning any specific arithmetic algorithm. But it provides the opportunity to get familiar with individual whole numbers up to one hundred and some small fractions. (Such knowledge is commonly called "number sense".) The logical structure of arithmetic requires that such activities include using negative numbers. So in all activities, red counters must be used only for negative numbers, and white counters only for positive numbers. Activities For the Four Small Boards In all activities below students may put only one counter on each square. Task 1 Find all configurations representing zero on the 2 by 2 and 3 by 2 boards. Represent all numbers from 1 to 100 with the smallest possible number of counters on the 3 by 4 integer board. (Use both white and red counters.) 29 = 30 - 1 87 = 60 + 30 - 3 Represent all fractions 1/60, 2/60, ..., 59/60 with the smallest possible number of counters on the 3 by 4 fraction board. (Use both white and red counters.) 19/60 = 1/3 - 1/60 51/60 = 1 - 1/10 - 1/20 Number Board index |