Some patterns resulting from certain operations on numbers are discussed, analyzed, and explained. A method for predicting the outcome of these operations for any number is developed.

Learning activities are given for instruction in the skill of associating numbers with sets of dots, a skill intermediate between counting and higher number concepts. (MP)

Completing these worksheets leads students to discover patterns in the distribution of even numbers and numbers obtained by successive additions of 9 (primary grades). Worksheets for intermediate grades involve counting the number of factorizations for integers, and addition of the first nine whole numbers. (SD)