Assessment Problem:

Find the next term:

a) 1, 2, 4, 8, …

b) 1, 3, 6, 10, …

c) 1, 4, 9, 16, …

d) 1, 1, 2, 3, 5, …

Common Responses:

a) 16, 32 (48%, 82%); 10 or 12 (23%, 11%)

b) 15, 21 (60%, 77%)

c) 25, 36 (41%, 64%)

d) 8, 13 (14%, 37%)*

Mathematical Issues:

Algebraic thinking is, at least initially, generalization. Researchers suggest that generalizing occurs in three stages: 1) seeing (recognizing the pattern), 2) saying (verbalizing a description), and 3) recording (creating a written representation).

Domain:

Variables & Expressions

Theme:

Pattern Completion

Common Core Standards:

F-LE: Linear, Quadratic, and Exponential models

Research References:

[iv] Mason(1996), p. 74. [v] Mason (1996), p. 65. [vi] Kaput (1999), p. 137.