Students interact with geometric and algebraic patterns of the rectangular and triangular number patterns. Geometric, algebraic, tabular, graphical, and numerical forms of the triangular numbers are presented. Students are able to scroll through the various representations to compare the relationships. Regression equations are used to extend the patterns to quadratic functions for predicting real number relationships to the area patterns. An animated puzzle pattern is given for investigation.

Copy TI_Nspire file to student calculators. Have viewscreen or multi-media projector available to display activity to class.

Students should work in pairs through the calculator activity with whole class discussion as needed.

Students should have written notes to summarize their observations and to study for follow-up discussion, project, or quiz.