In grades 3-5, algebraic ideas should emerge and be investigated as students: (a) identify or build numerical and geometric patterns; (b) describe patterns verbally and represent them with tables or symbols; (c) look for and apply relationships between varying quantities to make predictions; (d) make and explain generalizations that seem to always work in particular situations; (e) use graphs to describe patterns and make predictions; (f) explore number properties; and (g) use invented notation, standard symbols, and variables to express a pattern, generalization, or situation.