When introducing a more formal method of communicating, such as the language of algebra, it is helpful to revisit some of the situations used in previous grades. Since algebra is the language of patterns, the mathematics curriculum at this level needs to continue to focus on patterns . The use of letters to represent unknown quantities should gradually be introduced as a replacement for pictures and symbols. The use of function machines permits the introduction of letters without the need to move to formal symbolic algebra. Since they have had the opportunity to experience real function machines such as the calculator or a gum bank, where one penny yields two pieces of gum, the notation of function machines should make sense.
Students can use such symbols to communicate their generalization of patterns.
They determine not only what each input produces but also what input would produce a given output. Students should continue to communicate their generalizations of patterns through ordinary language, tables, and concrete materials. Graphs should be introduced as a method for quickly and efficiently representing a pattern or function. They should develop graphs which represent real situations and be able to describe patterns of a situation when shown a graph. For example, when given the graph at the right which shows the relationship between the number of bicycles and wheels in the school yard, they should be able to describe the relationship in words.