In sixth grade, students compared two rules verbally, numerically, graphically, and symbolically in the form of y = ax or y = x + a in order to differentiate between additive and multiplicative relationships. Students also were exposed to examples of rates as the comparison by division of two quantities having different attributes, including rates as quotients. In sixth grade, students also represented mathematical and real-world problems involving ratios and rates using scale factors, tables, graphs, and proportions.
In seventh grade, students must use their knowledge to represent constant rates of change, which is the predictable rate at which a given variable alters over a certain period of time by representing and identifying this change when given pictorial, vertical or horizontal tables, verbal, numeric, graphical, and algebraic
expressions. Students may encounter applying multiple representations to graphing relationships with constant rates of change.