In this session, participants will explore linear and proportional relationships and how to represent and analyze them. This session explores how students develop proportional reasoning from an understanding of ratios. The session focuses on unit rate, and the constant of proportionality (k), supporting students in recognizing patterns, generalizing across tables, and writing equations in the form y = kx. This conceptual understanding then serves as a bridge from linear relationships which are proportional to relationships where the constant becomes slope (m) and the equation generalizes to y = mx + b. Teachers will examine how students determine whether a relationship is proportional or not by analyzing graphs, tables, and real-world contexts. The session concludes with a comparative modeling experience that equips teachers to support deriving the equations y=mx and y=mx + b using unit rates and constant of proportionality and constant rate of change. The session will emphasize modeling and reasoning, where students will solve problems involving linear relationships and explain their reasoning.
