Investigating the steepness of stairs helps you understand the idea of steepness, or slope, of a line. Using what you know about linear relationships, you write a formula for converting temperatures and figure out why the Irish elk may have become extinct. This investigation poses the unit's central question of how we can determine whether a relationship is linear. The class conducts one or two experiments and observes that the data collected appear to lie in a straight line. At this stage, a linear relationship is described as one whose graph is a straight line.
Students use tables and graphs to make sense of and to make predictions from the data they collect.
Walking Rates Students take a closer look at rates in multiple representations, revisiting situations similar to some of those they encountered in the Variables and Patterns uint. The rates at which people walk and the pledge per mile paid by sponsors of a walkathon are two of the contexts for this investigation. Students explore constant rate and its effect on various representations. The y-intercept is introduced informally in problems that ask students to interpret the information represented by points on a line, entries in a table, or solutions to an equation, and how these representations are related. They also use the calculator to find points on a graph and relate the information in the coordinates to the situation and to other representations.