Intent

The activities in Traveling at a Constant Rate are designed to deepen students’ understanding of linear functions, including their representations and their use in modeling data and solving problems.

Mathematics

Linear functions are the specific focus of the activities in Traveling at a Constant Rate. Students fit lines to data using informal graphical methods (both by hand and with the support of technology) and use these lines to make predictions. They find symbolic rules for the lines and attend to two key features of linear functions—the starting value and the constant rate of change—and how these features are represented in graphs, tables, and rules.

Many of us have been taught that understanding linear functions means writing equations in a particular form. We may have a tendency to want to give students the abstract forms of equations of lines because that is our own experience. Rather than separating the symbolic work of algebra from reasoning within meaningful contexts, however, the intent in IMP is to give students extensive experiences with situations involving constant rate of change and finding linear functions for particular situations.

A major goal of the IMP curriculum is to provide students with contexts for developing mathematical concepts intuitively. Rate of change is a much bigger idea than slope of a line; slope is one specific case of the rate of change of a function. Looking at a variety of situations involving a constant rate of change gives students the opportunity to build a foundation for understanding the concept of slope. Through their work in Traveling at a Constant Rate, students will be able to write linear functions using situations and see the relationships among the rule, the table of values, and the graph.

Progression

Traveling at a Constant Rate begins with a set of activities that ask students to use given data to make predictions. The calculator is introduced as a graphing tool. As the activities unfold, students are asked to find linear rules and connect the numbers in these rules to features of graphs and tables, as well as to the context of the unit. In addition, students will present their results for the second POW of the unit and begin work on the third and final one.

Previous Travelers

Broken Promises

Sublette’s Cutoff

Who Will Make It?

The Basic Student Budget

Following Families on the Trail

Graphing Calculator In-Outs

Fort Hall Businesses

“Sublette’s Cutoff” Revisited

“The Basic Student Budget” Revisited

POW 8: On Your Own

All Four, One

Travel on the Trail

Moving Along

All Four, One—Linear Functions

Straight Line Reflections