Focus: In this unit, students apply their prior knowledge of rates and proportional relationships from Grade 7 as well their geometric skills from the previous Grade 8 unit. Students begin by revisiting different representations of proportions, including graphs, tables, and equations, and discuss the role of the constant of proportionality and how it may be interpreted in context.
They then move on to analyze a scenario in which the relationship is linear but not proportional—“How many cups are needed to stack to a height of 50 cm?”—which allows them an opportunity to explore multiple ways to solve a specific problem.
Students are introduced to the “rate of change” as a way to describe the rate per 1 and note its equivalence to the numerical value of the slope of the line that represents this same relationship.
As the unit progresses, students are introduced to a line with a negative y-intercept and consider equations that might represent it. They discuss situations represented by linear relationships with negative rates of change, graph these, and interpret coordinates of points on the graphs in context to discuss their mathematical ideas and respond to the ideas of others. To conclude the unit, students apply what they have learned to solve a real-world problem regarding a budget and use various representations of linear relations in context.
Number of Lessons: 14
Lesson Time: Approximately 45 minutes. Please note that each lesson is designed for one instructional block, and may be divided into shorter segments based on teacher pacing and student needs.
Additional Search Terms:
represent • scale • label • constant of proportionality • equation • rate of change • constant rate • slope • vertical intercept • y–intercept • initial value (amount) • relate • horizontal intercept • x–intercept • intersection point • constraint • variables • combination • solution to an equation • set of solutions • mathematical practices