In this Grade 8 enVision Mathematics lesson from Chapter 3, students learn how to sketch qualitative graphs of both linear and nonlinear functions based on verbal descriptions by identifying input and output variables and analyzing whether a function is increasing, decreasing, or constant over specific intervals. Students work through real-world contexts such as oxygen tank levels during a scuba dive, parasailing altitude over time, and javelin height to interpret and draw function behavior without precise numerical values. This lesson builds foundational skills in reading and representing functional relationships graphically.
Section 1
Identifying Independent and Dependent Variables
In a relationship between two quantities, the independent variable is the quantity that is changed or controlled (the cause).
The dependent variable is the quantity that is measured or observed as a result (the effect).
Section 2
Sketching Curves for Variable Rates of Change
A variable rate of change is represented by a curve. If the rate is increasing (e.g., "speeding up"), the curve gets steeper. If the rate is decreasing (e.g., "slowing down"), the curve gets flatter.
Section 3
Sketching a Qualitative Graph from a Story
To sketch a graph from a story, translate the verbal description into a visual representation by following these steps:
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter
Expand to review the lesson summary and core properties.
Section 1
Identifying Independent and Dependent Variables
In a relationship between two quantities, the independent variable is the quantity that is changed or controlled (the cause).
The dependent variable is the quantity that is measured or observed as a result (the effect).
Section 2
Sketching Curves for Variable Rates of Change
A variable rate of change is represented by a curve. If the rate is increasing (e.g., "speeding up"), the curve gets steeper. If the rate is decreasing (e.g., "slowing down"), the curve gets flatter.
Section 3
Sketching a Qualitative Graph from a Story
To sketch a graph from a story, translate the verbal description into a visual representation by following these steps:
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter