Lesson 17

Two Related Quantities, Part 2

Lesson Narrative

In this second lesson on representing relationships between two quantities, walking at a constant rate provides the context for writing an equation that represents the relationship. Students use and make connections between tables, graphs, and equations that represent the relationship between time and distance. They use their representations to compare rates and consider how each of the representations would change if the independent and dependent variables were switched. 

Learning Goals

Teacher Facing

  • Create a table, graph, and equation to represent the relationship between distance and time for an object moving at a constant speed.
  • Identify (in writing) the independent and dependent variable in a equation.
  • Interpret (orally and in writing) an equation that represents the relationship between distance and time for an object moving at a constant speed.

Student Facing

Let’s use equations and graphs to describe stories with constant speed.

Required Materials

Learning Targets

Student Facing

  • I can create tables and graphs to represent the relationship between distance and time for something moving at a constant speed.
  • I can write an equation with variables to represent the relationship between distance and time for something moving at a constant speed.

CCSS Standards

Glossary Entries

  • coordinate plane

    The coordinate plane is a system for telling where points are. For example. point \(R\) is located at \((3, 2)\) on the coordinate plane, because it is three units to the right and two units up.

    Point \(R\) on a coordinate plane, origin \(O\). Horizontal and vertical axis scale negative 4 to 4 by 1’s. The point has coordinates \(R\)(3 comma 2).
  • dependent variable

    The dependent variable is the result of a calculation.

    For example, a boat travels at a constant speed of 25 miles per hour. The equation \(d=25t\) describes the relationship between the boat's distance and time. The dependent variable is the distance traveled, because \(d\) is the result of multiplying 25 by \(t\).

    A graph of 10 points plotted in the coordinate plane.
  • independent variable

    The independent variable is used to calculate the value of another variable.

    For example, a boat travels at a constant speed of 25 miles per hour. The equation \(d=25t\) describes the relationship between the boat's distance and time. The independent variable is time, because \(t\) is multiplied by 25 to get \(d\).

    A graph of 10 points plotted in the coordinate plane.

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