Solving Problems with Systems of Equations

5 min

Teacher Prep
Setup
2 minutes quiet work time followed by whole-class discussion.

Narrative

The purpose of this Warm-up is to get students to reason about representing a context about distance as an expression. For students who use the equation d=rtd = rt to choose their answer, encourage them to explain how each part of the expression matches the context (MP3). 

Launch

Give students 2 minutes of quiet work time, and follow that with a whole-class discussion. 

Student Task

A car is driving toward home at 0.5 miles per minute. If the car is 4 miles from home at t=0t=0, which of these expressions can represent the distance that the car has left to drive?

  • 0.5t0.5t
  • 4+0.5t4+0.5t
  • 40.5t4 - 0.5t
  • 4(0.5t)4\boldcdot (0.5t)

Sample Response

40.5t4−0.5t represents the distance the car has left to drive toward home. Because 0.5t0.5t represents the distance traveled toward home, subtracting that from the 4 miles the car is from home will give us the distance left to drive. 

Activity Synthesis (Teacher Notes)

Invite students to share their selections and to explain their reasoning. After each explanation ask the rest of the class if they agree or disagree and how the context is represented in the expression.  

Standards
Building On
  • 6.EE.9·Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. <em>For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.</em>
  • 6.EE.C.9·Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. <span>For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation <span class="math">\(d = 65t\)</span> to represent the relationship between distance and time.</span>

35 min