When Are They the Same?

5 min

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

Narrative

The purpose of this Warm-up is for students to reason about two situations that can be represented with linear equations. Because the number of babysitting hours determines which situation would be most profitable, there is no one correct answer to the question. Students are asked to explain their reasoning.

Launch

Give students 2 minutes of quiet work time followed by a whole-class discussion. 

Student Task

If you were babysitting, would you rather 

  • Charge $5 for the first hour and $8 for each additional hour?

Or 

  • Charge $15 for the first hour and $6 for each additional hour? 

Explain your reasoning. 

Sample Response

Sample responses:

  • I would choose to charge $15 for the first hour and $6 for each additional hour if I only babysit for up to 5 hours.
  • It doesn’t matter which I choose if I babysit for 6 hours (the first hour plus 5 additional hours) because the amount I will earn is the same. 
  • I would choose $5 for the first hour and $8 for each additional hour if I babysit for more than 6 hours. 
Activity Synthesis (Teacher Notes)

Survey the class to determine which situation they would choose. Invite students from each side to explain their reasoning. Record and display these ideas for all to see. If no one reasoned about babysitting for less than 5 hours, and therefore chose the second option, mention this idea to students.

If students do not use linear equations or graphs to choose a situation, and there is time, ask students for the equation and graph that could be used to model each situation.

Standards
Addressing
  • 8.EE.8·Analyze and solve pairs of simultaneous linear equations.
  • 8.EE.C.8·Analyze and solve pairs of simultaneous linear equations.

10 min

15 min