Systems of Equations

5 min

Teacher Prep
Setup
Groups of 2. 3 minutes quiet work time, short partner discussion and then whole-class discussions.

Narrative

In the Warm-up, students are given a situation and asked to describe the graph without actually graphing the lines. Identify students who correctly use mathematically correct terminology such as “yy-intercept,” “slope,” "xx-intercept,” and “intersection” to describe the graph.

Launch

Arrange students in groups of 2. Give 3 minutes of quiet work time followed by time for a brief partner discussion for the last question.

Student Task

Diego and Lin are drinking water.

Lin’s glass has 12 ounces and she drinks 14\frac14 ounce per second.

Diego's glass has 20 ounces and he drinks 23\frac23 ounce per second.

  1. How long will it take Lin and Diego to finish their water?
  2. Without graphing, explain what the graphs in this situation would look like. Think about slope, intercepts, axis labels, units, and intersection points to guide your thinking.
  3. Discuss your description with your partner. If you disagree, work to reach an agreement.

Sample Response

  1. Lin will take 48 seconds and Diego will take 30 seconds.
  2. Sample response: The horizontal axis is labeled “time (seconds)” and the vertical axis is labeled “amount of water left (ounces).” The line for Lin’s graph starts at (0,12)(0,12) and decreases to the right to the point (48,0)(48,0). The line for Diego’s graph starts at (0,20)(0,20) and decreases more steeply than Lin’s line to the point (30,0)(30,0). The two lines intersect somewhere.
  3. No response needed.
Activity Synthesis (Teacher Notes)

The purpose of the discussion is for students to practice describing graphs in words using correct mathematical terminology.

Select previously identified students to share their descriptions of the graphs. After each student shares, ask the class if the description is clear and to identify any vocabulary they heard that made the description precise or any vocabulary that is unclear. If any vocabulary needs to be reinforced for student understanding, this is a good time to discuss these words.

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.

20 min

10 min