Piecewise Linear Functions

5 min

Narrative

This Warm-up prompts students to make sense of a new type of function, a piecewise linear function, before working with it and the mathematics that is involved (MP1). Students should notice that the points are not connected and wonder how well the lines model the sections of data they span, which is explored in a later activity. For that reason, the discussion should focus on collecting all the things students notice and wonder but not giving responses that explain the things they wonder about.

Launch

Arrange students in groups of 2. Display the image for all to see. Ask students to think of at least one thing they notice and at least one thing they wonder. Give students 1 minute of quiet think time and then 1 minute to discuss with their partner the things they notice and wonder.

Student Task

What do you notice? What do you wonder?

Scatterplot, horizontal, time in hours after midnight, 0 to 12 by ones, vertical, temperature in degrees Farenheit.
Scatterplot, horizontal, time in hours after midnight, 0 to 12 by ones, vertical, temperature in degrees Fahrenheit. Fifty points approximate a straight line from point 2 5 comma 50 increasing to 5 point 75 comma 59 and then decreasing from there to 12 comma 52 point 5.

 

Sample Response

Students may notice:

  • Not many of the points are on the blue lines.
  • The temperature gets warmer and then cooler as time goes on.
  • At about 5:45 a.m., it is the warmest— about 59 degrees.
  • The second blue line connects the highest point and the point furthest to the right.

Students may wonder:

  • What location does this data represent?
  • Why is it warmer at 6:00 a.m. than it is at noon?
  • Why aren’t the points connected?
  • Why is the second line lower than almost all the points?

Synthesis

Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary. If possible, record the relevant reasoning on or near the image. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and respectfully ask for clarification, point out contradicting information, or voice any disagreement.

If no one mentions that the dots are not connected or what they think the blue lines mean, bring these ideas to their attention, and tell them they will be working more with these ideas in the next activity.

Standards
Addressing
  • 8.F.B·Use functions to model relationships between quantities.
  • 8.F.B·Use functions to model relationships between quantities.

10 min

15 min

5 min