By now, students have had multiple opportunities to interpret graphs of functions and to create them (primarily by plotting known inputoutput pairs of a function or by using descriptions of the situation). Students have also acquired essential vocabulary to communicate about graphs of functions, and used average rate of change as a way to measure how a function changes.
In this lesson, students apply these insights and skills to interpret or create graphs of functions that are less well defined and that model reallife situations that are more complex. The lesson includes two main activities about flagraising and two optional activities that use other contexts.
Information about the functions is presented in the form of verbal descriptions, video clips, and images. More ambiguity is involved here than in cases students have previously encountered, so they will need to persevere in sense making and problem solving (MP1). At times, the information given may be inadequate, so students will need to make assumptions and decisions in order to produce graphs that show the desired behaviors or meet certain requirements. Along the way, students engage in important aspects of mathematical modeling (MP4).
Lesson overview
 8.1 Activity: Which One Doesn't Belong: Temperature Over Time (5 minutes)

8.2 Activity: Flag Raising (Part 1) (20 minutes)
 Includes "Are you Ready for More?" extension problem
 8.3 Activity: Flag Raising (Part 2) (10 minutes)
 8.4 Optional Activity: Two Pools (20 minutes)

8.5 Optional Activity: The Bouncing Ball (15 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 8.6 Cooldown: Caught in a Tree (5 minutes)
Learning goals:
 Given a verbal or visual representation of a situation, sketch a graph and show key features.
 Interpret the average rate of change in a situation.
 Practice interpreting key features of graphs and explaining (orally and in writing) their meaning in terms of a situation.
Learning goals (student facing):
 Let’s sketch graphs to represent situations.
Learning targets (student facing):
 I can explain the average rate of change of a function in terms of a situation.
 I can make sense of important features of a graph and explain what they mean in a situation.
 When given a description or a visual representation of a situation, I can sketch a graph that shows important features of the situation.
Required preparation:
 Devices are required for the digital version of the extension in the first main activity, Flag Raising (Part 1).
 Prepare access to the video clips needed in the second main activity, Flag Raising (Part 2), and in the second optional activity, The Bouncing Ball.
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