This is the first of several lessons in which students construct quadratic functions to represent various situations. Here they investigate the movement of freefalling objects. Students analyze the vertical distances that falling objects travel over time and see that they can be described by quadratic functions. They use tables, graphs, and equations to represent and make sense of the functions. In subsequent lessons, students build on the functions developed here to represent projectile motions, providing a context to develop understanding of the zeros, vertex, and domain of quadratic functions.
To express the relationship between distance and time, students need to see regularity in numerical values and express that regularity (MP8).
Lesson overview
 5.1 Warmup: Notice and Wonder: An Interesting Numerical Pattern (5 minutes)
 5.2 Activity: Falling from the Sky (15 minutes)

5.3 Activity: Galileo and Gravity (15 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 5.4 Cooldown: Where Will It Be? (5 minutes)
Learning goals:
 Explain (orally and in writing) the meaning of each term in a quadratic expression that represents the height of a freefalling object.
 Use tables, graphs, and equations to represent the height of a freefalling object.
 Write quadratic functions to represent the height of an object falling due to gravity.
Learning goals (student facing):
 Let’s measure falling objects.
Learning targets (student facing):
 I can explain the meaning of the terms in a quadratic expression that represents the height of a falling object.
 I can use tables, graphs and equations to represent the height of a falling object.
Required preparation:
 Be prepared to display a GeoGebra applet for all to see during the synthesis of the activity "Galileo and Gravity."
Standards:
 This lesson builds towards the standard(s): CCSS.HSFBF.A.1MS.FBF.1MO.A1.LQE.A.3
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