Mr. Taylor has a small pool full of water that needs to be emptied, cleaned, then refilled for his son's pool party. He uses a hose to drain and fill the pool with water. It is important to note that the hose drains and fills at the same rate.
Today's Learning Goal:
Interpret a story context to create the graph of a function without being given information about scale or shape.
Introduce features of functions in the context of graphing a common situation. Features include: Maximum/minimum Domain Range x-intercept, y-intercept Intervals of increase and decrease Continuous, discrete, discontinuous Rate of change
Reminders:
Continuous functions can have any value within a specific interval and values are connected. (measureable)
Domain of a function: The numbers that can be used as possible inputs
Today's Materials:
Laptop
Pencil
Binder
Please complete the Jump Start (activator). This is independent it should be silent.
Which one doesn't belong and why?
The following infomation describes the situation in order:
The pool starts with 12 gallons of water. (12 gallons is the maximum the pool holds)
Then, drained the pool with the hose at a rate of 3 gallons per minute for 2 minutes.
Then, stopped draining the pool to drink some lemonade for 3 minutes. (Removed the hose while drinking)
Next, started draining the pool again until it was empty.
Once empty, He cleaned the inside of the pool for 4 minutes.
NIce and clean, starts to fill the pool for 3 minutes at the same rate it was drained. (3 gallons per minute)
Stopped filling the pool to use the bathroom for 1 minute.
Finally, finished filling until the maximum amount of water was in the pool.
On the Guided Note sheet, (10 Minutes)
Sketch a possible graph showing the gallons of water in the pool over time, in minutes. Only on the graph that says "My Attempt". Use a ruler for straight lines!
Be sure to include all of the activities Mr. Taylor did to prepare the pool for the party. Remember that only one activity happened at a time. Think carefully about how each section of your graph will look, labeling where each activity occurs.
Answer the following questions based on the solution graph.
Create and write a 3 part short story that includes, in any order,
one interval of increase,
one interval of decrease,
and horizontal constant interval.
Sketch it on the graph. Label the maximum, minimum, increase, decrease, and y intercept.
How long did it take to drain, clean, and refill the pool?
What is happening in the situation when there is a decreasing line on your graph?
What is happening in the situation when there is a increasing line on your graph?
What intervals of time represents that the water was decreasing?
(Select all that apply)
What intervals of time represents that the water was increasing?
(Select all that apply)
What intervals of time represents that the water was remaining constant (no change in gallons)?
(Select all that apply)
What does the y-intercept represent in the situation?
Does the pool situation graph represent a function? Why or why not?
