Lesson 1 Getting Ready for a Pool Party Develop Understanding
Learning Focus
Graph a function to model a situation.
Interpret and identify key features of the graph.
How can we create a graph without equations or points being given?
How does a graph tell a story?
How do I describe key features of a graph?
Open Up the Math: Launch, Explore, Discuss
Sylvia has a small pool full of water that needs to be emptied and cleaned, then refilled for a pool party. During the process of getting the pool ready, Sylvia did all of the following activities, each during a different time interval.
Removed water with a single bucket | Filled the pool with a hose (same rate as emptying pool) |
Drained water with a hose (same rate as filling pool) | Cleaned the empty pool |
Sylvia and her two friends removed water with her three buckets | Took a break |
1.
Create a story of Sylvia’s process for emptying, cleaning, and filling the pool. Number the activities given in the table 1–6 to indicate the order in which they occurred in your story.
2.
Sketch a possible graph showing the height of the water level in the pool over time. Be sure to include all of the activities Sylvia 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.
3.
Does your graph represent a function? Why or why not? Would all graphs created for this situation represent a function?
Ready for More?
Write a story context that has one interval of increase, one interval of decrease, and one interval when the rate of change is
Takeaways
A relationship is a function if and only if:
Adding Notation, Vocabulary, and Conventions
Key features of functions:
Lesson Summary
In this lesson, we created graphs to model a story context. We learned the mathematical words to describe the key features of functions. These key features are used to analyze and compare functions.
1.
a.
Graph each of the functions on the same coordinate grid.
b.
What is similar and what is different about the graphs for these two functions?
2.
a.
Graph each of the functions on the same coordinate grid.
b.
What is similar and what is different about the graphs for these two functions?
3.
Solve each of the equations for