Lesson 1 Piggies and Pools Develop Understanding
Represent situations with different types of growth.
Compare models for situations that occur over time.
What type of situation can be modeled by a continuous graph? When is a graph of only separate points appropriate?
What are the similarities and differences between an arithmetic sequence and a linear function?
Can a geometric sequence be continuous?
Open Up the Math: Launch, Explore, Discuss
My little sister, Savannah, is three years old. She has a piggy bank that she wants to fill. She started with
Our family has a small pool for relaxing in the summer that holds
I’m more sophisticated than my little sister, so I save my money in a bank account that pays me
At the end of the summer, I decided to drain the
Compare problems 1 and 3. What similarities do you see? What differences do you notice?
Compare problems 1 and 2. What similarities do you see? What differences do you notice?
Compare problems 3 and 4. What similarities do you see? What differences do you notice?
Ready for More?
Use your model in problem 4 to find when the pool will be empty. Justify your answer.
A geometric sequence
Arithmetic and geometric sequences are
Adding Notation, Vocabulary, and Conventions
Domain of a function:
In this lesson, we learned that the possible inputs for a function are called the domain. We found that some situations are best described using a discrete model and others are represented better with a continuous model. Arithmetic sequences are part of the linear family of functions and geometric sequences are part of the exponential family of functions.
For each sequence, find the next two terms in the sequence and then state whether the sequence is arithmetic, geometric, or neither. Justify your answer.
Find the unit rate for each of the items.
A dozen ears of corn for
Three t-shirts for
Solve each of the equations.