Chapter 5: SequencesLesson 5.1.1

Problem 51
In the book Of Mice and Men by John Steinbeck, two good friends named Lennie and George dream of raising rabbits and living off the land. What if their dream came true. Suppose Lennie and George started with two rabbits and during the first month those rabbits have two babies. Also suppose that every month thereafter, each pair of rabbits has two babies. Your Task: With your team:

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Problem 53
Lennie and George want to raise as many rabbits as possible, so they have a few options to consider. They could start with a larger number of rabbits, or they could raise a breed of rabbits that reproduces faster. How do you think each of these options would change the pattern of growth you observed in the problem 5‑1? Which situation will yield the largest rabbit population after one year?
To help answer these questions, model each case below with a table for the first five months.
How many rabbits would they have in that case?
Lennie and George want to raise as many rabbits as possible, so they have a few options to consider. They could start with a larger number of rabbits, or they could raise a breed of rabbits that reproduces faster. How do you think each of these options would change the pattern of growth you observed in the problem 5‑1? Which situation will yield the largest rabbit population after one year?
To help answer these questions, model each case below with a table for the first five months.
 Case 2: Start with 10 rabbits; each pair has 2 babies per month.
 Case 3: Start with 2 rabbits; each pair has 4 babies per month.
 Case 4: Start with 2 rabbits; each pair has 6 babies per month.
How many rabbits would they have in that case?
Lesson 5.1.1 Homework Help!



Lesson 5.1.2  Rebound Ratios
How do you play SQUASH?

Below are “bounciness” standards for different kinds of balls.

Problem 519
THE BOUNCING BALL  How can you determine if a ball meets expected standards?
Your Task: With your team, calculate the rebound ratio for a ball. Your teacher will provide you with a ball and a measuring device. You will be using the same ball again later, so make sure you can identify which ball your team is using. Before you start your experiment, discuss the following questions with your team. What do we need to measure? How should we organize our data?
How can we be confident that our data is accurate? Graph your data HERE!
THE BOUNCING BALL  How can you determine if a ball meets expected standards?
Your Task: With your team, calculate the rebound ratio for a ball. Your teacher will provide you with a ball and a measuring device. You will be using the same ball again later, so make sure you can identify which ball your team is using. Before you start your experiment, discuss the following questions with your team. What do we need to measure? How should we organize our data?
How can we be confident that our data is accurate? Graph your data HERE!
Lesson 5.1.3  Exponential Decay
What is the difference between exponential growth and decay?
Exponential functions are patterns that get continuously multiplied by some number. It's exponential growth when the base of our exponential is bigger than one, which means those numbers get bigger. It's exponential decay when the base of our exponential is in between 1 and 0 and those numbers get smaller.
Online Task: Using the link below, gain a greater understanding of our conceptual study of exponential growth & decay by completing the three videos and two online practice quizzes.
Online Task: Using the link below, gain a greater understanding of our conceptual study of exponential growth & decay by completing the three videos and two online practice quizzes.
Lesson 5.2.1  How can I describe a sequence?
Today's WarmUp!
In the bouncing ball activity from Lessons 5.1.2, you used tables and graphs to represent a discrete or continuous situation. Today you will learn about a new way to represent a discrete pattern, called a sequence.
541. Samantha was thinking about George and Lennie and their rabbits. When she listed the number of rabbits George and Lennie could have at the end of each month, she ended up with the ordered list called a sequence. 6, 18, 54, 162, …
She realized that she could represent this situation using a sequencegenerating machine that would generate the number of rabbits each month by doing something to the previous month’s number of rabbits. She tested her generator by putting in a first term of 6 and she recorded each output before putting it into the next machine. Below is the diagram she used to explain her idea to her teammates.
In the bouncing ball activity from Lessons 5.1.2, you used tables and graphs to represent a discrete or continuous situation. Today you will learn about a new way to represent a discrete pattern, called a sequence.
541. Samantha was thinking about George and Lennie and their rabbits. When she listed the number of rabbits George and Lennie could have at the end of each month, she ended up with the ordered list called a sequence. 6, 18, 54, 162, …
She realized that she could represent this situation using a sequencegenerating machine that would generate the number of rabbits each month by doing something to the previous month’s number of rabbits. She tested her generator by putting in a first term of 6 and she recorded each output before putting it into the next machine. Below is the diagram she used to explain her idea to her teammates.
 What does Samantha’s sequence generator seem to be doing to each input?
 What are the next two terms of Samantha’s sequence? Show how you got your answer.
 Samantha decided to use the same sequence generator, but this time she started with a first term of 4. What are the next four terms in this new sequence?
Do you KNOW the difference?


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Chapter 5 Practice Booklet
Chapter 5 Practice Booklet
Chapter 5 Homework
Lesson 5.1.1
Representing Exponential Growth
56 thru 517
Lesson 5.1.2
How high will it bounce?
522 thru 525
Lesson 5.1.3
What is the pattern?
535 thru 539
Lesson 5.2.1
How can I describe a sequence?
545 thru 554
Lesson 5.2.2
How do arithmetic sequences work?
566 thru 571
Representing Exponential Growth
56 thru 517
Lesson 5.1.2
How high will it bounce?
522 thru 525
Lesson 5.1.3
What is the pattern?
535 thru 539
Lesson 5.2.1
How can I describe a sequence?
545 thru 554
Lesson 5.2.2
How do arithmetic sequences work?
566 thru 571