Generative Question or Problem:
How long will it take for a bacterial colony to grow as big as the earth?
Potential Student
Misconception(s):
This lesson will challenge student’s conventional thinking about the change process. Things are not always what they appear to be. Most students will think that it will take years for one small bacterium to divide enough to weigh as much as the
Key Science Concepts:

Exponential
Growth

Scientific Notation
Lesson Targets:
Use a variety of tools to model exponential growth in both biological and physical systems.
Use scientific notation to represent the exponential growth of very small and very large numbers.
Common Core
Standards:
Analytic modeling seeks to explain data on the basis of deeper theoretical ideas, albeit with parameters that are empirically based; for example, exponential growth of bacterial colonies (until cut-off mechanisms such as pollution or starvation intervene) follows from a constant reproduction rate.
Technology Resources/Connections:

Exponential Growth Excel Modeling Tool

Exponential Growth Wikipedia:
 http://en.wikipedia.org/wiki/Exponential_growth#Basic_formula
 The King’s Chessboard
by David Birch and Devis Grebu

The Raft Store: http://www.raft.net/main

Powers of Ten Video (Introduce students to the ideas of large and small numbers). http://www.youtube.com/watch?v=0fKBhvDjuy0

Relative Size of Bacteria
 http://learn.genetics.utah.edu/content/begin/cells/scale/
21 st Century Science Skill Focus:
Many natural phenomena defy common sense and must be understood and analyzed in ways that reveal their true properties and not their perceived properties. It will be a 21 st
century skills for students to use a modeling approach to study the growth of a population using a variety of analytical and technology tools to reveal surprises that occur in systems that grow exponentially.
Students will proceed from using concrete manipulatives to Excel to model the exponential growth of a bacterial colony. Students will be challenged to discover other natural systems that display exponential growth such as the buildup of carbon dioxide in the atmosphere that contributes to global warming.

Growing Exponentially Lesson earth. Functions are an important tool for analyzing such problems.
12/6/11
Key Academic Vocabulary:
Exponential Growth:
Growth of a system in which the amount being added to the system is proportional to the amount already present: the bigger the system is, the greater the increase. In everyday speech, exponential growth means runaway expansion, such as in population growth. (Source: American Heritage
Dictionary )
Scientific Notation:
A method of writing or displaying numbers in terms of a decimal number between 1 and 10 multiplied by a power of 10. The scientific notation of
10,492, for example, is 1.0492 × 10 4
. (Source: American Heritage Dictionary
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Growing Exponentially Lesson 12/6/11
Detailed Instructional Activities
5 E Elements : Engage, Explore, Explain, Elaborate, Evaluate (please clearly indicate where in lessons you are using 5E elements)
Engage:
The lesson will begin by reading the short story, the King’s Chessboard by David Birch and Devis Grebu to students. There will be a brief whole group discussion of the following questions:

What are some characteristics of the growth of the rice system within this story?

Can you identify other systems that demonstrate this kind of growth?
 How does this story reflect the saying: “Things are not always what they seem to be?”
Explore:
Clearly identify the Learning Targets for the lesson:

Understand the idea of exponential growth.

Use a variety of tools to model exponential growth in both biological and physical systems

Use scientific notation to represent the exponential growth of very small and very large numbers

Apply the idea of exponential growth to other natural biological and physical systems
Introduce the English Language objective for the lesson a long with the sentence frames that students will use to better understand the academic vocabulary used in this lesson.
The sentence frames that will help support both EL and non-El students better understand the vocabulary of exponential growth and scientific notation can be found at the end of this lesson.
The first formative assessment will be administered at this time. Students will have an opportunity to share their knowledge and understanding of the key outcomes for this lesson.
This initial formative assessment will also be used as an exit ticket at the end of the lesson to gauge how much students have learned about the key ideas of exponential growth and scientific notation.
Students will be introduced to the challenge problem: How long will it take for a bacterial colony to grow as big as the earth?

Students will be introduced to the size of a bacteria and the size of the earth. o Bacteria mass = 666 x 10
-15
Kilograms = 0.000000000000666 Kilograms

Most bacteria are only a few micrometers (millionths of a meter) long. o Earth mass = 6.0 x 1024 Kilograms = 6,000,000,000,000,000,000,000,000 Kilograms

Students will work in teams of two to begin a modeling process to better understand the doubling process involved in the growth of a bacterial colony.
Team members will use a small ring to represent a bacterium. They will put this ring on a pipe cleaner. They will then use another pipe cleaner to represent a doubling (two rings on pipe cleaner). They will then double this amount and add 4 rings to a third pipe cleaner. The teams will continue this process and record their results on a Bacteria Ring Simulator Worksheet.

When teams of two run out of resource, they will combine into teams of 4 and so on to combine resources to build out the growth model.

Eventually the whole class will collaborate to build out a grand model that will be taped to the white board at the front of the room.

There will be a brief discussion about the characteristics students observe emerging within this growth pattern.

Students will be asked to predict how many more divisions it will take for the model to exceed the mass of the earth!
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Growing Exponentially Lesson 12/6/11
Explain: o Eventually, there will not be enough ring resources to continue the division process. So it will be time to share with students how this process can be modeled using Excel. Students will go to the computer lab and use an Excel Template to continue working in teams to model the division and growing process. o Additionally, students will have problems representing both the number of bacteria as well as the weight of the bacteria using regular numbers. The teacher will define scientific notation and help students use the sentence frames to build their own examples. o The teacher will use the formative assessment of whiteboards to gauge the degree to which students can represent numbers using scientific notation.
Elaborate: o After students have used the Excel Model to identify how many divisions an and how long it will take for the bacteria to divide such that their overall weight is equal to that of the mass of the earth, students will learn how to graph the variables of this model in order to identify key characteristics of exponential growth such as: o Exponential growth starts slowly but at a certain point rapidly increases. o Exponential growth is best represented by a rapidly increasing curve rather than a straight line. o Exponential growth cannot be sustained after a certain point. o Students will be challenged to investigate the increase of CO
2 in
the atmosphere. This increase contributes to global warming. Students will be challenged to find out if this increase is an exponential growth or a linear growth. Students will also be challenged to find additional examples of exponential growth in Biology, physics, geology, and finance. o The teacher will also share the equation that can be used to calculate exponential growth at the end of the lesson. Students will be challenged to use this equation by manipulating the key variables that are key parts of exponential growth.
Evaluate: o There will not be a summative evaluation for this lesson. Instead, students will complete an exit ticket that is exactly the same as the initial formative assessment used at the beginning of this lesson. This information will be used by the teacher to gauge the degree to which all of the students achieved the learning targets for the lesson.
Lesson Differentiation Strategies (EL/ELA): o This lesson will focus on an English Language Objective of helping EL students better understand the academic vocabulary of Exponential growth and scientific notation. The teacher will use sentence frames to help students better understand and apply these concepts to real world situations. o The use of physical manipulatives in the forms of rings and pipe cleaners will help students better understand the concepts of exponential growth. o There will be frequent formative assessments during this lesson that the teacher will be able to use to provide differentiated support for all students but especially the EL students in the class.
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Growing Exponentially Lesson
12/6/11
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Growing Exponentially Lesson
(include rubrics/scoring guides where appropriate)
12/6/11 o Sentence frames will be used to engage students in using the key ideas of exponential growth and scientific notation. o There will be an initial formative assessment at the beginning of class to measure student understanding of the key concepts of exponential growth and scientific notation. o White boards will be used to gauge student understanding of the concept of scientific notation. o An exit ticket will be used at the end of class to gauge student understanding of the key concepts. o Sentence frames will be used to engage students in using the application of the concepts of exponential growth and scientific notation. o Students will submit their excel spreadsheets to gauge the degree to which they can apply the ideas of exponential growth and scientific notation. o There will be an initial formative assessment at the beginning of class to measure student understanding of the processes involved in calculating exponential growth using scientific notation. o An exit ticket will be used at the end of class to gauge student understanding of the application of exponential growth to real world problems.
There will not be a summative assessment that will be a part of this lesson.
There will not be a summative assessment that will be a part of this lesson.
(include rubrics/scoring guides where appropriate)
Websites and other Resources needed for the lesson (please include electronically)
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Growing Exponentially Lesson 12/6/11

Exponential Growth Excel Modeling Tool is attached with this lesson

Exponential Growth Wikipedia:
 http://en.wikipedia.org/wiki/Exponential_growth#Basic_formula
 The King’s Chessboard by David Birch and Devis Grebu (Available at http://amazon.com)

The Raft Store: http://www.raft.net/main (Source of manipulatives used to model exponential growth)

Powers of Ten Video (Introduce students to the ideas of large and small numbers). http://www.youtube.com/watch?v=0fKBhvDjuy0
 Relative Size of Bacteria

Micrometer
A unit of length equal to one thousandth (10-3) of a millimeter or one millionth (10-6) of a meter.
Nanometer
One billionth (10-9) of a meter.
Picometer
One-trillionth (10
-12
) of a meter.
Please be sure to include all materials, laboratories, handouts and resources needed for this lesson electronically.
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Growing Exponentially Lesson 12/6/11
Academic Vocabulary
Sentence Frames
Directions: There are two key academic vocabulary words that are a part of this lesson, exponential growth and scientific notation. Definitions from the American Heritage dictionary for these two important terms can be found below.
Exponential Growth:
Exponential Growth is the growth of a system in which the amount being added to the system is proportional to the amount already present: the bigger the system is the greater the increase. In everyday speech, exponential growth means runaway expansion, such as in population growth.
Scientific Notation:
Scientific notation is a method of writing or displaying numbers in terms of a decimal number between 1 and 10 multiplied by a power of 10. The scientific notation of 10,492, for example, is 1.0492 × 10 4
. (Source: American Heritage Dictionary .
Use the following sentence frames with students to help them use this vocabulary in ways that will help then better understand the concepts and to use them to solve the real world problems that are key part of this lesson.
Exponential Growth Sentence Frames:
When I double the number of rings on the pipe cleaner, I will increase the number of rings from _______ rings to ________ rings.
When I triple the number of rings on pipe cleaners, I will increase the number of rings from _______ rings to _________rings.
If the number of bacteria in a colony is 64 and I double the colony, then the new size of the colony will be _______ bacteria.
If the number of bacteria in a colony is 64 and I double the colony, then the new size of the colony will be _______ bacteria.
Scientific Notation
The number 100 can be written in scientific notation as ______________.
The number 0.0001 can be written in scientific notation as ____________.
The number 2.0 x 10
5
can be written as _____________________.
The number 3.0 x 10
-4
can be written as _________________.
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Growing Exponentially Lesson 12/6/11
Initial Formative Assessment
Exponential Growth and Scientific Notation
Student Name:____________________________________ Period:_____ Teacher:____________________ Date:__________
Standard : Ability to understand and model the exponential growth of both biological and physical systems using scientific notation and technology.
Learning Target :
I can describe the meaning of expontial growth:
I can give examples of exponential growth:
I met this target I need more practice I need help from my teacher
Student Name:____________________________________ Period:_____ Teacher:____________________ Date:__________
Standard : Ability to understand and model the exponential growth of both biological and physical systems using scientific notation and technology.
Learning Target :
I can describe the meaning of scientific notation:
I can give examples of scientific notation:
I met this target I need more practice I need help from my teacher
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Growing Exponentially Lesson 12/6/11
Exit Ticket Assessment
Exponential Growth and Scientific Notation
Student Name:____________________________________ Period:_____ Teacher:____________________ Date:__________
Standard : Ability to understand and model the exponential growth of both biological and physical systems using scientific notation and technology.
Learning Target :
I can describe the meaning of expontial growth:
I can give examples of exponential growth:
I met these targets I need more practice I need help from my teacher
Student Name:____________________________________ Period:_____ Teacher:____________________ Date:__________
Standard : Ability to understand and model the exponential growth of both biological and physical systems using scientific notation and technology.
Learning Target :
I can describe the meaning of scientific notation:
I can give examples of scientific notation:
I met this target I need more practice I need help from my teacher
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Growing Exponentially Lesson
Bacteria Ring Simulator Worksheet
Team Members: ________________________________________________________
12/6/11
Date: ______________________
Directions:
Team members should use this Worksheet to keep track of the number and weight of the bacteria that they are modeling using the Bactria Ring
Modeling system. Remember, the weight of one bacteria = 666 x 10
-15
Kilograms = 0.000000000000666 Kilograms.
Division Number Rings Number of Bacteria Modeled Total Weight of Bacteria
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