Introduction/ Cover Sheet
Algebra 1 – Fitting Exponential Models to Data, Section 6.7 Investigation
This lesson is prepared to engage students in learning about radioactive decay, and how scientists can
radioactive decay and carbon dating to find out how old once living objects are. This lesson was
adapted from a lesson developed Holt High School Mathematics Department.
To activate prior knowledge, students are first given a quick quiz on previous lessons.
During the activity, students will work independently but at tables of 4. Students will turn in
independent work, but will be allowed to discuss their ideas and understandings with each other.
This lesson is expected to take one class period.
GANAG Lesson Plan
Teacher: Mrs. Anne Heyt
Grade level: 9th Grade
Subject: Algebra 1
Lesson Title: Fitting Exponential Models to
Data, Section 6.7 Investigation on Radioactive
Decay
Goals: Common Core Standards for High School Mathematics
I can determine the best model for a real world problem (for example, growth or decay
models). (CED.2)
I can determine if an equation is expressing growth or decay by examining the equation.
(F.IF.7)
I can create a table or graph of an exponential function. (F.IF.7)
I can define a geometric sequence, and transform it into a recursive or explicit function.
(F.BF.1)
I can write a recursive or explicit expression to describe a real world problem. (F.BF.1)
Pre-assessment Strategy: Have students do a quick quiz with two problems prior to
the project. The quick quiz will determine where students are in respect to
understanding exponential equations. Immediately after the quick quiz, the instructor
will demonstrate the solutions to the problems, and ask the students to provide
feedback in the form of a thumbs up, thumbs down, or neutral on how they think they
did on the quick quiz.
Assessment Strategy: (matched to objectives) The assessment will be based on the
results of the quick quiz and the worksheet answers.
Instructional Procedure
Access Prior Knowledge Quick Quiz
New Information Video on Radioactive decay, do brief direct instruction on radioactive
decay, defining the term half-life and showing graph explaining half-life, the formula
for decay, and how it relates to the formula for growth.
Application/Analysis Radioactive Decay Worksheet (attached). Students are allows to
work with others at their table.
Generalize Discuss other applications for the use of the decay formula, such as
deprecation of the value of a car.
Accommodations for All Learners:
ELL: Instructor will read the introduction to the radioactive decay work sheet out loud
Gifted: See extra credit/bonus extension questions on the worksheet.
Lower Level: Provide additional time and instructional support to complete the
assignment.
Multiple Intelligences Used in Lesson:
Verbal/Linguistic: Reading and writing
Visual/Spatial: Using tables and graphs
Bodily/Kinesthetic: NA
Interpersonal: Students can use peer to peer interactions when completing the activity.
Intrapersonal: NA
Logical/Mathematical: Student’s use prior knowledge and reasoning to determine
results of activity.
Technology and Web Sites Used: You-tube video on Radioactive decay by Bill Nye the
science guy. http://www.youtube.com/watch?v=TFSbRYw5Mcw&feature=related
Quick Quiz
1. Mr. Bentley deposits $1200 in a savings account. The bank pays $3.5%
annual interest. How much money does he have in the account after 5
years?
2. Write an exponential equation for the above situation. Using your
equation, determine how much money Mr. Bentley would have in the
account in 40 years.
3. What do you think the term “half-life” means?
Algebra I
Exponential Situations
Name:
Date:
Hour:
Radioactive Decay
Elements in nature consist of atoms, which can have a stable or unstable nucleus,
depending on the ratio of protons to neutrons and their total number. Unstable nuclei
tend to adjust to be more stable, by spontaneous emissions of one or more nucleons.
This is what we call radioactivity. One use of radioactivity is to determine the age of
rocks, minerals, or fossils. Carbon-14 is a radioactive atom of carbon that is in all living
plants and animals (which means we are radioactive!). In our bodies, and in those of all
living things, the amount of Carbon-14 stays constant, since the amount lost is
counteracted by what we take in from the atmosphere. When a plant or animal dies, no
more is gained, and the radioactivity decreases with time (meaning that the less of the
C-14 there is, the slower it decays). Therefore, scientists can measure the amount of
Carbon-14 in a fossil and, knowing how long it takes the amount of Carbon-14 to
decrease itself in half, can estimate the age of the fossil. C-14 takes about 5,600 years
to decrease itself in half (and therefore 5600 years is called its "half-life").
Say something dies today with 50 grams of C-14 measured in it. Fill in the table below
to tell how much C-14 is left in the object.
Age (years)
Amount of
Carbon-14
(grams)
0
5600
11200
a. Find the ratio of Carbon 14 remaining between half life time periods.
b. Write a recursive routine which shows the relationship between the number of years
and the amount of carbon 14 remaining.
c. Scientists find a fossil that originally had 1200 grams of C-14 in it, and now only has
15 grams. How old is it? Make a table to show your data.
Extra Credit Questions
d. Let's say you discover a new element, and call it Burkeinum after your best math
teacher. You discover that it has a half-life of 247 years. If the substance originally had
6400 grams of Burkeinum in it and only has 300 left, how old is it? Show your work.
e. If Y is the amount of Burkinium in a substance when decay begins, write an equation
that we can use to find the amount left after x years.