Base � The number that is rais ed to
a power in an ex ponential expres-
sion.
Compound Growth � Another term
for exponential growth, usually used
when talki ng about the monetary
val ue of an investment
Decay Factor � The constant factor
that each value in an exponential de-
cay pattern in multipli ed by to get the
next val ue.
Exponent � A number that indicates
how many times another number (the
bas e) is to be used as a factor. Expo-
nents are written as raised numbers
to the right of the bas e. In the ex-
pression 3
5
, read �3 to the fifth
power,� 5 is the exponent.
Exponential Decay � a pattern of
decrease in which each value is
found by multiplyi ng the previous
value by a constant factor greater
than 0 and less than 1.
Exponential Growth � A pattern of
increase in which each value is found
by multiplyi ng the previous value by a
constant factor greater than 1. For
example, the pattern 1,2,4,8,16, 32
� shows exponential growth.
Standard For m � The most common way to ex press a quantity. For exam-
ple, 27 is the standard form of 3
3
.
Growing, Growing, Growing
Glossary
Connected Mathematics
Project
Everett Public Schools
Mathematics Program
Proposed Time Frame:
Approximately 6 weeks
Growing, Growing, Growing
Algebra
Unit Goals:
Building and analyzin g exponential
mode ls
Reasoning with and about
exponential relati onships
Exploring the significan ce of shapes
of gr aphs and patterns in tables
Making sense of the symbo ls in the
express y = a(b
2
)
Exploring rates of growth
Recognizing and describi ng
situations that can be modeled with
exponential functions
Using exponents
Web Resources
WWW.illuminations.nctm.org
Shedding Light on the Subjec t: Func-
tion Mo dels of Light Decay
Tips for Helping at Home
Good questions and good listening w ill
help children make se nse of mathemat-
ics an d build self-confidence. A good
question opens up a problem and su p-
ports different ways of thinking about it.
Here are some questions you might try,
notice that none of them can be an-
swered with a simple �yes � or �no�.
Getting Started
What do you need to find ou t?
What do you need to know?
What terms do you understan d or
not understand?
While Working
How can you organize the inf orma-
tion?
Do you see any patterns or relation-
ships that w ill help solve this?
What would happen if�?
Reflecting about the Solution
How do you know your answer is
reasonable?
Has the question been answ ered?
Can you explain it another w ay?
At Home:
1 Talk with your child about
what�s going on in mathem atics
class.
2 Look for ways to link mathe-
matical learning to daily activi-
ties. Encourag e your child to
figu re out the amounts for halv-
ing a recipe, estimating gas
mileage, or figuring a restau-
rant tip.
3 Encourage y our child to sched-
ule a regular time for home-
work and provide a comfortable
place for their study , free from
distractions.
4 Monitor y our child�s home-
work on a regular basis by
looking at one problem or ask-
ing your child to briefly de-
scribe the focus of the home-
work. When your child asks
for help, work with them in-
stead of doing the problem for
them.
At School
1 Attend Open House, Back to
School Nigh t, and after school
ev ents.
2 Join the parent-teacher organi-
zation
Investigation 1: Exponential Growth
Gain an intuitive understanding of basic ex -
perimental growth patterns
Begin to recognize exponential patterns in
tables, graphs, and equations
Solve problems involving exponential growth
Express a number that is the product of i den-
tical factors in exponential form and standard
form
Investigation 2: Growth Patterns
Recognize patterns of exponential growth in
tables and equations
Compare and contrast exponential growth to
linear growth
Reason with and solve problems involving
exponents and exponential growth
Determine the growth factor in a given ex po-
nential model
Investigation 3: Growth Factors
Determine growth factors and create repre-
sentations of an exponential population
model given sample population data
Investigate increases in the value of an as set
due to compound growth
Review and extend understanding of percent
Investigation 4: Exponential Decay
Recognize patterns of exponential decay in
tables, graphs, and equations
Use knowledge of exponents to write equa-
tions for models of exponential decay
Reason about problems involving exponents
and exponential decay.
Describe the effects of varying the values of
a and b in the equation y = a(b
2
). On the
graph of that equation.
Connected Mathematics Project
Mathematics in
Investigations
Phone: 425-385-4062
Fax: 425-385-4092
Email: mstine@everett.wednet.edu