This document provides resources for teaching graphing exponential functions to 10th grade students using technology integration. It includes websites like Khan Academy with instructional videos, the ThinkWell blog with explanations and videos, and YouTube videos created by others. Worksheets for practice are also provided from different sources. The document emphasizes using online graphing calculators, real world examples of exponential growth, and subject-specific overviews to enhance understanding of graphing exponential functions. Reliability of sources is noted, with educational websites generally considered more trustworthy.
2. Technology Integration
Rationale: When graphing exponential
functions it is important to see the differences
in functions based on varying factors in the
equation. Visuals such as the St. Louis arch
can show students how it appears in everyday
life and other web based technologies can
show students the different behaviors of these
functions.
3. Internet Content
There are a lot of different examples on the
internet of graphing different exponential
functions.
The next several slides show examples of
information from the internet to enhance this
lesson
4. Khan Academy
Khan Academy is a very reliable source for
helping teach material that someone is
struggling with. This link takes you to a video
from them that addresses graphing
exponential functions:
https://www.khanacademy.org/math/algebra/
algebrafunctions/graphing_functions/v/graphingexponential-functions
5. ThinkWell Blog
On this site there is a lot of information that
help fully grasp the idea of graphing
exponential functions. There are some helpful
videos as well as explanations that will
address different areas of graphing.
http://blog.thinkwell.com/2011/03/graphingexponential-functions-useful-patterns.html
6. YouTube Video
Thsere are a lot of videos on YouTube that are
created by different people to address
graphing exponential functions. These all have
different approaches and can help if a couple
ways do not make sense because there are
different ways of looking at it. Here is one
example:
http://www.youtube.com/watch?v=ls78_2UBcdY
7. Agency for Population Growth
Exponential functions are used to monitor
population growth which can be a rising
problem for different species. Here is one
organization that looks at population growth:
http://www.csa.com/discoveryguides/ern/01
mar/overview.php
8. Population Control of Cats and Dogs
Population control of everything can be
monitored through different exponential
functions. This is an agency that speaks to
monitoring the population of cats and dogs.
https://www.avma.org/KB/Policies/Pages/Dog
-And-Cat-Population-Control.aspx
9. Animal Population Control
This is the CT state agency that monitors
animal population in general. They also use
exponential functions and this gives a
background of why it is necessary to do this:
http://www.ct.gov/doag/cwp/view.asp?a=136
7&q=259104
10. Inspiration
Step by Step guide of how to graph after a
lesson in case a student forgets the order of
the steps
11. Online Graphing Calculator
On this website students can enter equations
and graph them to see how different
equations can change the graph that comes
from it. This can be very beneficial to seeing
the different behaviors of the graphs.
http://www.meta-calculator.com/online/
12. Worksheets to practice
The following website links have worksheets
for practice for the students
http://www.kutasoftware.com/FreeWorkshee
ts/Alg2Worksheets/Graphing%20Exponential
%20Functions.pdf
http://www.utdanacenter.org/mathtoolkit/do
wnloads/lessons/alg2_exponential_ws1.pdf
http://sites.tenafly.k12.nj.us/~jmoreng/Precal
culus/P%7BE(x)%7DOld.pdf
13. Subject Specific Resource
This website gives a very in depth explanation
and background of exponential functions. This
could be used in a classroom by having the
students do a little research before actually
learning about the functions. It gives a very good
overview and could have the students learn some
on their own before the real lesson
http://www.purplemath.com/modules/graphexp.
htm
14. Uses of Internet
Similar to a previous website this one allows students
to graph any function they want and see the behavior.
This could be very helpful to realizing patterns in the
way graphs look:
http://www.walterzorn.de/en/grapher/grapher_e.htm
It could also be very beneficial for students to see how
it is applied in real life so a website that lists some of
these could be interesting for them. This is one that I
found that does it but there are a lot of possibilities:
http://www.uiowa.edu/~examserv/mathmatters/tutori
al_quiz/log_exp/realworldappsexponential.html
15. Web 2.0
On Facebook there is a page where you can like
exponential functions and it shows you other people
who have. This gives you an opportunity to connect
with other people who know about the topic:
https://www.facebook.com/pages/Exponentialfunction/109582162394532
It can also be difficult to do some problems so there is
a website that students could ask questions on and
anyone can post helpful hints and solutions. This could
connect people from all over the world on this one
topic: http://mathhelpboards.com/pre-calculus21/help-exponential-function-word-problem3434.html
16. Reliability of Sources
Some of the sources used for this are much
more reliable than others. Those that came
college or other educational website I trust
much more than those that didnt. Similarly
those who anyone can post to can be tough
because people do not always know as much
about a subject as they believe they do. In the
notes all of the URLs are listed.
Editor's Notes
#11: This makes it simpler to see the step by step process in order to graph the equation. It builds on itself and could be used to show students the steps as we progress through. It enhances understanding because it is easy to follow and is simpler than reading a paragraph explaining the steps.