2. Technology Integration
• Rationale
– Composing functions can be
difficult for many students to
understand because the
necessary steps and calculations
are performed from right to left.
When teaching such an obscure
concept to students, technology
can help tremendously. Teachers
can use the many different web
resources in this presentation to
ensure students can both
understand and effectively
compose functions.
3. Internet Content
• The Internet is a great place to find helpful
teaching resources. By effectively
searching, one can find many different
educational tools to aid in the teaching of a
particular topic. The following three slides
are examples of blogs, podcasts, and
instructional videos that pertain to
composition of functions.
4. Internet Blog
• Hands On Math is an Internet blog with the
goal of creating a more hands-on, fun
approach to learning math. The link above is a
blog that teaches composition of functions
using an example involving almonds.
5. Podcast
“Polynomial
Operations” by The
Math Dude is a
video podcast
found for free on
iTunes. It covers
addition,
subtraction, and
multiplication of
polynomials.
Click above to view the podcast.
6. Instructional Video 1
• Below is a link to a YouTube video about
composition of functions. The information in
this video is great for those learning
composition of functions for the first time.
• YouTube Video
7. Instructional Video 2
• Below is a link to a Kahn Academy video about
composition of functions. The information in
this video is very well explained, but at a
higher difficulty level than the previous video.
• Kahn Academy Video
8. Internet Resources
• The Internet is full of great educational
resources for teachers and students. There are
many organizations and government agencies
that are dedicated to helping people learn.
The following three slides are organizations
that teachers and students can use to improve
their educational experience.
9. Regents Prep
• Regents Prep is a nonprofit New York based
organization that offers free help to students
in all areas of high school mathematics.
Although the courses and topics are geared
towards preparing for New York State Regents
exams, the website can be used by anyone to
review almost any high school math topic.
10. Algebra Lab
• Algebra Lab is an organization created in
Florida by a group of math teachers and
computer programmers. The website offers
tons of lessons and activities covering a wide
variety of math topics.
11. Khan Academy
• Khan Academy is a nonprofit organization that
offers an extremely wide variety of
instructional videos, practice problems, and
interactive challenges for free to all users. The
website is great for both students and
teachers.
16. There’s an app for that!
• Math Ref is a
reference app that
includes over 1,400
formulas, figures,
tips, examples, and
concepts.
Google Play Store Link
App Store Link
17. Subject Specific Resource
• Math Goodies
– This site offers helpful materials for both teachers
and students. Students can search by class, then
topic. Teachers can find lesson plans, worksheets,
and learning games.
18. Uses of the Internet
• WCC Online Math Center
– This site offers frequently asked math questions,
helpful pdf documents, and links to other great
math sites.
• A Plus Math
– This site offers interactive flash cards that students
and teachers can use. The user can choose
whether they want to include or exclude addition,
subtraction, multiplication, or division of
binomials.
19. Web 2.0
• Facebook
– Facebook can be an extremely helpful resource for
teachers and students. Teachers can make a class
page where they can collaborate with students.
• YouTube
– YouTube is an excellent resource for students and
teachers. With thousands of math video tutorials,
teachers and students can find just about anything
they’re looking for.
Source:http://handsonmath.blogspot.com/2011/08/composite-functions-and-almonds-fgx.htmlFor other fun, hands-on blogs, take a look at the Hands On Math blog homepage: http://handsonmath.blogspot.com
Addition, subtraction, and multiplication of polynomials are essential skills for students to have before they learn to compose functions. This video serves as a great instructional tool to teachers and students to prepare for a lesson on composition of functions.
Regents Prep allows students to choose either algebra, trigonometry, or algebra 2/ trigonometry on the home screen. Once a course is chosen, students can then choose specific topics in that course they would like to learn more about. Note: The website has links to “Math A” and “Math B” that only allow students to reroute themselves to of of the three topics mentioned previously. “Math A” and “Math B” were the previous names New York State identified their courses by.
One outstanding feature of Algebra Lab is that all key math terms are clickable links. For example, if a sentence says, “Evaluate the function at 2,” the word function would be a clickable link. When clicked, a pop-up window gives a helpful definition, along with great pictures and examples to help user understand the word or concept.
Khan Academy has teacher and student specific features. Students can track their own statistics, get badges that reward them and to challenge them to do even better, and work on practice problems. Teachers can track their students’ progress and class statistics and use the extensive library of instructional videos in their classrooms.
This diagram would be used at the introduction of the lesson. As the instructor is explaining how to simplify and plug in at each step, this diagram will serve as a helpful visual aid to the students. This visual enhances student understanding because it has two different visual representations of how to perform this process, allowing students to choose the one that makes most sense to them. The visual is also helpful because both diagrams have numbered labels, so it is easy to compare the two methods.
Worksheet found at: http://www.edhelper.com/Functions6.htm
SMART Notebook has an interactive graphing capabilities included in the software. This tool can be used to give students a visual representation of the functions they are working with to help them better understand them.
Lesson Plan found at: http://www.teach-nology.com/lessons/lsn_pln_view_lessons.php?action=view&cat_id=5&lsn_id=26051
Math Ref is available on both Android and iOS mobile devices, $1.99 from the App Store, $0.99 from the Google Play Store.
Source: http://www.mathgoodies.com For students, click “Students” on the homepage, for teachers, click “Teachers” on the homepage.
WCC Online Math Center would be useful in teaching composition of functions because the pdf document about functions includes notations, practice problems, and examples of composition of functions. A Plus Math would be helpful in teaching composition of functions because it offers a fun and interactive method of practicing how to add, subtract, multiply, and divide binomials, which is a necessary skill in composing functions.