Composition of Functions
Mathematics
11th-12th Grade
By Michael Alfano
Technology Integration
• Rationale
– Composing functions can be
difficult for many students to
understand because the
nece...
Internet Content
• The Internet is a great place to find helpful
teaching resources. By effectively
searching, one can fin...
Internet Blog
• Hands On Math is an Internet blog with the
goal of creating a more hands-on, fun
approach to learning math...
Podcast
“Polynomial
Operations” by The
Math Dude is a
video podcast
found for free on
iTunes. It covers
addition,
subtract...
Instructional Video 1
• Below is a link to a YouTube video about
composition of functions. The information in
this video i...
Instructional Video 2
• Below is a link to a Kahn Academy video about
composition of functions. The information in
this vi...
Internet Resources
• The Internet is full of great educational
resources for teachers and students. There are
many organiz...
Regents Prep
• Regents Prep is a nonprofit New York based
organization that offers free help to students
in all areas of h...
Algebra Lab
• Algebra Lab is an organization created in
Florida by a group of math teachers and
computer programmers. The ...
Khan Academy
• Khan Academy is a nonprofit organization that
offers an extremely wide variety of
instructional videos, pra...
Inspiration Diagram
2

4
5

5

1

3

3
4

1
2

Diagram created using Inspiration
Edhelper
SMART Software
Teach-nology
There’s an app for that!
• Math Ref is a
reference app that
includes over 1,400
formulas, figures,
tips, examples, and
con...
Subject Specific Resource
• Math Goodies
– This site offers helpful materials for both teachers
and students. Students can...
Uses of the Internet
• WCC Online Math Center
– This site offers frequently asked math questions,
helpful pdf documents, a...
Web 2.0
• Facebook
– Facebook can be an extremely helpful resource for
teachers and students. Teachers can make a class
pa...
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Alfano, Michael Composition of Functions

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  • Image source: http://olmipa.ub.ac.id/wp-content/uploads/2013/06/math-time-backgrounds-wallpapers-1024x805.jpg
  • 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.
  • Source: http://www.facebook.comSource: http://www.youtube.com
  • Alfano, Michael Composition of Functions

    1. 1. Composition of Functions Mathematics 11th-12th Grade By Michael Alfano
    2. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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.
    12. 12. Inspiration Diagram 2 4 5 5 1 3 3 4 1 2 Diagram created using Inspiration
    13. 13. Edhelper
    14. 14. SMART Software
    15. 15. Teach-nology
    16. 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. 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. 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. 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.
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