KRegan


 * Annotated Text Set** **Kathleen Regan EDC 448**

**Context for using the text set:** This set is geared to an 8th grade geometry lesson on the Pythagorean Theorem. I designed the set to mix history, instruction of the theorem and higher level proof skills in varying ways to link all three for a greater degree of relevance. I included sections on review of coordinate systems, graphing and areas of polygons to connect those topics as prior knowledge. I also included a range of reading level material that contains similar information. The higher level material will be used as vocabulary instruction. The students range from 6th grade to 9th grade reading level. I have included visual and audio material to aid the lower reading levels. Most of the text will be used in conjunction with manipulatives. The Pythagorean Theorem has over 100 proofs so I wanted to include plenty of proofs and proofing exercises. I also wanted to make sure the important connection to the distance formula was made.


 * A. Print Resources:**
 * Text #1: What’s your angle, Pythagoras?**
 * Citation: Ellis, J. (2004). //What’s your angle, Pythagoras?// Watertown, MA: Charlesbridge.
 * Text Summary: This is a fictitious illustrated picture book based on the childhood of Pythagoras. Young Pythagoras discovers a special number pattern and uses it to solve problems involving right triangles.
 * Rationale: I selected this text because it is visually pleasing and offers a variety to the other text books. It would be appropriate for an average 8th grade reader. It offers relevance and history and would spark prior knowledge.
 * Use of text: The Students would read this book on their own and then answer the questions in the edhelper.com worksheets.

**Text #2: Algebra 1**  **Text #3: Looking for Pythagoras**  **Text #4: Barron’s E-Z Geometry**  **Text #5: The Pythagorean Theorem**
 * Citation: Ellis, W., Hollowell, K., Kennedy, P., & Schultz, J. (2003). //Algebra 1// (pp. 24-29). Austin, TX: Holt, Rinehart and Winston.
 * Text Summary: This is an 8th grade Algebra book that includes a section on the coordinate system.
 * Rationale: I included these pages because the go in depth into the coordinate system with many problems to solve. This would not only serve to review the coordinate system but also key vocabulary that the students will need in the Pythagorean lesson.
 * Use of text: Students will read this text as part of a coordinated learning exercise. Students with team up and work to solve the problems with graphing supplies.
 * Attachment: #1
 * Citation: Fey, J. T., Fitzgerald, W. M., Friel, S. N., Lappan, G., & Phillips, E. D. (1998). //Looking for Pythagoras.// Upper Saddle River, NJ: Dale Seymour Publications.
 * Text Summary: This a supplement text book focusing on the Pythagorean Theorem. It includes review of the coordinate systems and area and lengths. The format includes history text frames, problem solving and applications. Irrational numbers are introduced in later chapters.
 * Rationale: I selected this text because it offers a nice variety of examples and content. Many of the activities could also be taught with the applets, Sketchpad, or manipulatives.
 * Use of text: This would be the main text for the unit on Pythagorean Theorem. I would use this to model think alouds initially. The students would be using this text for problem solving, application and making connections.
 * Citation: Leff, L. S. (2009). //Barron’s e-z geometry// (pp. 237-243)//.// Hauppauge, NY: Barron’s Educational Series, Inc.
 * Text Summary: This is an in-depth self teaching guide to Geometry. It provides instruction, vocabulary, exercises and cumulative review questions.
 * Rationale: I included this book because it goes in depth in teaching the proper forms of proof writing. It introduces the Pythagorean Triplets. It would also be very useful for assessment.
 * Use of text: Students will get practice at proof writing. It utilizes a variety of review vocabulary. I would use it also as homework pages.
 * Attachment: #2.
 * Citation: Lindauer, H. (1998). //The Pythagorean theorem.// Retrieved March 3, 2010 from the University of Kentucky department of mathematics website at http://www.ms.uky.edu/~lee/ma502/pythag/pythag.htm.
 * Text Summary: This is a website that gives a short introduction to the history of Pythagoras and then provides two of the more basic proofs.
 * Rationale: I selected this site because it provides history and proofs that are more suitable for the lower level reading level. It provides a simpler version of two proofs that we could supplement with manipulatives.
 * Use of text: Students will read the text and use the proofs provided to visualize the application of the theorem.
 * Attachment: #3

**Text #6: Some tips for studying mathematics** http://www.sfcc.edu.hk/academic_subjects/mathematics/web/1998_1999_projects/Janet%20Lo/Bb/home.html.
 * Citation: Lo, J. (n.d.). //Some tips for studying mathematics.// Retrieved March 3, 2010 from website at http://www.sfcc.edu.hk/academic_subjects/mathematics/web/1998_1999_projects/Janet%20Lo/Bb/study.htm. Homepage at
 * Text Summary: This site provides tips for studying Mathematics written by a 17 year old high school student.
 * Rationale: This is a great text for group discussion, think aloud questions, B/D/A questions and vocabulary discussion.
 * Use of text: The students would read the text one section at a time and discuss the key concepts and vocabulary. Prior knowledge questions would be asked prior to reading, reflection discussions would occur during the reading and application questions would be discussed after reading.
 * Attachment: #4

**Text #7: Geometry for the clueless**
 * Citation: Miller, B. (2006). //Geometry for the clueless// (pp. 74-80)//.// New York, NY: McGraw-Hill.
 * Text Summary: This is a geometry book written by a college math professor. It presents text in a humorous way to students. It includes instruction, proofs and exercises.
 * Rationale: I chose this text because it approaches the topic from a more friendly humorous way. It offers full proofs in standard format. It also introduces the triplets.
 * Use of text: The students would read along while I read the text and model the interpretation of the text. Students could also combine these problems with board work.
 * Attachment:#5

**Text #8: History topics: Pythagoras’ Theorem** Homepage at http://www-history.mcs.st-andrews.ac.uk/history/.
 * Citation: O’Connor, J. J., & Robertson, E. (2000). //History topic: Pythagoras’s theorem in babylonian mathematics.// Retrieved March 3, 2010 from The mactutor history of mathematics website at http://www.gap-system.org/~history/HistTopics/Babylonian_Pythagoras.html __.__
 * Text Summary: This is a historical account of the babylonian evidence of the pythagorean theorem with proofs.
 * Rationale: This is a higher level historical text that would offer vocabulary challenge. It would also be great to generate discussions and reflections on the historical aspect of the theorem.
 * Use of text: Students would read this text after completing exercises in proof reading and writing. It can be used to generate historical discussions and activate prior knowledge.
 * Attachment: #6

**Text #9: The Pythagorean Theorem worksheets**
 * Citation: n.a., n.d. //The Pythagorean theorem// worksheets. Retrieved on March 3, 2010 from Edhelper.com website at http://www.edhelper.com/math/area_perimeter12.htm. Homepage at http://www.edhelper.com/.
 * Text Summary: Edhelper.com is a membership based website offering newly generated worksheets on all subjects and topics for k-12.
 * Rationale: I included this site because of it’s usefulness in offering exercises that you can vary for level.
 * Use of text: These sheets provide homework practice in solving Pythagorean Theorem problems. The students would read the text at home and come back with solutions.
 * Attachment: #7

**Text #10: What’s your angle, Pythagoras? worksheets**
 * Citation: n.a., n.d. //What’s your angle, Pythagoras?// worksheets. Retrieved on March 3, 2010 from Edhelper.com at http://www.edhelper.com/books/Whats_Your_Angle_Pythagoras.htm. Homepage at http://www.edhelper.com/.
 * Text Summary: Edhelper.com is a membership based website offering newly generated worksheets on all subjects and topics for k-12.
 * Rationale: These worksheets are connected to the //What’s your Angle, Pythagoras?// text.These worksheets provide activities to explore the interdisciplinary aspect of the Pythagorean Theorem.
 * Use of text: Students would read the text and do the research asked for and provide answers to the questions. There are questions for B/D/A the reading. There is also reflection questions based on the text.
 * Attachment: #8



**Text #11: Pythagorean theorem what’s the point?** 
 * B. **Media Resources**
 * Citation: Navarrette, S. (2009). //Pythagorean theorem what’s the point?// Podcast retrieved from the website at http://webclass.org/podcasts/utech/PythagoreanTheorem_Navarrette.xml. Homepage at http://sites.google.com/site/episdsanavarr/.
 * Text Summary: A podcast by middle school teacher Susan Navarrette, demonstrating the Pythagorean theorem, proofs and exercises.
 * Rationale: I included this podcast to offer the theorem with an audio/visual instruction for the students that are at a lower reading level.
 * Use of text: Students watch podcast and follow along with the exercises.

**Text #12: Easy Pythagorean Theorem Proofs and Problems** http://www.math-videos-online.com/easy-pythagorean-theorem-proofs.html. Homepage at http://www.math-videos-online.com/index.html..
 * Citation: Popovici, D. (2007). //Easy Pythagorean theorem proofs and problems.// Videos retrieved from
 * Text Summary: This is a video clip that explains the Pythagorean theorem in word problem format.
 * Rationale: I chose this video clip because it models think aloud examples for the students.
 * Use of text: Students watch the video clip and follow with the exercises.

**C. Online interactive resources**  **Text #14: The Geometer’s Sketchpad**
 * Text #13: Manipula math applet collections**
 * Citation: International Education Software (IES Inc.) (2003). //Manipula math applet collections.// Retrieved March 7, 2010 from Math education and technology International Education Software website at http://www.ies.co.jp/math/products/geo2/menu.html. Homepage at http://www.ies.co.jp/math/products/.
 * Text Summary: Numerous applets based on the Pythagorean Theorem.
 * Rationale: I selected these applets because they offer the students an interactive way of proving the Pythagorean Theorem and apply different data to the applications.
 * Use of text: Students can use the computer or smartboard to answer questions from the teacher in a visual way.
 * Attachment: #9
 * Citation: Jackiw, N. (2010). Key Curriculum Press: The geometer’s sketchpad (version 5.0) [software]. Available from http://www.keypress.com/x24070.xml.
 * Text Summary: Computer software designed to build and investigate mathematical models, objects, figures, diagrams and graphs.
 * Rationale: I selected this software as an important teaching aid in the classroom. Used in conjunction with a smartboard it provides visual, interactive stimulation for the student.
 * Use of text: I would use this as a teaching tool as well as a tool the students would use themselves to manipulate geometric forms. I would model a tutorial of the program for the students prior to instruction.
 * Attachment:#10

**Text #15: Pythagoras’ theorem**
 * Citation: Pierce, R. (2006). //Pythagoras’ theorem.// Retrieved on March 3, 2010 from Mathisfun.com website at http://www.mathsisfun.com/pythagoras.html. Homepage at http://www.mathsisfun.com/.
 * Text Summary: A math website that instructs on the Pythagorean Theorem and provides proof and example.
 * Rationale: I chose this as a lower reading level text that provides simple proofs. The layout is colorful and uncluttered.
 * Use of text: Students read the text and follow the exercises. It can be used alone or with the applets or geometer’s sketchpad.
 * Attachment: #11

**D. Instructional Resources**

 **Text #17: The Pythagorean theorem session 6** http://www.learner.org/courses/learningmath/geometry/session6/video.html?pop=yes&pid=1804#. Homepage at http://www.learner.org/.
 * Text #16: Geometry**
 * Citation: Demme, S. (2005). //Geometry//. Math-u-see curriculum. Retrieved from http://www.mathusee.com/default.php?language=RhodeIsland.
 * Text Summary: This is a home education geometry curriculum course with teacher manual, dvd instructions, student text of problems and assessment book.
 * Rationale: I included this curriculum because of the quality of the dvd instruction and amount of exercises. It is manipulative based.
 * Use of text: The dvd is geared for teacher viewing but students can also watch the dvd on their sections, and solve the accompanying problems. Group work with manipulatives is supported with this plan.
 * Citation: n.a., n.d. //The Pythagorean theorem session 6 video.// Washington, DC: Annenberg Media. Retrieved on March 3, 2010 from
 * Text Summary: This is a teacher educating website that provides credited course work and instructional video. The session 6 video concentrates on the Pythagorean Theorem.
 * Rationale: I found this to be an interesting video selection on lesson planning. It gave me some ideas on activities for my lesson.
 * Use of text: To provide examples of lesson plans dealing with various mathematical topics as well as teacher discussion and interview.

**Using these texts together in the classroom:** The focus of my text set is to provide information on the discovery, instruction, application and proof of the Pythagorean Theorem. Considering there are over 100 proofs to this theorem, I wanted to make sure I had material that would address the proofs at an 8th grade level. I also wanted to devote time to historical information both on Pythagoras and the Babylonians and relate the discovery to the relevance of the theorem to today’s society. I would use the //Looking for Pythagoras// text as a main source throughout the lesson. I would then supplement that text with review material on coordinate systems and area. The students would use manipulative and software to aid in their review process with sections in the //Algebra 1// and //Barron’s// text. We would use this opportunity to collect vocabulary words that will be important to the rest of the lesson. The history text would be introduced with a variety of sources at different reading levels. Audio/visual components will aid in the understanding as we begin our instruction of the theorem. Software and applets will be involved in group activities and exploration. There will be daily work on proofs utilizing the simpler proofs first and working towards the more complex. Homework will be given in exercise worksheets and essay questions. Vocabulary segments will be addresses throughout with every text to reinforce. Students will be required to read all material with scaffolding activities. Some material they will read independently after all vocabulary has been addressed. All will participate in the interactive activities. The //Tips for studying Math// text will be utilized as a higher level reflection exercise.

**Learning Objectives:**

Content: M(G&M)–8–2 __**Applies the Pythagorean Theorem** to find a missing side of a right triangle, or in problem solving situations__. (Local).

M(G&M)–5–9 **Demonstrates understanding of spatial relationships using location and position** by interpreting and giving directions between locations on a map or coordinate grid (__all four quadrants__); __plotting points in four quadrants in context (e.g., games, mapping, identifying the vertices of polygons as they are reflected, rotated, and translated)__; and determining horizontal and vertical distances between points on a coordinate grid in the first quadrant. (Local)

Reading:
 * R–7–7 Demonstrate initial understanding of informational texts (expository and practical texts) by.**

R–7–7.1 Obtaining information from text features (e.g., table of contents, glossary, index, transition words/phrases, transitional devices, bold or italicized text, headings, subheadings, graphic organizers, charts, graphs, or illustrations) (State)

R–7–7.2 Using information from the text to answer questions, to state the main/central ideas, or to provide supporting details (State)

**R–7–7 Demonstrate initial understanding of informational texts (expository and practical texts) by.**

R–7–7.4 Generating questions before, during, and after reading to enhance understanding and recall; expand understanding and/or gain new information (Local)

**R–7–8 Analyze and interpret informational text, citing evidence as appropriate by...** •

R–7–8.1 Explaining connections about information //within// a text, //across// texts, or to related ideas (State)

R–7–8.2 Synthesizing and evaluating information within or across text(s) (e.g., constructing appropriate titles; or formulating assertions or controlling ideas (State)

//Comments from Monica Van Horn Who knew you could find 17 different texts about the Pythagorean Theorem!// //The picture book sounds like a great way to present the human side of mathematics--remembering the people created the ideas we study today. I also really appreciated the math tips website. Reminding students of HOW to learn is often ignored as we try to teach WHAT to learn. Perhaps your students could create their own tips at the end of the year. I'm going to have to check out __Geometry for the Clueless__. I'm glad to see more engaging math books coming out.//

