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TITLE: The Pythagorean Theorem |
AUTHOR: Franco A. DiPasqua |
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GRADES: 8 & 9 SUBJECTS: 8th grade mathematics & Course I Algebra |
SCHOOL: Whitesboro Middle School |
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KEYWORDS: Interdisciplinary (Mathematics & English) |
TITLE OF CAREER ZONE LESSON:
The Pythagorean Theorem
LEARNING CONTEXT:
NYS MATH Standard 7: Students develop and apply the Pythagorean principle in the solution of problems.
NYS MATH Standard 3: Students use number sense and numeration to develop an understanding of the multiple uses of numbers in the real world, the use of numbers to communicate mathematically and the use in the development of mathematical ideas.
NYS MATH Standard 1: Students explore and use the operations dealing with roots and powers.
NYS ELA Standard 1: Students will read, write and speak for information and understanding.
NYS MATH Standard 2: Students will access, generate, process and transfer information using appropriate technologies (Internet use and word-processing use).
PROCEDURE:
Before I explain the procedure it is important to note a few items:
The students will explore who Pythagoras was and complete a 3-5 research paper, with diagrams in conjunction with ELA. The students will also complete four real-life problems involving the Pythagorean Theorem (A problem sheet will be provided). This is a two-week project (out of class for math, in class for English) activity and counts as a test grade (a separate grade for each class). Students will be given a list of questions that must be answered on who Pythagoras was (the questions must have references and be answered in essay form). Students will have access to computers with Internet connections, as well as encyclopedias during English class. .
INSTRUCTIONAL/ENVIRONMENTAL MODIFICATIONS:
Arrangements will be made to use the media center and computer lab for computers with word processing and Internet connections. It has been taken into consideration that not all students have Internet Access at home, so the students will have the opportunities to work in English class, lunch, before school and after school on this project. Media Specialists will have books on Pythagoras, Encyclopedia CD-ROMs available, as well as print sets. The Media Specialists will also direct the students to the proper use of the Internet in school, as well as at home. Arrangements with English teacher on our team will be made to teach the students how to write an essay with documentation. In the classroom calculators are provided for this project.
Special Need Students will be given extended time, if so stated on their IEP’s. The Special Education Teacher will be kept up to date on what is going on in the classroom as this project progresses.
MATERIALS AND SUPPLIES:
Computers with word processing and Internet connections (studenst will have to do internet searches on Pythagoras)
Encyclopedias – print and CD-ROM
Books on Pythagoras
Question Sheets
Math Worksheets
TIME REQUIRED: Assigned on a Monday……due in 11 nights.
ASSESSMENT TOOLS & TECHNIQUES:
English Teacher will correct paper for grammar and mechanics.
Math teacher will correct paper for mathematical accuracy.
Each teacher will have their own rubric and will assign their own grade. The math rubric’s highest score is 12/12 (100%) and the ELA rubric’s highest score is 8/8 (100%). It is up to the teacher if they want to make a scale for the various grades or if they want to change the percentages to raw numbers.
REFLECTION:
This activity was a great way to get my students to do a research project on a great mathematician. Not only did they get to do the math involved, but they received an opportunity to integrate English and History skills into the project also. When the students completed this take home project they seemed enlighten about who Pythagoras was and why we study the Pythagorean Theorem.
I recommend to any Math/English team that they do this project. It makes the students see the connections between Math and English. It also helps the students visualize who came up with a theorem, one of which we all have to learn at some point in school to graduate.
In closing, let me tell you that I have done much work with the Pythagorean Theorem in the past, but it just didn’t seem to have a "flare" to it, but now that I have done it this way,
And
ATTACHMENTS: Enclosed you will find the following:
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Score: |
Students will read, write and speak for information and understanding - (NYS ELA Standard 1) |
Students will access, generate, process and transfer information using appropriate technologies (Internet use and word-processing use.) - (NYS MATH Standard 2; this is a nice cross-over into English) |
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4 |
The research paper shows a clear understanding of spelling, grammar and mechanics. The student clearly conveys thoughts and ideas. The paper itself, is at least 5 pages in length and has all the necessary components. |
The research paper shows that the student accessed the correct data from the Internet and wrote this data into their paper by using Microsoft WORD or a similar software. Also, the student had little trouble using the Internet and WORD, after several teacher examples were given. |
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3 |
The research paper shows a clear understanding of spelling, grammar and mechanics with minor flaws and/or mistakes. The student conveys thoughts and ideas with little difficulty. The paper itself, is between 3-5 pages in length and has all the necessary components. |
The research paper shows that the student had not accessed much data from the Internet. The student wrote this data into their paper by using Microsoft WORD or a similar software. Also, the student had much trouble using the Internet and WORD, after several teacher examples were given. |
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2 |
The research paper has several spelling, grammar and mechanics with major flaws and/or mistakes. The student does not clearly convey thoughts and ideas. The paper itself, is no longer than 3 pages in length. Missing some components. |
The research paper shows that the student had accessed little to no data from the Internet. The student wrote this data into their paper by using Microsoft WORD or a similar software. Also, the student had much trouble using the Internet and WORD, after several teacher examples were given. It was not evident that the student put much time or energy outside of class seeking help to use the technology. |
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1 |
The research paper has many spelling, grammar and mechanics with major flaws and/or mistakes. The student does not clearly convey thoughts and ideas. The paper itself, does not meet length requirements. Missing many components. |
The research paper shows that the student had accessed no data from the Internet. The student wrote this data into their paper by using Microsoft WORD or a similar software. Also, the student could not use the Internet and WORD, after several teacher examples were given. It was extremely evident that the student did not put much time or energy outside of class seeking help to use the technology. |
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Score: |
Students develop and apply Pythagorean Principle in the solution of problems - (NYS Math Standard 7) |
Students use number sense and numeration to develop an understanding of the multiple uses of numbers in the real world, the use of numbers to communicate mathematically and the use of numbers in the development of mathematical ideas - (NYS Math Standard 3) |
Students explore and use the operations dealing with roots and powers - (NYS Math Standard 1) |
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4 |
The problems clearly show the use of the Pythagorean Theorem. The formula is written and the work is easily followed. |
Student clearly demonstrated in the paper that they understand who Pythagoras was and how he worked with the Pythagorean Principle. The paper demonstates the understanding of the multiple uses of the Theorem and how it fits into real life applications today. |
Four Problems have complete work with exponents of 2. Student has demonstrated all the proper steps in dealing with the exponents and in taking square roots. Problems that say simplest radical form are in simplest radical form, not rounded to the nearest tenths place. |
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3 |
The problems clearly show the use of the Pythagorean Theorem. The formula is written and the work is not so easily followed (perhaps a little messy or sloppy). |
Student clearly demonstrated in the paper that they understand who Pythagoras was and how he worked with the Pythagorean Principle. The paper does not clearly demonstate the understanding of the multiple uses of the Theorem and how it fits into real life applications today. |
Some Problems are missing work, the answers are correct but there are missing parts in the problems. The student has not shown that he/she has squared a number or that a square root has been taken. Required answers are not in simplest radical form, but are to the nearest tenths place. |
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2 |
Problems are unclear how they were solved. Student has not clearly written the sides a,b, and c in the proper parts of the equation but gets most of the correct answers. |
Student has shown an understanding of who Pythagoras was and how he used the Theorem but paper doesn't convey 100% understanding on his/her part. Areas are missing or do not quite make sense. There are no ties to real-life applications. |
One problems has an incorrect answer. The student has not shown that he/she has squared a number or that a square root has been taken. Required answers are not in simplest radical form, but are to the nearest tenths place. |
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1 |
Theorem is incorrectly used. Student shows considerable difficulty in solving the problem. |
Paper shows student lacks understanding who Pythagoras is and why the Theorem is important in real-life. |
The use of exponents and square roots is not clearly found. Student has not shown enough work to show his/her understanding of how to work with these mathematical operations. |