INTRODUCTION

This WebQuest is intended to teach the Pythagorean Theorem, test the understanding by solving problems using the Pythagorean Theorem and use it in everyday life’s problems.

The Pythagorean Theorem is one of the fundamental theorems of geometry.  This Webquest will teach you about Pythagoras, the creator of the theorem; the different parts of a triangle and also the formula that makes up the Pythagorean Theorem.  You will then be put to the test by solving problems using the Pythagorean Theorem.  Finally, you will be given the challenge of coming up with a problem that you would experience in everyday life in which you can use the Pythagorean Theorem.

TASK

You are required to accomplish four tasks in this Webquest.

1. Research the history of Pythagoras and how he came up with the Pythagorean Theorem.
2. Watch a PowerPoint that introduces you to the Pythagorean Theorem.  In this, you will learn the different parts of a triangle, and it will also show you how to use the Pythagorean Theorem formula to solve problems. 
3. Once you understand how to use the formula, your skills will then be tested when you will have to complete a worksheet of problems using the Pythagorean Formula.
4. A lot of times, students wonder what they will ever use this "stuff" for when they are out of school.  It turns out, though, that the Pythagorean Theorem can be used in solving all kinds of everyday problems, even in your own home.  So next, now that you have mastered your skills on how to use the Pythagorean Theorem, complete the activity related to real-life situations in which you could use the Pythagorean Theorem to come up with the answer to your problem.

PROCESS AND RESOURCES

First, you need to research the history of Pythagoras and the Pythagorean theorem.  While doing your research, you will need to either write out or type up the answers to the following questions on both topics:

Pythagoras

1. When was he born?
2. Where did he live when he discovered the theorem?
3. Which two people did he acquire his knowledge from?

Pythagorean Theorem

1. What is the formal definition of the Pythagorean Theorem?
2. Give a detailed example of the Pythagorean Theorem.

You can use these videos and websites to find your answers:

• Video - https://www.youtube.com/watch?v=FdMXjJunb1o  - The history of Pythagoras and his Theorem
• Video - https://www.youtube.com/watch?v=KVnuUjat4ZU  - The history of Pythagoras and his Theorem
• Website - https://www.britannica.com/science/Pythagorean-theorem - The history of Pythagoras and his Theorem
• Video - https://www.youtube.com/watch?v=HYulFhPtoAo - Pythagoras  Biography
• Video - https://www.youtube.com/watch?v=PdmJAyPaCxw - Pythagoras  Biography
• Website - https://mathshistory.st-andrews.ac.uk/Biographies/Pythagoras/ - Pythagoras  Biography
• Video - https://www.youtube.com/watch?v=AhFjfCdG61Y  – Pythagoras Theorem
• Website - https://www.mathplanet.com/education/pre-algebra/right-triangles-and-algebra/the-pythagorean-theorem - Pythagoras Theorem

After you have finished that task, now move on to the next task.  Watch the following PowerPoint.  This will teach you the basics of the Pythagorean Theorem and how to use it to solve problems. Pythagorean Theorem Powerpoint

After watching the PowerPoint, you should now understand the basics of how to use the Pythagorean theorem.  Now, complete the following worksheet (# 1-10), print it out, and turn it in. Pythagorean Theorem Worksheet

Finally, you may be wondering how you could use the Pythagorean Theorem to solve problems in everyday life.  Well, to get you started, watch this video https://www.youtube.com/watch?v=jG6XVCgdGLA&feature=emb_title  and then try to solve the following two real-life problems

Real Life problems

From this, come up with your own idea on how you could use the Pythagorean Theorem in your own home.  For instance, you could use it to find out how big of television you can get to fit in the space that you have. Write down some thoughts, and see how common is to use the Pythagorean Theorem in your everyday life!!!

CONCLUSION

Having now completed this webquest, you should have a firm understanding on the Pythagorean Theorem and be able to use it not just in your home, but everywhere you go!  And don't forget, even though you may not realize it, most math that you learn in school can be applied either in your home or anywhere that you go.

Evaluation of learning achievements

In this section we will not dive very deep into the underlying educational theories about evaluation and testing: there’s too much out there than we could possibly cover in this small project report.

Instead, we want to concentrate on procedures that enable both students/pupils and their teachers to establish if the learning goals of the Webquest were achieved and, if so, to what extent. We recommend teachers make use of a combined evaluation procedure, that consists of:

1. Statements by learners (after being asked to do so)
   • telling what they learned about the subject (knowledge-oriented self-evaluation): now (after going through the Webquest) I know that …
   • telling what he/she learned about herself/himself (formative evaluation, in this case, diagnostic self-evaluation): now (after going through the Webquest) I know about myself that I …
     This pair of basic statements add up to a so-called learner report, in which the pupil/student reflects on what the Webquest brought him/her in terms of acquired knowledge and new personal views and attitudes concerning the subject.

   For instance:

   • ‘I learned that in medieval times the hygiene of people was hardly a concern which helped to let epidemic diseases like the Plague cause so many casualties’ Or:
   • ‘I learned the facts and I know the earth is warming, but I cannot understand why people were so stupid to pollute the world and let it warm up so much.
   • ‘I learned from the information about diseases that this subject is more appealing to me than I would expect in advance: maybe I should consider a medical career’. Or:
     ‘The Webquests confirms what I thought already: I could not care less about the climate and global warming. In fact, I thought it was all a hoax and I still do!’

   This kind of assessment seems more subjective than it actually is: in his standard work on testing and evaluation (and much more), simply called Methodology (1974), Prof. A.D. de Groot described how consistent the student’s self-evaluations appeared to be: when asked again after 5 or 10 years, their evaluation would almost be the same. De Groot advised teachers to use the learner report as a start for joint evaluations, striving for consensus between teacher and student/pupil about the learning outcomes and their value for the learner, but also compared with the learning objectives as stated in the curriculum.

2. The learning achievements are visible in the output produced by the students: it is physical evidence: reports, answers to questions asked in the Webquest, presentations, and performance during presentations (preferably recorded). The teacher completes an evaluation grid stating clearly what the learning outcomes for the student/pupil are. The categories in the grid can be modified by the teacher to cover more precisely the content of a Webquest.

   >We advise teachers to use the grid to start a joint evaluation discussion, aiming at consensus or at least understanding between the teacher and the student/pupil about the learning outcomes: were they achieved (as planned in the curriculum and communicated before the Webquest started) and to what extent? To communicate the learning goals clearly before any learning activity starts, is a transparency requirement that is widely acknowledged in the educational community. The history of making learning objectives explicit goes back to the evaluation ‘Bible’ by Bloom, Hastings and Madaus: ‘Handbook on formative and summative evaluation of student learning’ (1971), a standard work that also served as inspiration for the earlier mentioned Prof. De Groot.

The procedure also applies when students/pupils have worked together on a Webquest. The teacher will ask questions about individual contributions: ‘What did you find? What part did you write? How did you find the illustrations? Who made  the final presentation?’

All the evidence (of learning efforts and outcomes plus joint evaluations) is preferably stored in the learning portfolio of the student, or in any other suitable storage system (folders with written or printed documents, online collection of files, etcetera ).

Changes in personal points of view and feelings are harder to value and here the consensus between teacher and student/pupil about experiences during the learning process provides essential insights.

The grid below gives an example of how the evaluation of the learning process and achievements can be shaped: what kind of reactions to the Webquest does the teacher expect and how valuable are they? Is the teacher capable to explain the value or score allocated to answers or presentations given by pupils? Does the pupil/student understand the evaluation outcomes, and does he/she agree? If an agreement (consensus is not possible, it is still the teacher who decides how to value the student’s work.

Please note that the text in the grid addresses the pupil/student directly: this is important and it is in fact a prerequisite for using such an evaluation grid: it is specifically meant to enable a discussion of learning results between teacher and student and not to communicate learning achievements of learners to others who had no direct role in the Webquest.

Evaluation Grid