Mathematics 8th Grade: Pythagorean Theorem by Ms. Lejtman https://padlet.com/mslejtman/mslejtman Who, What, When, Where and Why? en-us 2014-11-03 03:58:51 UTC 2015-04-22 13:54:22 UTC hello@padlet.com http://d262le4z25sx36.cloudfront.net/portraits/random.jpg Who? mslejtman https://padlet.com/mslejtman/mslejtman/wish/39475609 Pythagoras. Enough Said. :)

]]> 2014-11-03 04:13:07 UTC https://padlet.com/mslejtman/mslejtman/wish/39475609 What? mslejtman https://padlet.com/mslejtman/mslejtman/wish/39475759 a2 + b2 = c2 - The Pythagorean Theorem!

]]> 2014-11-03 04:16:41 UTC https://padlet.com/mslejtman/mslejtman/wish/39475759 When? mslejtman https://padlet.com/mslejtman/mslejtman/wish/39475908 569 B.C.E. - 500 B.C.E.

]]> 2014-11-03 04:20:16 UTC https://padlet.com/mslejtman/mslejtman/wish/39475908 mslejtman https://padlet.com/mslejtman/mslejtman/wish/39476341 Who was Pythagoras; When and Where did he live; What did he (and his school) discover; Why are his theorems so famous?

]]> 2014-11-03 04:33:34 UTC https://padlet.com/mslejtman/mslejtman/wish/39476341 Where? mslejtman https://padlet.com/mslejtman/mslejtman/wish/39476377 First Greece....

]]> 2014-11-03 04:34:53 UTC https://padlet.com/mslejtman/mslejtman/wish/39476377 Where? mslejtman https://padlet.com/mslejtman/mslejtman/wish/39476398 ...and then Egypt

]]> 2014-11-03 04:35:31 UTC https://padlet.com/mslejtman/mslejtman/wish/39476398 Why? mslejtman https://padlet.com/mslejtman/mslejtman/wish/39476451 One of the many proofs.

]]> 2014-11-03 04:36:58 UTC https://padlet.com/mslejtman/mslejtman/wish/39476451 Essential Questions: mslejtman https://padlet.com/mslejtman/mslejtman/wish/39476863 1. Who was Pythagoras and what is the Pythagorean theorem?
2. What are the proofs for the Pythagorean theorem?

3.  In what ways was the Pythagorean theorem an
  important addition to the field of mathematics? 
4. How is the Pythagorean Theorem applicable in everyday
  life? 

]]> 2014-11-03 04:52:12 UTC https://padlet.com/mslejtman/mslejtman/wish/39476863 Unit Goals mslejtman https://padlet.com/mslejtman/mslejtman/wish/39476868 1.  Identify the parts of a triangle as leg, leg, and hypotenuse

2. Evaluate the Pythagorean theorem and its proofs

3. Analyze a triangle and utilize the Pythagorean theorem to find the value of any side

4. Compare and contrast the proofs that have been developed over the years

5. Use the Pythagorean theorem to discover distances between points on a graph

6. Derive the equation of a circle using the Pythagorean Theorem

7. Describe who Pythagoras was and what mathematical principles he discovered, along with the school that he created

8. Discover and discuss when the Pythagorean theorem is used in real life 

]]> 2014-11-03 04:52:19 UTC https://padlet.com/mslejtman/mslejtman/wish/39476868 4 Common Core Standards that Lessons in this THEMATIC Unit will Address mslejtman https://padlet.com/mslejtman/mslejtman/wish/39476889 1. CCSS.Math.Content.8.G.B.6., Geometry » Understand and apply the Pythagorean Theorem. Explain a proof of the Pythagorean Theorem and its converse.

2. CCSS.Math.Content.8.G.B.7.Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

3. CCSS.Math.Content.8.G.B.8.,Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

4. G. GPA. 1 >>Derive the equation of a circle of given center and radius using the Pythagorean Theorem.

]]> 2014-11-03 04:53:33 UTC https://padlet.com/mslejtman/mslejtman/wish/39476889 Proof for Pythagorean Theorem mslejtman https://padlet.com/mslejtman/mslejtman/wish/41247423 This video explains one of the simplest proofs for the Pythagorean Theorem.

]]> 2014-11-16 18:03:46 UTC https://padlet.com/mslejtman/mslejtman/wish/41247423 Proofs over the centuries mslejtman https://padlet.com/mslejtman/mslejtman/wish/41247742 There have been various proofs found for the Pythagorean Theorem over the centuries. One was even found by a United States President!

We will discuss four of these proofs, found on this website, in depth. Get a head start by clicking on the attachment and checking them out!

]]> 2014-11-16 18:13:45 UTC https://padlet.com/mslejtman/mslejtman/wish/41247742 Easy as ABC, 123 mslejtman https://padlet.com/mslejtman/mslejtman/wish/41247886 The Pythagorean Theorem isn't only something  associated with a, b, and c. We can also use it to help us find the distance between points on a graph. We will discuss this in detail in class, but here is a video to give you a head start.  

]]> 2014-11-16 18:17:39 UTC https://padlet.com/mslejtman/mslejtman/wish/41247886 Worksheet to Practice mslejtman https://padlet.com/mslejtman/mslejtman/wish/41248001 Here is a worksheet to practice finding the distance between two points on a graph using Pythagoras's famous theorem.

]]> 2014-11-16 18:21:01 UTC https://padlet.com/mslejtman/mslejtman/wish/41248001 Triangles, Squares, Rectangles....and Circles? mslejtman https://padlet.com/mslejtman/mslejtman/wish/41248167 The Pythagorean Theorem also helps us derive the equation of a circle. Read the attached presentation and see how this is even possible.

]]> 2014-11-16 18:25:32 UTC https://padlet.com/mslejtman/mslejtman/wish/41248167 What does this have to do with my life? mslejtman https://padlet.com/mslejtman/mslejtman/wish/41248242 This is the question that students have asked from time immemorial. Check out this article which begins to touch upon how useful the Pythagorean Theorem is in real life, while also simultaneously reviewing the key elements of the theorem and its proof.

]]> 2014-11-16 18:28:09 UTC https://padlet.com/mslejtman/mslejtman/wish/41248242 In case you were interested in more life applications... mslejtman https://padlet.com/mslejtman/mslejtman/wish/41248300 Here is a fascinating article about some other applications of the theorem.

]]> 2014-11-16 18:29:48 UTC https://padlet.com/mslejtman/mslejtman/wish/41248300 And some more... mslejtman https://padlet.com/mslejtman/mslejtman/wish/41248329 Here are 10 more practical uses of the Pythagorean Theorem.

]]> 2014-11-16 18:30:35 UTC https://padlet.com/mslejtman/mslejtman/wish/41248329 Three Examples of Usage of Technology During This Unit mslejtman https://padlet.com/mslejtman/mslejtman/wish/41248426

1. After the students first discover the theory on their own (sage on stage vs. guide on the side), the first lesson in the unit will be concluded with a video about Pythagoras, his life, and an overview of his theory. http://bit.ly/1ES3uIj 

2. As a mid-unit assessment, on a smart board,  the teacher will begin creating different right triangles using GEOMETER’s SKETCHPAD. Each one will have a measurement missing. The students will use the theorem to solve for the missing sides.

3. The final assessment of the unit lesson will not only include a paper-and-pencil test with regards to the history of Pythagoras and computing sides of triangles and the equations of circles, but will also utilize the InterACTIVE Pythagorean Explorer. http://bit.ly/1vkc6Wu


]]> 2014-11-16 18:34:04 UTC https://padlet.com/mslejtman/mslejtman/wish/41248426 Pythagorean Theorem and Cirlces mslejtman https://padlet.com/mslejtman/mslejtman/wish/41279490 An image that will be utilized in order to demonstrate how the theorem facilitates the derivation of the equation of a circle.

]]> 2014-11-17 04:53:42 UTC https://padlet.com/mslejtman/mslejtman/wish/41279490 Further Reading mslejtman https://padlet.com/mslejtman/mslejtman/wish/41279608 1. "The Pythagorean Theorem: A 4,000 Year Old History" by Eli Maor

2. "Hidden Harmonies" By Robert and Ellen Kaplan

3. "Pythagoras, What's Your Angle?" by Julie Ellis

]]> 2014-11-17 04:58:45 UTC https://padlet.com/mslejtman/mslejtman/wish/41279608