Roselle School District

Mathematics Curriculum

Grade 8 Unit 10: Pythagorean Theorem

Essential Question(s) Enduring Understanding(s) How can you use any two sides of a right triangle to find the third The Pythagorean theorem relates the side lengths of a right triangle. side? Will the Pythagorean theorem work for triangles that are not right triangles?

Common Core Standards, 2010

Understand and apply the Pythagorean Theorem.

 8. G.6. Explain a proof of the Pythagorean Theorem and its converse.  8. G.7. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.  8. G.8. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.  W8.2 Write informative/explanatory texts to examine a topic and convey ideas, concepts and information through the selection, organization, and analysis of relevant content.

Learning Activities/Resources Student Formative Technology Integration Expectations Strategies/Modifications/ Assessments TLWBAT… Differentiation Model a proof of Pythagorean theorem introduction: Small group instruction Exit ticket http://www.basic- the Pythagorean Students will research the philosopher Review of printed notes  Find the mathematics.com/pythagorean- Theorem and its Pythagoras and his contribution to the from smart board. Activities hypotenuse theorem-calculator.html converse. theorem. completed in small group for  Find the Students will see how the theorem was more of an understanding distance http://www.ehow.com/info_85710 introduced (i.e. how it takes three between 30_ways-make-pythagorean- squares to make a triangle). Students will Individualized instruction these two theorem-cool.html answer questions given in a journal Handout on Geometry level points assignment. for advance students http://www.ehow.com/info_81782 Journal entry 18_maths-projects-pythagorean- Introduction to Pythagorean theorem on Peer tutoring What’s the error? theorem.html Smart board. Students will create a Students work in pairs for  A student said reference sheet with formula and the assistance and help the side Pythagorean game: variable representations of a, b, and c. lengths 41, http://www.math- Various examples will be given in order to Use of manipulatives 40, and 9 do play.com/Pythagorean-Theorem- allow students to practice their skills and Squares put together to not form a Game.html knowledge. make triangles right triangle because 9 Jeopardy game: Converse Introduction: Computer activities for squared + 41 http://www.quia.com/cb/278769.h Choose two students to stand should-to- remediation squared = tml?AP_rand=1700839161 shoulder. Mark the standing location. See attached technology and 1762 and 40 Have the students walk forward along resource portion squared = lines perpendicular to each other. Stop 1600. What the students after a few steps. Choice activities error did the Demonstrate with a measuring stick Menu given on Google Site student when you add the squares of the distance for advance students make? each students is from the starting point, the sum is the square of the distance Chunking information Do now between the students. Students then Reference sheet chunking POD from LOTI have an open discussion in ways to apply information displayed this demonstration to ordered pairs on a Quiz coordinate grid. Video tutorials from Pythagorean Theorem textbook quiz Guided practice work: Distance quiz Examples from power point on Holt POW McDougal 4-9 Independent practice: Test Find the distance between these two Summative points: Assessment Examples given on smart board Find the length of the hypotenuse to the Oral questioning nearest tenth (on smart board) IEP recommendation Transfer and apply Formula reference sheet creation

Homework Holt McDougal worksheets Apply the Introduction: Small group instruction Exit ticket http://www.kidsnumbers.com/pyth Pythagorean Review of Pythagorean theorem with Review of printed notes Find the side lengths agorean-theorem-game.php Theorem to identifying the legs and hypotenuse on from smart board. Activities of each hypotenuse to determine erasable white boards. Examples given completed in small group for the nearest Pythagorean theorem board: unknown side by teacher. more of an understanding hundredth. http://www.glencoe.com/sec/math lengths in right /t_resources/gamezone/pdfs/mac3 triangles in real- Power point presentation on Smart board Individualized instruction Journal entry _04/class_ch03.pdf world. with finding the unknown side of any Handout on Geometry level Two airplanes leave given length for each leg. Practice for advance students the same airport at the Apply the problems are given for review. same time. The first Pythagorean Peer tutoring plane flies to a landing Theorem to Guided Practice: Students work in pairs for stirp 350 miles south, determine Problems Solving Strategies given: assistance and help whoel the other plane unknown side Real world scenarios given for applying flies to an airport 725 lengths in right Pythagorean theorem and its converse in Use of manipulatives miles west. How far triangles in power point slide with pictures in order Squares put together to apart are the two mathematical to depict real world scenarios. make triangles planes after they land? problems in two Draw a figure and tell and three Independent Practice: Computer activities for me how to solve it. dimensions. Students will complete power point on remediation their own. See attached technology and Do now Extra work given if needed. resource portion POD from LOTI

Choice activities Quiz Menu given on Google Site Pythagorean Theorem for advance students quiz Distance Quiz Chunking information Test Reference sheet chunking Summative information displayed Assessment

Video tutorials from Oral questioning textbook IEP recommendation if needed Homework Holt McDougal worksheets

Apply the Converse Introduction: Small group instruction Exit ticket http://www.basic- Pythagorean Choose two students to stand should-to- Review of printed notes Find the length of the mathematics.com/pythagorean- Theorem to find shoulder. Mark the standing location. from smart board. Activities diagonal of the theorem-calculator.html the distance Have the students walk forward along completed in small group for rectangle between two lines perpendicular to each other. Stop more of an understanding http://www.ehow.com/info_85710 points in a the students after a few steps. Journal entry 30_ways-make-pythagorean- coordinate Demonstrate with a measuring stick Individualized instruction Draw a triangle. theorem-cool.html system. when you add the squares of the distance Handout on Geometry level Explain how to use the each students is from the starting point, for advance students converse of the http://www.ehow.com/info_81782 the sum is the square of the distance Pythagorean theorem 18_maths-projects-pythagorean- between the students. Students then Peer tutoring to decide whether it is theorem.html have an open discussion in ways to apply Students work in pairs for a right triangle. this demonstration to ordered pairs on a assistance and help Pythagorean game: coordinate grid. Do now http://www.math- Use of manipulatives POD from LOTI play.com/Pythagorean-Theorem- Guided practice work: Squares put together to Game.html Worksheet on distance formula examples make triangles Quiz Pythagorean formula Jeopardy game: Independent practice: Computer activities for Distance Formula http://www.quia.com/cb/278769.h Practice problems 4-9 lesson online quiz remediation tml?AP_rand=1700839161 from textbook See attached technology and Test resource portion Summative http://www.kidsnumbers.com/pyth Assessment agorean-theorem-game.php Chunking information Reference sheet chunking Oral questioning Pythagorean theorem board: information displayed IEP recommendation if http://www.glencoe.com/sec/math needed /t_resources/gamezone/pdfs/mac3 Video tutorials from _04/class_ch03.pdf textbook Homework Holt McDougal worksheets