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Foundations of Technology Pythagorean Theorem

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Presentation on theme: "Foundations of Technology Pythagorean Theorem"— Presentation transcript:

1 Foundations of Technology Pythagorean Theorem
STEMCenter for Teaching & Learning™ Engineering byDesign™ 12/01/2009 Foundations of Technology Pythagorean Theorem TITLE SLIDE Teacher Resource – Unit 2 Lesson 1 © 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology © International Technology Education Assoc

2 STEMCenter for Teaching & Learning™ Engineering byDesign™
12/01/2009 The BIG Idea Big Idea: The Engineering Design Process is a systematic, iterative problem-solving method that produces solutions to meet human needs and wants. [Authors: Please include teacher notes appropriately.] © 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology © International Technology Education Assoc

3 STEMCenter for Teaching & Learning™ Engineering byDesign™
12/01/2009 Rationale Engineers use mathematical equations as tools to help them create technical solutions, structures, and products to meet the needs and desires of society. Throughout the Foundations of Technology course, students will apply mathematics to solve practical problems and work through design challenges. The Pythagorean Theorem is an excellent place to start because it applies simple logic and basic algebra. [Authors: Please include teacher notes appropriately.] © 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology © International Technology Education Assoc

4 STEMCenter for Teaching & Learning™ Engineering byDesign™
12/01/2009 Pythagorean Theorem The Pythagorean Theorem applies to right triangles and states that the square root of the hypotenuse is equal to the square root of the sum of the squares of the adjacent sides. Algebraically: a² + b² = c² Where “c” is the hypotenuse and “a” and “b” are the adjacent sides Hypotenuse (c) Adjacent Sides (a + b) [Authors: Please include teacher notes appropriately.] Right (90º) Angle © 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology © International Technology Education Assoc

5 STEMCenter for Teaching & Learning™ Engineering byDesign™
12/01/2009 Practice Problems Solve for the unknown variable: c = ____ a = 4in b = 3in [Authors: Please include teacher notes appropriately.] © 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology © International Technology Education Assoc

6 STEMCenter for Teaching & Learning™ Engineering byDesign™
12/01/2009 Practice Problems Solve for the unknown variable: c² = a² + b² c² = (4in)² + (3in)² c² = 16in² + 9in² c² = 25in² √c² = √25in² c = 5in c = 5in a = 4in b = 3in [Authors: Please include teacher notes appropriately.] © 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology © International Technology Education Assoc

7 STEMCenter for Teaching & Learning™ Engineering byDesign™
12/01/2009 Practice Problems Solve for the unknown variable: c = 15in a = ____ b = 9in [Authors: Please include teacher notes appropriately.] © 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology © International Technology Education Assoc

8 STEMCenter for Teaching & Learning™ Engineering byDesign™
12/01/2009 Practice Problems Solve for the unknown variable: c² = a² + b² c² - b² = a² a² = (15in)² - (9in)² a² = 225in² - 81in² a² = 144in² √a² = √144in² a = 12in c = 15in a = 12in b = 9in [Authors: Please include teacher notes appropriately.] © 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology © International Technology Education Assoc

9 STEMCenter for Teaching & Learning™ Engineering byDesign™
12/01/2009 Practice Problems Solve for the unknown variables: c = ______ a = 12in [Authors: Please include teacher notes appropriately.] b = 10in © 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology © International Technology Education Assoc

10 STEMCenter for Teaching & Learning™ Engineering byDesign™
12/01/2009 Practice Problems Solve for the unknown variables: c² = a² + b² c² = a² + (½b)² c² = (12in)² + (5in)² c² = 144in² + 25in² c² = 169in² √c² = √169in² c = 13in c = 13in a = 12in [Authors: Please include teacher notes appropriately.] b = 10in © 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology © International Technology Education Assoc

11 STEMCenter for Teaching & Learning™ Engineering byDesign™
12/01/2009 Practice Problems Calculate the total amount of material required to construct the crane boom: [Authors: Please include teacher notes appropriately.] © 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology © International Technology Education Assoc

12 STEMCenter for Teaching & Learning™ Engineering byDesign™
12/01/2009 Practice Problems Calculate the total amount of material required to construct the crane boom: c2 = _____ c1 = _____ a = 10 cm b1 = 15 cm [Authors: Please include teacher notes appropriately.] b2 = 30 cm b3 = 40 cm © 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology © International Technology Education Assoc

13 STEMCenter for Teaching & Learning™ Engineering byDesign™
12/01/2009 Practice Problems Calculate the total amount of material required to construct the crane boom: c2 = 14.1cm c1 = 18.0cm c² = a² + b² c1² = (10cm)² + (15cm)² c1² = 100cm² + 225cm² c1² = 325cm² √c1² = √325cm² c1 = 18.0cm c2² = (10cm)² + (10cm)² c2² = 100cm² + 100cm² c2² = 200cm² √c2² = √200cm² c2 = 14.1cm a = 10 cm b1 = 15 cm [Authors: Please include teacher notes appropriately.] b2 = 30 cm b3 = 40 cm © 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology © International Technology Education Assoc

14 STEMCenter for Teaching & Learning™ Engineering byDesign™
12/01/2009 Practice Problems Calculate the total amount of material required to construct the crane boom: b1 = 15 cm b2 = 30 cm b3 = 40 cm c1 = 18.0cm a = 10 cm c2 = 14.1cm Segments Quantity Length (total) a 3 30cm b2 1 b3 40cm c1 2 36cm c2 14.1cm Total: 150.1cm [Authors: Please include teacher notes appropriately.] © 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology © International Technology Education Assoc

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