pythagorean theorem foundations of technology pythagorean theorem © 2013 international technology...
TRANSCRIPT
Foundations of Technology
Pythagorean TheoremPythagorean Theorem
© 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology
Teacher Resource – Unit 2 Lesson 1
The BIG IdeaThe BIG Idea
Big Idea:
The Engineering Design Process is a systematic, iterative problem-solving method that produces solutions to meet human needs and wants.
© 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology
RationaleRationale
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.
© 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology
Pythagorean TheoremPythagorean 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
© 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology
Hypotenuse(c)
Right (90º) Angle
Adjacent Sides
(a + b)
Practice ProblemsPractice Problems
© 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology
c = ____
a = 4in
b = 3in
Practice ProblemsPractice Problems
© 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology
c = 5in
a = 4in
b = 3in
c² = a² + b²
c² = (4in)² + (3in)² c² = 16in² + 9in²
c² = 25in²
√c² = √25in²
c = 5in
Practice ProblemsPractice Problems
© 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology
c = 15in
a = ____
b = 9in
Practice ProblemsPractice Problems
© 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology
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
Practice ProblemsPractice Problems
© 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology
a = 12in
b = 10in
c = ______
Practice ProblemsPractice Problems
© 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology
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
b = 10in
Practice ProblemsPractice Problems
© 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology
b1 = 15 cm
Calculate the total amount of material required to construct the crane boom:
Practice ProblemsPractice Problems
© 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology
a = 10 cm
b2 = 30 cm
b3 = 40 cm
c1 = _____ c2 = _____
Calculate the total amount of material required to construct the crane boom:
Practice ProblemsPractice Problems
© 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology
c² = a² + b²
c1² = (10cm)² + (15cm)²c1² = 100cm² + 225cm²c1² = 325cm²√c1² = √325cm²c1 = 18.0cm
c2² = (10cm)² + (10cm)²c2² = 100cm² + 100cm²c2² = 200cm²√c2² = √200cm²c2 = 14.1cm
b1 = 15 cm
b2 = 30 cm
b3 = 40 cm
c1 = 18.0cm
a = 10 cm
c2 = 14.1cm
Calculate the total amount of material required to construct the crane boom:
Practice ProblemsPractice Problems
© 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology
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 30cm
b3 1 40cm
c1 2 36cm
c2 1 14.1cm
Total: 150.1cm