ALEX Classroom Resource

  

Applying the Pythagorean Theorem

  Classroom Resource Information  

Title:

 Applying the Pythagorean Theorem

URL:

 https://aptv.pbslearningmedia.org/resource/muen-math-g-pythagorean/pythagorean-theorem/

Content Source:

 PBS
Type: Audio/Video

Overview:

In this video, learn how using the Pythagorean Theorem can help people solve real-world problems involving distances. In the accompanying classroom activity, students develop their problem-solving, spatial reasoning, and geometry skills by putting the Pythagorean Theorem to use. After a brief discussion about how to use the theorem to find the distance between two points on a coordinate grid, students partner up and play a game in which they generate (and then calculate the distance between) two or more points on the grid. As the game increases in complexity, students begin working in all quadrants and begin identifying multiple triangles that they can use to determine the distance between points.

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 8
27. Apply the Pythagorean Theorem to find the distance between two points in a coordinate plane.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Given real-world and mathematical problems that can be represented on a coordinate plane, apply the Pythagorean Theorem in order to solve problems and justify solutions and solution paths for finding side lengths (distances between points) in right triangles within the problem contexts.
Teacher Vocabulary:
  • Pythagorean Theorem
Knowledge:
Students know:
  • The Pythagorean Theorem.
  • The operations and labeling within a coordinate system.
Skills:
Students are able to:
  • Solve equations involving one variable and square root.
  • Represent real-world and mathematical contexts involving right triangles in a variety of formats (drawings on coordinate planes, equations).
  • Justify solutions and solution paths using conceptual understandings and vocabulary related to the Pythagorean Theorem (right angle, hypotenuse).
Understanding:
Students understand that:
  • The properties of right triangles can be used to solve problems.
  • Theorems represent general relationships that are true for all shapes that fit certain criteria.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.8.27.1: Recall how to name points on a Cartesian plane using ordered pairs.
M.8.27.2: Recognize ordered pairs (x, y).
M.8.27.3: Solve problems using the Pythagorean Theorem, with or without a calculator.
M.8.27.4: Identify right triangles.
M.8.27.5: Demonstrate how to find square roots, with or without a calculator.
M.8.27.6: Solve problems with exponents, with or without a calculator.

Prior Knowledge Skills:
  • Define area, special quadrilaterals, right triangles, and polygons.
  • Analyze the area of other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes.
  • Apply area formulas to solve real-world mathematical problems.
  • Demonstrate how the area of a rectangle is equal to the sum of the area of two equal right triangles.
  • Explain how to find the area for rectangles.
  • Select manipulatives to demonstrate how to compose and decompose triangles and other shapes.
  • Recognize and demonstrate that two right triangles make a rectangle.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.8.27 Use the pythagorean theorem to find the hypotenuse when given the measures of two legs in a real-world context. Limit to Pythagorean triples.
Mathematics
MA2019 (2019)
Grade: 8
Accelerated
49. Apply the Pythagorean Theorem to find the distance between two points in a coordinate plane. [Grade 8, 27]
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Given real-world and mathematical problems that can be represented on a coordinate plane, apply the Pythagorean Theorem in order to solve problems and justify solutions and solution paths for finding side lengths (distances between points) in right triangles within the problem contexts.
Teacher Vocabulary:
  • Pythagorean Theorem
  • Right triangle
  • hypotenuse
  • leg
  • Coordinate plane
  • ordered pair
Knowledge:
Students know:
  • Pythagorean Theorem.
  • Operations and labeling within a coordinate system.
Skills:
Students are able to:
  • Solve equations involving one variable and square root.
  • Represent real-world and mathematical contexts involving right triangles in a variety of formats (e.g., drawings on coordinate planes, equations).
  • Justify solutions and solution paths using conceptual understandings and vocabulary related to the Pythagorean Theorem (right angle, hypotenuse).
Understanding:
Students understand that:
  • The properties of right triangles can be used to solve problems,
  • Theorems represent general relationships that are true for all shapes that fit certain criteria.
Diverse Learning Needs:
Tags: distance, length, Pythagorean Theorem, quadrants, right triangle
License Type: Public Domain
For full descriptions of license types and a guide to usage, visit :
https://creativecommons.org/licenses
AccessibilityVideo resources: includes closed captioning or subtitles
Comments

This resource includes an activity page.

  This resource provided by:  
Author: Kristy Lacks
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