MA.8.G.2.4Archived Standard

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Validate and apply Pythagorean Theorem to find distances in real world situations or between points in the coordinate plane.

Remarks

Example 1: You are wrapping a gift for your teacher's birthday. It is a very long and skinny pencil. You want to wrap it in a box so that your teacher can not tell what shape it is. Your friend has a shoe box that measures 10 inches by 7 inches by 5 inches. The pencil is 13 inches long. Will you be able to fit the pencil into the shoe box and close the lid? Justify your answer with mathematics.

 

Example 2: You are sailing your boat to Key West from Pensacola. Key West is 82°W and 25°N, and your boat is 84°W and 29°N. What is the distance from your boat to Key West? Assume 1° change in longitude or latitude is 70 miles.

 

 

 

 

General Information
Subject Area: X-Mathematics (former standards - 2008)
Grade: 8
Body of Knowledge: Geometry
Idea: Level 2: Basic Application of Skills & Concepts
Big Idea: BIG IDEA 2 - Analyze two- and three-dimensional figures by using distance and angle.
Date Adopted or Revised: 09/07
Content Complexity Rating: Level 2: Basic Application of Skills & Concepts - More Information
Date of Last Rating: 06/07
Status: State Board Approved - Archived
Assessed: Yes
Test Item Specifications
  • Item Type(s): This benchmark may be assessed using: MC , GR item(s)

  • Clarification :
    Students will identify and apply the Pythagorean theorem to find distances in real world situations or between points on the coordinate plane.
  • Content Limits :
    Graphics of three-dimensional figures may be included in items, but only two-dimensional figures may be assessed.

    Items may assess vertical distance, horizontal distance, and grade-level appropriate applications of the Pythagorean theorem.
  • Stimulus Attributes :
    Items may use coordinate planes.

    Graphics should be used in most of these items, as appropriate.

    Items should be set in either a real-world or mathematical context.
  • Response Attributes :
    When the responses are decimal approximations, they should be rounded to the nearest hundredths.
Sample Test Items (2)
  • Test Item #: Sample Item 1
  • Question: On the coordinate plane below, ΔRST shows the path bicycle riders will follow on one of their weekly rides.

    graph

    What is the total distance from point R to S to T and back to point R?
  • Difficulty: N/A
  • Type: MC: Multiple Choice
  • Test Item #: Sample Item 2
  • Question: A truss is a triangular structure that helps to support the roof of a building.

    truss



    the truss above has one side measuring 12 feet and another side measuring 16 feet. how long, in feet, is the third side of the truss, from point a to point b?
  • Difficulty: N/A
  • Type: GR: Gridded-Response

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Lesson Plans

Bike Club Trip:

In this activity the students will rank different locations for a bike club's next destination. In order to do so, the students must use Pythagorean Theorem and well as analyze data of the quantitative and qualitative type.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

Alas, Poor Pythagoras, I Knew You Well! #2:

Using different activities, students will find real life uses for the Pythagorean Theorem.

Type: Lesson Plan

Presentation/Slideshow

Pythagoras' Theorem:

This resource can be used to introduce the Pythagorean Theorem to students. It provides sketches, applets, examples and easy-to-understand visual proofs as well as an algebra proof for the theorem.

It also includes interactive multiple choice practice questions on solving for a side of a right triangle, and applications involving right triangles, as well as a hands-on activity for students to do that allows them to create their own proof.

Type: Presentation/Slideshow

Problem-Solving Task

It's Raining!!! (Compare areas of wiped windshields):

In this problem-solving task, students are challenged to determine whether the windshield wipers on a car or a truck allow the drivers to see more area clearly. To solve this problem, students must apply the Pythagorean theorem and their ability to find area of circles and parallelograms to find the answer. Be sure to click the links in the orange bar at the top of the page for more information about the challenge. From NCTM's Figure This! Math Challenges for Families.

Type: Problem-Solving Task

Text Resource

The Pythagorean Theorem:

This overview of the Pythagorean Theorem covers its purpose, equation, application, and validity. The site also provides a number of illustrations which help students visualize the theorem, and links to related resources for further understanding.

Type: Text Resource

Virtual Manipulative

Demonstrate the Pythagorean Theorem:

Representation to illustrate the Pythagorean Theorem.

Type: Virtual Manipulative

STEM Lessons - Model Eliciting Activity

Bike Club Trip:

In this activity the students will rank different locations for a bike club's next destination. In order to do so, the students must use Pythagorean Theorem and well as analyze data of the quantitative and qualitative type.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Problem-Solving Task

It's Raining!!! (Compare areas of wiped windshields):

In this problem-solving task, students are challenged to determine whether the windshield wipers on a car or a truck allow the drivers to see more area clearly. To solve this problem, students must apply the Pythagorean theorem and their ability to find area of circles and parallelograms to find the answer. Be sure to click the links in the orange bar at the top of the page for more information about the challenge. From NCTM's Figure This! Math Challenges for Families.

Type: Problem-Solving Task

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.