### General Information

**Subject Area:**Mathematics

**Grade:**8

**Domain-Subdomain:**Geometry

**Cluster:**Level 2: Basic Application of Skills & Concepts

**Cluster:**Understand and apply the Pythagorean Theorem. (Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

**Date Adopted or Revised:**02/14

**Date of Last Rating:**02/14

**Status:**State Board Approved

**Assessed:**Yes

### Test Item Specifications

**Assessment Limits :**

For the converse, only perfect roots should be used.**Calculator :**Yes

**Context :**Allowable

### Sample Test Items (3)

**Test Item #:**Sample Item 1**Question:**Which set of numbers forms a right triangle?**Difficulty:**N/A**Type:**MC: Multiple Choice

**Test Item #:**Sample Item 2**Question:**The side lengths of a triangle are given.3, 4, 5

Explain how you know which side will be opposite the right angle.

**Difficulty:**N/A**Type:**OR: Open Response

**Test Item #:**Sample Item 3**Question:**Select three side lengths, in centimeters (cm), that can form a right triangle.

**Difficulty:**N/A**Type:**MS: Multiselect

## Related Courses

## Related Access Points

## Related Resources

## Formative Assessments

## Lesson Plans

## Presentation/Slideshows

## Problem-Solving Task

## Text Resource

## Tutorials

## Video/Audio/Animations

## Virtual Manipulatives

## MFAS Formative Assessments

Students are asked to explain the steps of a proof of the converse of the Pythagorean Theorem.

Students are asked to explain the steps of a proof of the Pythagorean Theorem that uses similar triangles.

Students are asked to explain how a pair of figures demonstrates the Pythagorean Theorem and its converse.

## Student Resources

## Presentation/Slideshow

This lesson teaches students about the history of the Pythagorean theorem, along with proofs and applications. It is geared toward high school Geometry students that have completed a year of Algebra and addresses the following national standards of the National Council of Teachers of Mathematics and the Mid-continent Research for Education and Learning: 1) Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships; 2) Use visualization, spatial reasoning, and geometric modeling to solve problems; 3) Understand and apply basic and advanced properties of the concepts of geometry; and 4) Use the Pythagorean theorem and its converse and properties of special right triangles to solve mathematical and real-world problems. The video portion is about thirty minutes, and with breaks could be completed in 50 minutes. (You may consider completing over two classes, particularly if you want to allow more time for activities or do some of the enrichment material). These activities could be done individually, in pairs, or groups. I think 2 or 3 students is optimal. The materials required for the activities include scissors, tape, string and markers.

Type: Presentation/Slideshow

## Tutorials

This video demonstrates Bhaskara's proof of the Pythagorean Theorem.

Type: Tutorial

This video shows a proof of the Pythagorean Theorem using similar triangles.

Type: Tutorial

## Video/Audio/Animation

This resource gives an animated and then annotated proof of the Pythagorean Theorem.

Type: Video/Audio/Animation

## Virtual Manipulative

This web address, from the National Library of Virtual Manipulatives, will help teachers and students validate the Pythagorean Theorem both geometrically and algebraically. It can be used interactively with the Smartboard and the Promethean Board to create a better understanding of the topic.

Type: Virtual Manipulative

## Parent Resources

## Virtual Manipulative

This web address, from the National Library of Virtual Manipulatives, will help teachers and students validate the Pythagorean Theorem both geometrically and algebraically. It can be used interactively with the Smartboard and the Promethean Board to create a better understanding of the topic.

Type: Virtual Manipulative