Standard Information

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

Content Complexity Rating: Level 2: Basic Application of Skills & Concepts - More Information

Date of Last Rating: 02/14

Status: State Board Approved - Archived

Assessed: Yes

Related Resources

Formative Assessments

Pythagorean Squares Students are asked to explain how a pair of figures demonstrates the Pythagorean Theorem and its converse.
Explaining a Proof of the Pythagorean Theorem Students are asked to explain the steps of a proof of the Pythagorean Theorem that uses similar triangles.
Converse of the Pythagorean Theorem Students are asked to explain the steps of a proof of the converse of the Pythagorean Theorem.

Lesson Plans

Discovering and Using the Pythagorean Theorem Students will be introduced to the Pythagorean Theorem via a discovery activity. Students will manipulate the formula to isolate either a leg or a hypotenuse and practice using each to solve a variety of scenarios. Pythagorean triples are explored, and steps for using a scientific calculator are included.
Discover and Make Sense of the Pythagorean Theorem This lesson unit helps teachers assess how well students can use the area of right triangles to deduce the areas of other shapes, use dissection methods for finding areas, organize an investigation systematically, and collect data to deduce a generalizable method for finding lengths and areas (The Pythagorean Theorem).
A Hypotenuse is a WHAT???? Students are guided through a short history of Pythagoras and a discovery of the Pythagorean Theorem using the squaring of the sides of a right triangle.

Presentation/Slideshow

The Pythagorean Theorem: Geometry’s Most Elegant Theorem 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.

Problem-Solving Task

Converse of the Pythagorean Theorem This task is for instruction purposes. Part (b) is subtle and the solution presented here uses a "dynamic" view of triangles with two side lengths fixed. This helps pave the way toward what students will see later in trigonometry but some guidance will likely be needed in order to get students started on this path.

Tutorials

Bhaskara's Proof of the Pythagorean Theorem This video demonstrates Bhaskara's proof of the Pythagorean Theorem.
Pythagorean Theorem Proof Using Similar Triangles This video shows a proof of the Pythagorean Theorem using similar triangles.