# MA.8.GR.1.1

Apply the Pythagorean Theorem to solve mathematical and real-world problems involving unknown side lengths in right triangles.

### Clarifications

Clarification 1: Instruction includes exploring right triangles with natural-number side lengths to illustrate the Pythagorean Theorem.

Clarification 2: Within this benchmark, the expectation is to memorize the Pythagorean Theorem.

Clarification 3: Radicands are limited to whole numbers up to 225.

General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Geometric Reasoning
Date Adopted or Revised: 08/20
Status: State Board Approved

## Related Courses

This benchmark is part of these courses.
1205050: M/J Accelerated Mathematics Grade 7 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))
1205070: M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7812030: Access M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.8.GR.1.AP.1: Find the hypotenuse of a two-dimensional right triangle using the Pythagorean Theorem.

## Related Resources

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

## Formative Assessments

Three Dimensional Diagonal:

Students are asked to determine the length of a side of a right triangle in a real-world problem.

Type: Formative Assessment

Pythagorean Squares:

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

Type: Formative Assessment

New Television:

Students are asked to determine the length of a side of a right triangle in a real-world problem.

Type: Formative Assessment

How Far to School:

Students are asked to determine the length of a side of a right triangle in a real-world problem.

Type: Formative Assessment

## Lesson Plans

Just Plane Ol' Area!:

Students will construct various figures on coordinate planes and calculate the perimeter and area. Use of the Pythagorean theorem will be required.

Type: Lesson Plan

Pythagoras - You Clever Dog:

This lesson starts with an introduction of the Pythagorean Theorem. It introduces vocabulary, formulas and concepts related to right triangles and the use of the Pythagorean Theorem in the real world. Students will learn the basics through real world application.

Type: Lesson Plan

## Original Student Tutorials

Pythagorean Theorem: Part 3:

Use the Pythagorean Theorem to find the legs of a right triangle in mathematical and real worlds contexts in this interactive tutorial.

This is part 3 in a 3-part series. Click below to explore the other tutorials in the series.

Type: Original Student Tutorial

Pythagorean Theorem: Part 2:

Use the Pythagorean Theorem to find the hypotenuse of a right triangle in mathematical and real worlds contexts in this interactive tutorial.

This is part 2 in a 3-part series. Click below to explore the other tutorials in the series.

Type: Original Student Tutorial

Pythagorean Theorem: Part 1:

Learn what the Pythagorean Theorem and its converse mean, and what Pythagorean Triples are in this interactive tutorial.

This is part 1 in a 3-part series. Click below to explore the other tutorials in the series.

Type: Original Student Tutorial

## Perspectives Video: Expert

Measuring a Grid for Underwater Archeology:

Don't be a square! Learn about how even grids help archaeologists track provenience!

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

## Perspectives Video: Teaching Idea

KROS Pacific Ocean Kayak Journey: Kites, Geometry, and Vectors:

Set sail with this math teacher as he explains how kites were used for lessons in the classroom.

Related Resources:
KROS Pacific Ocean Kayak Journey: GPS Data Set [.XLSX]
KROS Pacific Ocean Kayak Journey: Path Visualization for Google Earth [.KML]

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Teaching Idea

## Text Resource

Pythagoras Explained:

This informational text resource is intended to support reading in the content area. The text describes a method for predicting the win-loss record for baseball teams based on runs scored and runs allowed, using the "Pythagorean Expectation" formula invented by Bill James. The text goes on to show the relationship of the prediction formula to the Pythagorean theorem, pointing out a very cool application of the theorem to the world of sports.

Type: Text Resource

## MFAS Formative Assessments

How Far to School:

Students are asked to determine the length of a side of a right triangle in a real-world problem.

New Television:

Students are asked to determine the length of a side of a right triangle in a real-world problem.

Pythagorean Squares:

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

Three Dimensional Diagonal:

Students are asked to determine the length of a side of a right triangle in a real-world problem.

## Original Student Tutorials Mathematics - Grades 6-8

Pythagorean Theorem: Part 1:

Learn what the Pythagorean Theorem and its converse mean, and what Pythagorean Triples are in this interactive tutorial.

This is part 1 in a 3-part series. Click below to explore the other tutorials in the series.

Pythagorean Theorem: Part 2:

Use the Pythagorean Theorem to find the hypotenuse of a right triangle in mathematical and real worlds contexts in this interactive tutorial.

This is part 2 in a 3-part series. Click below to explore the other tutorials in the series.

Pythagorean Theorem: Part 3:

Use the Pythagorean Theorem to find the legs of a right triangle in mathematical and real worlds contexts in this interactive tutorial.

This is part 3 in a 3-part series. Click below to explore the other tutorials in the series.

## Student Resources

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

## Original Student Tutorials

Pythagorean Theorem: Part 3:

Use the Pythagorean Theorem to find the legs of a right triangle in mathematical and real worlds contexts in this interactive tutorial.

This is part 3 in a 3-part series. Click below to explore the other tutorials in the series.

Type: Original Student Tutorial

Pythagorean Theorem: Part 2:

Use the Pythagorean Theorem to find the hypotenuse of a right triangle in mathematical and real worlds contexts in this interactive tutorial.

This is part 2 in a 3-part series. Click below to explore the other tutorials in the series.

Type: Original Student Tutorial

Pythagorean Theorem: Part 1:

Learn what the Pythagorean Theorem and its converse mean, and what Pythagorean Triples are in this interactive tutorial.

This is part 1 in a 3-part series. Click below to explore the other tutorials in the series.

Type: Original Student Tutorial

## Perspectives Video: Expert

Measuring a Grid for Underwater Archeology:

Don't be a square! Learn about how even grids help archaeologists track provenience!

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

## Parent Resources

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

## Perspectives Video: Expert

Measuring a Grid for Underwater Archeology:

Don't be a square! Learn about how even grids help archaeologists track provenience!

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert