# ALEX Lesson Plan

## Distance "The Pythagoras Way"

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This lesson provided by:
 Author: Morgan Boyd Organization: Retirement
General Lesson Information
 Lesson Plan ID: 35589 Title: Distance "The Pythagoras Way" Overview/Annotation: In this lesson, the teacher will demonstrate how to use the Pythagorean Theorem to find distance between two points in the coordinate system. In the coordinate plane, the difference in the x- and y-values will determine the numbers to calculate the distance. This lesson will use online graphing tools as well as graph paper to plot the points. This lesson can also be used to show the relationship between the distance formula and the Pythagorean Theorem.This lesson results from the ALEX Resource Gap Project.
Associated Standards and Objectives
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 TheoremKnowledge: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.

Local/National Standards:

Primary Learning Objective(s):

The student will apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

The student will be able to calculate the distance between two points in the coordinate plane.

The student will be able to use technology to represent two points in the coordinate plane.

The student will be able to manipulate the GEOGEBRA website with the given interactive controls.

Preparation Information
 Total Duration: 31 to 60 Minutes Materials and Resources: Notebook paperPenciliPad, Chromebook, or MacBook for each studentDesktop computer and interactive whiteboard for lessonGraph Paper (make 3 copies for each student)Ruler or another device with a straight edgeGraph paper in the attachment section (Make copies front and back, each student will need two copies) Worksheet from the attachment section titled "Points for Pythagorean Theorem" (make copies for each student)Worksheet from the attachment section titled "Exit Slip Pythagorean" (make copies for each student)Worksheet from the attachment section titled "Distance to the Moon" (make enough copies so that you will be able to give to the students that finish the primary assignment early) Technology Resources Needed: Website for interactive graphing in the coordinate plate (https://www.geogebra.org/m/jmMXpzuM)iPad, Chromebook, MacBook for each student to follow the steps as the teacher explains the process of calculating the distanceDesktop computer and interactive whiteboard for teacher and student use during the lesson Background/Preparation: Teacher:The teacher will need to understand how to use the screenshot mode of the interactive whiteboard. The interactive whiteboard will be able to take a picture of the coordinate plane. The teacher will need to save the graph to the desktop of the computer. The teacher and the students will need to be able to plot points on a graph. The teacher will need to use the correct mathematical terminology related to this lesson. The teacher will need to practice with the website “GEOGEBRA” prior to teaching the lesson. As the teacher introduces the website, he or she needs to allow extra time for the students to learn how to manipulate the website. Finally, the teacher will need to randomly select graph points to use as examples.Student:The student will need to have colored pencils, especially blue and red. The student will need to understand the distance between two points on a graph by counting and by finding the difference between numbers on the coordinate plane. The student will demonstrate knowledge of correct mathematical vocabulary. The terms that students will use in this lesson are difference, squared, square root, and sum. The student should be able to round to the given place value. Finally, the student should be able to plot points on a coordinate plane.
Procedures/Activities: