Pythagorean Theorem

David Ream

Introduction:
The Really Rich Architecture Association is offering a million dollar reward for the first pair of engineers to determine the span between Monstrous Mesa and Cataclysmic Cliff over Ransacked River. This area is where they are planning to build an automobile bridge to reduce traffic fatalities and reduce commuter times for residents on both sides of the river. To these residents you will become a living legend. This lesson will provide you with the skills to solve the problem, win the reward and be the recipient of the undying adoration of thousands of people.

Objective:
7th grade Measurement and Geometry Objective #3.3 "Students know and understand the Pythagorean Theorem and use it to find the length of the missing side of a right triangle and the lengths of other line segments, and, in some situations, empirically verify the Pythagorean Theorem by direct measurement."

Evaluation:
Three types of assessment; (a) by walking around the room and talking to students, (b) the completion of the collaborative Lab Task Sheet, and (c) the Lab Write-Up Sheet (html) / (pdf) to be completed independently.

Prior Knowledge:
Properties and parts of a right triangle (right angle, legs, and hypotenuse). Definition of a rectangle - A rectangle is a quadrilateral with four right angles. Squares and Square Roots, Solving addition equations involving squares and square roots. Students know their partner, how to work in pairs at the computer.

Learning Advice:
Items to consider:

Classroom organization - one demonstration PC w/Internet in your classroom, access to a computer lab or your classroom computers
The time required to complete the lesson is about three class periods - one day to introduce the Lab Task Sheet, One day for the pair to do the first part of the lab, One more day to complete the lab and do the Lab Write-Up Sheet (html) / (pdf).
Students learn to; use the paint program and the calculator in Windows™, and print. This lesson uses a blended instructional strategy approach, specifically Direct Instruction and Peer Practice.
The expectation for Lab Task Activity should be that every student gets it 100% correct or they do it over again. After all, they create the worksheet they get step-by-step help from their partner, they can use a calculator, and can consult with the teacher.

Resources:
PC w/ Windows™ operating system and an Internet connection, Color Printer, PC projector, Overhead Projector and overhead Pens, Lab Write-Up Sheet (html) / (pdf) and Lab Task Sheet, Internet Resources Page, pencil, paper and a ruler with both the metric scale and the U. S. customary scale.

Process:
Each day the teacher: States the objective. Reviews prior knowledge.

Day one: Introduces the Pythagorean Theorem. Demonstrates it twice, once using the 'Classic' 3, 4, 5 right triangle and one more right triangle. Calls on students to assist and checks for understanding. Distributes task sheets. Demonstrates the entire lab activity from the task sheet on the PC, line-by-line and step-by step before students go to the computer lab. Models the computer task for the class.
Day two: Assigns partners. Reviews rules for working in pairs and using the computer. Takes class to the computer lab or to classroom computers. Informally assesses and assists students as they complete the first part of the lab.
Day three: Students check and correct the lab work and do the Lab Write-Up

Extensions:

Students can create complex two-dimensional figures (or three-dimensional figures) and use the Pythagorean Theorem to find the lengths of the sides for pentagons, hexagons, tetrahedrons, etc.
Students use the Internet Resources Page to delve deeper.
Students can write and present a brief talk on Pythagoras, his life and their experiences with the lab.

Conclusion:
How does one find the length of the span and win the prize? Students use the Problem Solving Page

SCORE Mathematics | | SCORE Mathematics Lessons Index | | SCORE Mathematics Search

California Mathematics Academic Standards:

Grade 7:
Measurement and Geometry
3.0 Students know the Pythagorean Theorem and deepen their understanding of plane and solid geometric shapes by constructing figures that meet given conditions and by identifying attributes of figures:
3.3 Know and understand the Pythagorean Theorem and its converse and use it to find the length of the missing side of a right triangle and the lengths of other line segments and, in some situations, empirically verify the Pythagorean Theorem by direct measurement.

Grade 8-12:
Geometry
15.0 Students use the Pythagorean theorem to determine distance and find missing lengths of sides of right triangles.

NCTM - 5-8:

STANDARD 9: ALGEBRA
STANDARD 12: GEOMETRY
STANDARD 13: MEASUREMENT

Table of Angles and Lengths

Internet Resources