TEL Lesson Plan
Applying the Pythagorean Theorem

Grade Level: 8
Subject: Mathematics
Time Frame: 1-2 hours, depending on if 1 or 2 scenarios are us

Summary

Complete activities to learn about the Pythagorean theorem and how to apply it and other geometric concepts to real-world scenarios.

Databases/Other Resources

Student Edition - K12

Procedures

Steps

Steps for Teacher

  1. Ensure the students have graph paper, rulers, and scissors.
  2. Prior to the lesson, access the Tennessee Electronic Library . Under the search box, select Browse by School Grades and then select Middle School Resources
  3. Click on the Student Edition - K 12 link.
  4. Conduct the search, read the entries, and calculate the answers to the provided questions (see Steps/Activities by the Student below).
  5. Create additional appropriate questions for the students to answer using the retrieved articles as a guide.

 

Steps for Librarian

  1. Show students how to access Student Edition - K 12.
  2. Read the instructions for the search technique to use in the database and show students how to conduct the search or assist them as needed in conducting the search.

Steps for Student

  1. Access the Tennessee Electronic Library . Under the search box, select Browse by School Grades and then select Middle School Resources
  2. Click on the Student Edition - K 12 link.
  3. Enter the search term geometry.
  4. Select See Also: 5 Subdivisions under the heading Geometry.
  5. Select Humor and Anecdotes.
  6. The article “Up From Euclid” from Fortune, Sept 28, 1987.
  7. Read the article.
  8. Suppose the private plane was also 150 feet to the front of the helicopter. Plot the locations of the helicopter and the private plane on a three dimensional graph using the x, y, and z axes.
  9. Give the coordinate for the location of the private plane.
  10. Connect the helicopter to the private plane with a line. Determine the equation for this line.
  11. Answer the following questions. How far would a horse have to travel to get to the rail by the end of the first turn if it was 13 feet from the rail at the beginning of the race? 14 feet from the rail at the beginning of the race? 15 feet from the rail at the beginning of the race? 16 feet from the rail at the beginning of the race? 17 feet from the rail at the beginning of the race? 18 feet from the rail at the beginning of the race? 19 feet from the rail at the beginning of the race? 20 feet from the rail at the beginning of the race?
  12. Using the previous answers, graph the distances that the horse would need to travel if it were 12-20 feet from the rail at the beginning of the race.
  13. Extend the line so that you can determine the distance that the horse would need to travel if it were 25 feet from the rail at the beginning of the race.
  14. What is the slope of the line created?
  15. What is the equation for this line?
  16. Create another real-world scenario to apply the Pythagorean theorem. Share it with the class.

Related Activities

  1. Access Tennessee Electronic Library using steps listed above.
  2. Access Student Edition - K 12.
  3. Enter the search terms number secrets and select Find.
  4. Select the article “Number secrets: in the world of Pythagoras, ‘all is number’” from the periodical titled Odyssey.
  5. Read the article and complete the activities listed in the article using graph paper.
  6. Calculate the area of the triangle for the activity in the first part of the Adding Squares exercise in the article. Measure two sides of the triangle. Estimate the length of the third side using the Pythagorean theorem. Calculate the exact length of the third side using the Pythagorean theorem.

Content Standards

Mathematics--Grade 8

Standard 1: Mathematical Processes

Standard 3: Algebra

Standard 4: Geometry & Measurement

 

Learning Expectations/Grade Level Expectations

Standard 1: Mathematical Processes

Grade Level Expectations:

GLE 0806.1.3 Develop independent reasoning to communicate mathematical ideas and derive algorithms and/or formulas.

GLE 0806.1.4 Move flexibly between concrete and abstract representations of mathematical ideas in order to solve problems, model mathematical ideas, and communicate solution strategies.

GLE 0806.1.5 Use mathematical ideas and processes in different settings to formulate patterns, analyze graphs, set up and solve problems and interpret solutions.

GLE 0806.1.6 Read and interpret the language of mathematics and use written/oral communication to express mathematical ideas precisely.

Standard 3: Algebra

Grade Level Expectations:

GLE 0806.3.4 Translate among verbal, tabular, graphical and algebraic representations of linear functions.

GLE 0806.3.5 Use slope to analyze situations and solve problems.

 

Standard 4: Geometry & Measurement

Grade Level Expectations:

GLE 0806.4.1 Derive the Pythagorean theorem and understand its applications.

GLE 0806.4.2 Understand the relationships among the angles formed by parallel lines cut by transversals.

GLE 0806.4.3 Understand the necessary levels of accuracy and precision in measurement.

GLE 0806.4.5 Use visualization to describe or identify intersections, cross-sections, and various views of geometric figures.

 

Performance Indicators State

Standard 1: Mathematical Processes

 Checks for Understanding (Formative/Summative Assessment):

0806.1.6 Use models (such as dynamic geometry software, patty paper and geo boards) to explore relationships among angles (complementary, supplementary, interior, exterior, vertical, and corresponding).

0806.1.8 Use a variety of methods to solve real-world problems involving multi-step linear equations (e.g., manipulatives, technology, pencil and paper).

 

Standard 3: Algebra

Checks for Understanding (Formative/Summative Assessment):

0806.3.4 Understand the relationship between the graph of a linear inequality and its solutions.

0806.3.6 Identify x- and y-intercepts and slope of linear equations from an equation, graph or table.

0806.3.7 Analyze situations and solve problems involving constant rate of change.

0806.3.8 Recognize a proportion as a special case of a linear equation and understand that the constant of proportionality is the slope, and the resulting graph is a line through the origin.

 

Standard 4: Geometry & Measurement

Checks for Understanding (Formative/Summative Assessment):

0806.4.1 Model the Pythagorean Theorem.

0806.4.4 Understand how the precision of measurement influences accuracy of quantities derived from these measurements.

0806.4.5 Analyze the congruent and supplementary relationships of angles formed by parallel lines and transversals (such as alternate interior, alternate exterior, corresponding, and adjacent).

0806.4.8 Build, draw, and work with 2- and 3-dimensional figures by means of orthogonal views, projective views, and/or nets.


Standard 1: Mathematical Processes

State Performance Indicators:

SPI 0806.1.1 Solve problems involving rate/time/distance (i.e., d = rt).
SPI 0806.1.2 Interpret a qualitative graph representing a contextual situation.

 

Standard 3: Algebra

State Performance Indicators:

SPI 0806.3.4 Translate between various representations of a linear function.

SPI 0806.3.5 Determine the slope of a line from an equation, two given points, a table or a graph.

 

Standard 4: Geometry & Measurement

State Performance Indicators:

SPI 0806.4.1 Use the Pythagorean Theorem to solve contextual problems.

SPI 0806.4.2 Apply the Pythagorean theorem to find distances between points in the coordinate plane to measure lengths and analyze polygons and polyhedra.

SPI 0806.4.3 Find measures of the angles formed by parallel lines cut by a transversal.

SPI 0806.4.4 Convert between and within the U.S. Customary System and the metric system.

SPI 0806.4.5 Identify the intersection of two or more geometric figures in the plane. 

 

 

 

Assessment

Checks for Understanding (Formative/Summative Assessment):

0806.1.6 Use models (such as dynamic geometry software, patty paper and geo boards) to explore relationships among angles (complementary, supplementary, interior, exterior, vertical, and corresponding).

0806.1.8 Use a variety of methods to solve real-world problems involving multi-step linear equations (e.g., manipulatives, technology, pencil and paper).

0806.3.4 Understand the relationship between the graph of a linear inequality and its solutions.

0806.3.6 Identify x- and y-intercepts and slope of linear equations from an equation, graph or table.

0806.3.7 Analyze situations and solve problems involving constant rate of change.

0806.3.8 Recognize a proportion as a special case of a linear equation and understand that the constant of proportionality is the slope, and the resulting graph is a line through the origin.

0806.4.1 Model the Pythagorean Theorem.

0806.4.4 Understand how the precision of measurement influences accuracy of quantities derived from these measurements.

0806.4.5 Analyze the congruent and supplementary relationships of angles formed by parallel lines and transversals (such as alternate interior, alternate exterior, corresponding, and adjacent).

0806.4.8 Build, draw, and work with 2- and 3-dimensional figures by means of orthogonal views, projective views, and/or nets.

ISTE Computer Literacy and Usage Standards

1.Creativity and Innovation

Students demonstrate creative thinking, construct knowledge, and develop innovative products and processes using technology. Students:

a. apply existing knowledge to generate new ideas, products, or processes.
b. create original works as a means of personal or group expression.
c. use models and simulations to explore complex systems and issues.
d. identify trends and forecast possibilities.

3. Research and Information Fluency

Students apply digital tools to gather, evaluate, and use information. Students:

a. plan strategies to guide inquiry.
b. locate, organize, analyze, evaluate, synthesize, and ethically use information from a variety of sources and media.
d. process data and report results.

 

4. Critical Thinking, Problem Solving, and Decision Making

Students use critical thinking skills to plan and conduct research, manage projects, solve problems, and make informed decisions using appropriate digital tools and resources. Students:

a. identify and define authentic problems and significant questions for investigation.
b. plan and manage activities to develop a solution or complete a project.
c. collect and analyze data to identify solutions and/or make informed decisions.
d. use multiple processes and diverse perspectives to explore alternative solutions.

5. Digital Citizenship

Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior. Students:

a. advocate and practice safe, legal, and responsible use of information and technology.
b. exhibit a positive attitude toward using technology that supports collaboration, learning, and productivity.
c. demonstrate personal responsibility for lifelong learning.

 

AASL Standards for the 21st Century Learner

1. Inquire, think critically, and gain knowledge

1.1 Skills
1.16 Read, view, and listen for information presented in any format (e.g., textual, visual, media, digital) in order to make inferences and gather meaning.
1.3 Responsibilities
1.3.5 Use information technology responsibly.
1.4 Self-Assessment Strategies
1.4.4 Seek appropriate help when needed.

2 Draw conclusions, make informed decisions, apply knowledge to new situations, and create new knowledge.

2.1 Skills
2.1.3 Use strategies to draw conclusions from information and apply knowledge to curricular areas, real-world situations, and further investigations.
2.2 Dispositions in Action
2.2.3 Employ a critical stance in drawing conclusions by demonstrating that the pattern of evidence leads to a decision or conclusion.

2.3 Responsibilities
2.3.1 Connect understanding to the real world.
2.4 Self-Assessment Strategies
2.4.2 Reflect on systematic process, and assess for completeness of investigation.
2.4.3 Recognize new knowledge and understanding.

3. Share knowledge and participate ethically and productively as members of our democratic society.

3.1 Skills
3.1.5 Connect learning to community issues.
3.1.6 Use information and technology ethically and responsibly.
3.3 Responsibilities
3.4 Self-Assessment Strategies
3.4.1 Assess the processes by which learning was acheived in order to revise strategies and learn more effectively in the future.


4 .Pursue personal and aesthetic growth.

4.1 Skills
4.1.5 Connect ideas to own interests and previous knowledge and experience.
4.2 Dispositions in Action
4.2.2 Demonstrate motivation by seeking information to answer personal questions and interests, try8ing a variety of formats and genres, and displaying a willingness to go beyond academic requirements.
4.4 Self Assessment Strategies
4.4.1 Identify own areas of interest.