Subject Area: Mathematics | Grade Level: 8th grade
Unit Summary
In this Unit: Pythagorean Theorem Fun, we will explore how the Pythagorean Theorem came to be and why and how we use this Theorem. The Pythagorean Theorem is a widely known geometric theorem, which can be used to help us determine a variety of information about right triangles, such as the missing length of a right triangle, or if a triangle is a right triangle or not. As you think about the world in which you live, imagine where you might see some right triangles (For example, the pyramids, within baseball and soccer fields layouts, building applications, such as ladders or homes, and the list goes on!). The Pythagorean Theorem can help us analyze these real life right triangles through helping us find the missing distances for objects (such as length or height). In addition, the Pythagorean Theorem can be applied to the coordinate plane. This unit is organized into 3 lessons and the activities and goals are described below.
In Lesson 1, we’ll focus on learning about the Pythagorean Theorem, its history, the Converse (a reverse application of the Theorem), and 2D and 3D application of the Theorem. We’ll also get to informally prove the Theorem using our knowledge of area.
In Lesson 2, we’ll complete a webercise activity, which will lead us to more advanced practice of using the Pythagorean Theorem in 2D and 3D applications, as well as interact with the coordinate system to calculate the distance between coordinates. Get ready to use your research skills!
Finally in Lesson 3, we’ll research and organize important connections between the Theorem and related information in a concept map using a web-based program. Following all assignments, we’ll work to design our own Pythagorean Theorem Test and present it to the class. I will also include an example of the assignment on that lesson's page.
Throughout this unit, we will challenge ourselves with theoretical and real world application of the Pythagorean Theorem, while incorporating fun individual and collaborative class activities, and opportunities to build on our 21st Century Skills. Some of the 21st Century skills we will integrate into our lesson include teamwork, critical thinking and problem solving and using technology and research to further our knowledge.
Subject Area: Mathematics
Grade Level: 8th grade
Subject Area: Mathematics
Grade Level: 8th grade
CA Content Standards Addressed in this Unit
- CCSS.MATH.CONTENT.8.G.B.6: Explain a proof of the Pythagorean Theorem and its converse.
- CCSS.MATH.CONTENT.8.G.B.7: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
- CCSS.MATH.CONTENT.8.G.B.8: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
Big Ideas and Questions – What we’ll be exploring:
Big Ideas
- Right triangles are distinct from other triangles, and the Pythagorean Theorem is a helpful tool for us to use to analyze information about them.
- The Pythagorean Theorem applies to 2D and 3D applications. It also applies to the coordinate system.
- We will sharpen our critical thinking skills through exploring proofs. Knowing why something works helps us understand it better, and proofs will help us realize the converse of the Theorem is true.
- We will use projects involving research, problem-solving, critical thinking skills, collaboration, evaluation and synthesis of information, to help us deepen our knowledge about the Pythagorean Theorem and related mathematical processes.
- We will develop our sense of problem-solving and critical thinking skills through various collaborative and independent tasks which focus on the Pythagorean Theorem and its application.
- We will work to develop vital 21st century skills, through integrating various tasks and activities that strengthen these skills, such as using specific technology for creation of projects, and teamwork and collaboration.
- What is the Pythagorean Theorem and why is it important to me? Where did it come from?
- How can we know for sure the Pythagorean Theorem is true?
- What information can I find out about a triangle using the Pythagorean Theorem?
- How can I apply the Pythagorean Theorem to 2 dimensional and 3 dimensional real world problems?
- How does the Pythagorean Theorem apply to the coordinate system? What information can we learn about coordinates using this Theorem?
Student Learning Objectives
Lesson 1- Lecture Student Learning Objectives:
STUDENTS will…
STUDENTS will…
STUDENTS will…
STUDENTS will…
- Recall facts about the Pythagorean Theorem’s history.
- Express the Pythagorean Theorem and its converse through written and verbal communication and recognize that the Pythagorean Theorem only applies to right triangles.
- Informally prove the Pythagorean Theorem using area.
- Recognize 2 dimensional and 3 dimensional Pythagorean Theorem related problems and visualize and practice solving each type of problem.
- Use the converse of the Pythagorean Theorem to classify if a given triangle is indeed a right triangle or not.
STUDENTS will…
- Apply their knowledge of the Pythagorean Theorem to analyze and solve advanced 2D and 3D problems involving the Pythagorean Theorem (such as real world word problems in 2D or finding the diagonal of a rectangular prism in 3D).
- Relate the Pythagorean Theorem to the coordinate system, and formulate a way to calculate and solve for the distance between two coordinates. Construct a problem in the x-y plane and solve for it.
- Assess various internet sources and evaluate and utilize information to aid in problem-solving.
STUDENTS will…
- Conduct independent research, collect, and synthesize information, and use this information to create a concept map, which will convey detailed information about the Pythagorean Theorem’s 4 main applications: The converse, 2D, 3D, and coordinate plane application.
- Use research sources and their own research, to answer What? And How? questions and provide relevant and concrete examples.
- Utilize mathematical reasoning skills and analyze complex word problems involving 2D, 3D and coordinate applications involving the Pythagorean Theorem.