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Lesson Plan
Curated OER

Getting It Right! An Investigation of the Pythagorean Theorem

For Teachers 6th - 8th
Learners construct a variety of right triangles using a right-angled set square, cutting corners from pieces of paper or cardboard, and using dynamic geometry software. They measure the sides of these various right triangles and record...
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AP Test Prep
College Board

Why We Use Theorem In Calculus

For Teachers 11th - Higher Ed
Young scholars read an article to explain the reasoning behind theorems. In this calculus lesson, students understand the underlying principles of theorems and how it helps them make sense of the problems. They know why they do what they...
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Lesson Plan
Curated OER

The Notorious Four-Color Problem

For Teachers 9th - 12th Standards
Take a walk through time, 1852 to 2005, following the mathematical history, development, and solution of the Four-Color Theorem. Learners take on the role of cartographers to study a United States map that is to be colored. One rule: no...
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Printables
Chapman University

Proof of L’Hospital’s Rule

For Teachers 10th - Higher Ed
Understanding how calculus formulas were derived connects learners to the idea that the study of mathematics is continuous and cumulative. Learners will also develop a deeper appreciation for the derivative's application in simplifying...
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Worksheet
Curated OER

Pythagorean Theorem

For Students 5th - 6th
In this finding the missing units in triangles worksheet, learners apply the Pythagorean Theorem to solve. Students solve 10 problems. 
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Interactive
Curated OER

Proofs with Triangles Self-check Practice

For Students 8th - 10th
In this triangle theorems worksheet, students identify the theorem used to prove the specified triangular relationship. Students are shown an illustration of two or more triangles. They identify the postulate that would be used to prove...
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Lesson Plan
Virginia Department of Education

Congruent Triangles

For Teachers 9th - 11th Standards
Is this enough to show the two triangles are congruent? Small groups work through different combinations of constructing triangles from congruent parts to determine which combinations create only congruent triangles. Participants use the...
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Lesson Plan
2
2
Illustrative Mathematics

Shortest Line Segment from a Point P to a Line L

For Teachers 9th - 11th Standards
One of the hardest skills for many young geometers to grasp is to move beyond just declaring obvious things true, and really returning to fundamental principles for proof. This brief exercise stretches those proving muscles as the class...
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Interactive
Shodor Education Foundation

Squaring the Triangle

For Students 8th - 12th Standards
Teach budding mathematicians how to square a triangle with an interactive that shows a graphical proof of the Pythagorean Theorem. Pupils alter the lengths of the legs using sliders. Using the inputted lengths, the applet displays the...
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Workbook
1
1
University of Utah

Geometry: Angles, Triangles, and Distance

For Students 8th Standards
The Pythagorean Theorem is a staple of middle school geometry. Scholars first investigate angle relationships, both in triangles and in parallel lines with a transversal, before proving and applying the Pythagorean Theorem.
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Unit Plan
Mathematics Vision Project

Module 3: Geometric Figures

For Teachers 9th - 12th Standards
It's just not enough to know that something is true. Part of a MVP Geometry unit teaches young mathematicians how to write flow proofs and two-column proofs for conjectures involving lines, angles, and triangles.
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Unit Plan
Mathematics Vision Project

Connecting Algebra and Geometry

For Teachers 9th - 10th Standards
Connect algebra and geometry on the coordinate plane. The eighth unit in a nine-part integrated course has pupils develop the distance formula from the Pythagorean Theorem. Scholars prove geometric theorems using coordinates including...
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Lesson Plan
EngageNY

The Power of Algebra—Finding Pythagorean Triples

For Students 10th - 12th Standards
The Pythagorean Theorem makes an appearance yet again in this lesson on polynomial identities. Learners prove a method for finding Pythagorean triples by applying the difference of squares identity. 
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Lesson Plan
Curated OER

Pythagorean Theorem Triples

For Teachers 9th - 12th
Learners research the concept of the Pythagorean Theorem. In this Pythagorean Theorem lesson, students use the Internet to learn about the Pythagorean Theorem. Learners construct proofs of the Pythagorean Theorem.
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Worksheet
Curated OER

Geometric Proof and Angles

For Students 10th
In this geometry learning exercise, 10th graders write two-column and paragraph proofs to prove angle pair relationships.  The one page learning exercise contains five problems.  Answers are not included. 
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Worksheet
Curated OER

Proofs with Triangles

For Students 9th - 12th
In this geometry worksheet, students prove triangle congruence by making statements with reasons and concluding with the AAS or HL theorem. There are 2 proofs.
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Lesson Plan
Curated OER

Pythagorean Theorem

For Teachers 7th - 12th
Students investigate the Pythagorean Theorem.  In this seventh through twelfth grade geometery lesson, students explore the Pythagorean Theorem and its converse and use it to find the length of the missing side of a right triangle.
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Lesson Plan
Curated OER

Discovering Math: Concepts in Geometry

For Teachers 8th - 12th
Middle and high schoolers explore the concept of proving the Pythagorean Theorem. They research proofs of the Pythagorean Theorem. Pupils create posters of proofs, and research Greek mathematicians.
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Lesson Plan
Curated OER

Central Valley Math Project

For Teachers 7th - 8th
Middle schoolers study the Pythagorean Theorem. They describe what it means to square a number. Pupilsuse the Pythagorean Theorem to prove the sides of given triangles, and use geometric pieces of paper to create a right triangle and...
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Lesson Plan
Curated OER

The Right Stuff

For Teachers 7th - 9th
Studentsare introduced to the Pythagorean Theorem by exploring right triangles and the squares built on each side. They apply the Pythagorean Theorem to real-world problems. Students u se informal and nonformal arguments of proof (i.e.,...
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Unit Plan
Mathematics Vision Project

Module 6: Congruence, Construction, and Proof

For Teachers 8th - 10th Standards
Trace the links between a variety of math concepts in this far-reaching unit. Ideas that seem very different on the outset (like the distance formula and rigid transformations) come together in very natural and logical ways. This unit...
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Lesson Plan
EngageNY

Base Angles of Isosceles Triangles

For Students 9th - 10th Standards
Build confidence in proofs by proving a known property. Pupils explore two approaches to proving base angles of isosceles triangles are congruent: transformations and SAS. They then apply their understanding of the proof to more complex...
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Lesson Plan
EngageNY

The Graph of a Linear Equation in Two Variables Is a Line

For Teachers 8th Standards
Show your class that linear equations produce graphs of lines. The 20th segment in a unit of 33 provides proof that the graph of a two-variable linear equation is a line. Scholars graph linear equations using two points, either from...
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Lesson Plan
EngageNY

Unknown Angle Problems with Inscribed Angles in Circles

For Teachers 9th - 10th Standards
We know theorems about circles—now what? Class members prove a theorem, with half the class taking the case where a point is inside the circle and half the class taking the case where a point is outside the circle. The lesson plan then...