Curated OER
The Intermediate Value Theorem
You and your calculus learners will appreciate this description, discussion, and examples of the Intermediate Value Theorem. Applications of the theorem are also discussed.
Curated OER
Lesson 3.4 Practice A: Theorems and Postulates
In this theorem and postulate worksheet, students identify theorems and postulates that justify given statements. They determine the measure of specified angles. This two-page worksheet contains a total of 37 problems. These two...
Illustrative Mathematics
Shortest Line Segment from a Point P to a Line L
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...
Curated OER
Proofs of the Pythagorean Theorem
Working individually and collaboratively, geometers gain a clear understanding of the Pythagorean theorem. They create, explain, and compare proofs of the theorem. Proofs involve areas of trapezoids, squares, and triangles, congruent...
EngageNY
The Power of Algebra—Finding Pythagorean Triples
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.
EngageNY
Looking More Carefully at Parallel Lines
Can you prove it? Making assumptions in geometry is commonplace. This resource requires mathematicians to prove the parallel line postulate through constructions. Learners construct parallel lines with a 180-degree rotation and then...
Curated OER
The Pythagorean Theorem Lesson 2
Learners discuss and review examples of the Pythagorean Theorem using a GSP, Geometer's Sketchpad, activity.
Curated OER
Euclidean Direct Proofs
Learning how to prove theorems in geometry can be challenging. This resource explains what a proof is, and the different styles for proofs. It also contains links to web-based practice problems that help guide learners though example...
Curated OER
Indirect Proof and Inequalities in one Triangle
In this geometry worksheet, 10th graders complete an indirect proof and order the sides or angles of a triangle. Also, students determine if a triangle can have sides with the given lengths. The two page worksheet contains twelve...
Curated OER
The Four-Color Problem: Concept and Solution
Take a walk through time, 1852 to 1994, following the mathematical history and development of the Four-Color Theorem. Learners take on the role of cartographers to study an imaginary world of countries that need to be...
EngageNY
End-of-Module Assessment Task: Grade 8 Mathematics (Module 7)
It's time to discover what your classes have learned! The final lesson in the 25-part module is an assessment that covers the Pythagorean Theorem. Application of the theorem includes distance between points, the volume of...
Mathematics Assessment Project
College and Career Readiness Mathematics Test A1
A six-page test covers content from several different high school math courses. It incorporates a few short answer, graphing, and word problems. It also allows room for mathematical reasoning and analysis.
Curated OER
The Truth About Triangles And Proofs
High schoolers engage in a lesson that is about the classification of triangles and the mathematical proofs involved in working with them. They work on a variety of problems that are created by the teacher with the focus upon the...
Curated OER
The Notorious Four-Color Problem
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...
Chapman University
Proof of L’Hospital’s Rule
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...
Virginia Department of Education
Inductive and Deductive Reasoning
Introduce pupils to the two types of reasoning, inductive and deductive. Classmates work in pairs or small groups to learn the difference between the two and apply these reasonings to develop valid conclusions.
Virginia Department of Education
Logic and Conditional Statements
If there is a conditional statement, then there is a hypothesis and conclusion. Pupils learn how to identify the parts of conditional statements. Class members continue to work with conditional statements and rewrite them in their many...
Virginia Department of Education
High School Mathematics Geometry Vocabulary Word Wall Cards
Having a good working knowledge of math vocabulary is especially important for geometry learners. Here are 119 pages worth of wonderfully constructed definitions, constructions, formulas, properties, theorems, and postulates. This is a...
Curated OER
The Proof of the Century!
Students do Web research in the field of mathematics. They explore mathematical proofs and apply them to the Pythagorean theorem. They also explore the general ideas of Fermat's Last Theorem
Curated OER
The Pythagorean Theorem
Learners create both a visual and formal proof of the Pythagorean theorem, as well as view four additional geometric demonstrations of the theorem. They construct a square and conjecture the following theorem: The sum of the areas of...
Curated OER
The Pythagorean Theorem
Seventh graders relate the Pythagorean theorem to the real world. In this algebra lesson, 7th graders identify important properties of the Pythagorean theorem and use it to solve word problems. They create a step by step plan to...
Curated OER
Pythagorean Theorem
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...
University of California
Euclidean Geometry
Go back to where it all began! Investigate how axiomatic systems and Euclidean geometry are based on undefined terms, common notions, postulates, and propositions by examining passages from Euclid's Elements. (Social studies teachers...
EngageNY
Scale Factors
Is it bigger, or is it smaller—or maybe it's the same size? Individuals learn to describe enlargements and reductions and quantify the result. Lesson five in the series connects the creation of a dilated image to the result. Pupils...