Lesson Plan
Curated OER

Eulerian Paths and Circuits

For Teachers 9th - Higher Ed
Young scholars explore the concept of euler paths and circuits. In this euler paths and circuits lesson plan, students discuss the bridges of Königsberg problem. Young scholars discuss how to determine if an euler circuit exists....
Worksheet
Curated OER

Polygons and Vertices

For Students 9th - 12th
In this geometry learning exercise, learners analyze different polygons and relate it to a circuit board. They find the odd degree Euler circuit and identify the vertices of the odd degree. There are 3 questions with an answer key.
Worksheet
Curated OER

Practice Exam Part 1: Vocabulary

For Students 4th - 6th
In this geometry worksheet, students practice constructing a variety of graphs with various degrees of vertices. Students determine whether 12 graphs have an Euler circuit or path.
Worksheet
Curated OER

Math Matching Worksheet

For Students 9th - 12th
In this math worksheet, learners match math vocabulary to definitions and then solve problems using Euler's theorem and Fleury's algorithm. Students complete 24 problems.
eBook
Other

Discrete Mathematics: Euler Paths and Circuits

For Students 10th - 12th
Explanation and questions about Euler paths and circuits with solutions to the questions.
Interactive
National Council of Teachers of Mathematics

Nctm: Illuminations: Euler's Line

For Students 9th - 10th
Discover and explore Euler's Line.
Handout
Wolfram Research

Wolfram Math World: Hamiltonian Path

For Students 9th - 10th
A description of a Hamiltonian path, also called a Hamilton path.
Activity
National Council of Teachers of Mathematics

The Math Forum: The Beginnings of Topology Leonard Euler

For Students 9th - 10th
This site gives a general description of one of Euler's contributions, topology. It also presents one of the more famous problems of mathematics, The Bridges of Konigsberg.
Graphic
Math Medics

S.o.s. Math: Bernoulli and Euler's Numbers

For Students 10th - 12th
Definitions and formulas pertaining to Bernoulli and Euler numbers.
Handout
Math Open Reference

Math Open Reference: Euler Line

For Students 9th - 10th
Learn about the Euler line with this handy reference guide. Provides a detailed definition and an interactive activity that enhances further explanation. Includes links to related topics.
Handout
University of Toronto (Canada)

University of Toronto: Hamiltonian Path Problem

For Students 10th - 12th
Brief description of Hamiltonian Path and solving the Hamiltonian Path problem.
Article
Other

The University of Edinburgh: Discrete Mathematics Graphs

For Students 10th - 12th
This article is an in-depth look at graphs. Topics covered are graph models, terminology, representations of graphs, graph isomorphism, connectivity, Euler and Hamiltonian Paths, and more. Examples and explanations are included.
Interactive
National Council of Teachers of Mathematics

Nctm: Illuminations: Graph Creator

For Students 3rd - 8th
Use this vertex-edge tool to create graphs and explore them. Investigate ideas such as planar graphs, complete graphs, minimum-cost spanning trees, and Euler and Hamiltonian paths.
Handout
Wikimedia

Wikipedia: Seven Bridges of Konigsberg

For Students 9th - 10th
This Wikipedia site introduces the seven bridges of Konigsberg problem, a classic graph theory problem solved by the mathematician Euler in the 18th century.
Activity
Texas Instruments

Texas Instruments: Numb3 Rs: The Konigsberg Bridge Problem

For Teachers 9th - 10th
Based off of the hit television show NUMB3RS, this lesson introduces students to the world of Graph Theory, by having them explore the Konigsberg Bridge Problem. Through this lesson, students will be able to determine if Euler paths...
Article
Other

Free Codecamp: How to Think in Graphs

For Students 10th - 12th
In this article, we're going to demonstrate various applications of graph theory. These applications will contain detailed illustrations. As the author states, if you've been looking for a "graph theory and everything about it tutorial...
Lesson Plan
Other

Elmwood Park High School: Vertex Edge Graphs

For Students 10th - 12th
In this Unit, you will use vertex-edge graphs and Euler Circuits to help find optimum paths. Included are two lessons that help you develop the understanding and skill needed to solve problems about optimum paths and conflicts.
Activity
Other

Mega Mathematics: Graphs and Graph Theory

For Students 9th - 10th
Contains a clear explanation of the basic terminology of graph theory. The useful for a first introduction to graphs and graph theory.
Activity
Varsity Tutors

Varsity Tutors: Hotmath: Algebra Review: Traceability of Graphs

For Students 9th - 10th
Find a quick, concise explanation of how to test the traceability of graphs. An example is given and clearly explained.
Professional Doc
Annenberg Foundation

Annenberg Learner: Robots

For Students 9th - 10th
The owner of a factory has two expensive robots to automate a manufacturing process. Use the topological concept of a configuration space to coordinate their actions and maximize their efficiency on the manufacturing floor.

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