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Worksheet
Curated OER

Discovering Euler’s Formula for Planar and 3D Figures

For Students 10th
In this Geometry worksheet, 10th graders investigate the number of regions, edges, and vertices of sixteen planar figures in order to discover Euler’s Formula.  The two page worksheet contains a chart for the results of the investigation...
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Lesson Plan
Pennsylvania Department of Education

Euler's Formula

For Teachers 7th - 9th
Students explore geometry by defining a list of vocabulary terms. In this shape characteristics lesson, students identify a number of different shapes and discuss the amount of edges, vertices, and faces using the Euler formula. Students...
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Interactive
Annenberg Foundation

Geometry 3D Shapes: Euler's Theorem

For Students 6th - 10th Standards
How do you get a theorem named after you? Euler knows what it takes! The third lesson of five asks pupils to use an interactive activity to compare the faces, vertices, and edges of seven different three-dimensional solids. They use...
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Lesson Plan
West Contra Costa Unified School District

Interest and the Number e

For Teachers 10th - 12th Standards
Mary, Mary, quite continuously, how does your money grow? Uses examples to examine the difference between simple interest and compound interest, and to take a look at different rates of compounding. Learners explore what would happen as...
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Worksheet
Curated OER

Euler's Theorem

For Students 10th
In this Euler's Theorem worksheet, 10th graders solve and complete 15 various types of problems. First, they find the distance and midpoint of a segment given its endpoints. Then, students identify the number of vertices, edges, and...
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Handout
Thomson Brooks-Core

Complex Numbers

For Students 10th - 12th
A straightforward approach to teaching complex numbers, this lesson addresses the concepts of complex numbers, polar coordinates, Euler's formula, De moivres Theorem, and more. It includes a practice problems set with odd answers and a...
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Activity
Curated OER

Solidly Platonic

For Teachers 9th - 12th Standards
When they do, they learn. Using this resource, young mathematicians learn about platonic solids by actually building, touching, and examining the shapes. They connect their observations about the shapes to Euler's formula.
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Worksheet
Curated OER

Slope Fields and Euler's Method

For Students Higher Ed
For this slope field worksheet, students use a slope field for a rate equation. Using Euler's Method, they identify the piecewise linear function approximating the solution of the initial value problem. This four-page worksheet...
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Worksheet
Curated OER

Lab 2: Euler's Method and Riemann's Sums

For Students Higher Ed
In this Euler's Method and Riemann's Sum worksheet, students identify the best situation in which to use Euler's Method and Riemann's Sum. They identify the initial value of a problem and use the accumulation formula to determine the...
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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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Handout
West Contra Costa Unified School District

Interest and the Number “e”

For Students 9th - 12th Standards
Make a connection between different types of interest and how they are calculated! This algebra II lesson progresses from simple interest to compound interest to continually compounded interest. Formulas are developed rather than given,...
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Worksheet
Curated OER

Countdown Challenge: Platonic Solids - Part I

For Students 7th - 8th
Use a Platonic solids worksheet to record the number of faces, edges, and vertices of five polyhedra whose faces, edges, and vertices are all identical. For each figure, learners write a proof of Euler's formula (F+V=E+2). They create a...
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Lesson Plan
Curated OER

Shapes with Sticks

For Teachers 3rd
Third graders investigate three dimensional shapes. They examine a variety of shapes and the relationship between the number of faces, edges, and vertices. Students determine Euler's formula and they create a variety of three dimensional...
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Lesson Plan
Curated OER

Introduction to Polyhedra

For Teachers 9th - 11th
Students investigate Euler's Formula. In this geometry lesson, students perform an inductive activity of Euler's Formula using nets to identify a variety of prism, pyramids, cylinders, and cones.
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Worksheet
Curated OER

Complex Analysis: Polar & Exponential Forms

For Students Higher Ed
In this polar and exponential form worksheet, students use Euler's Formula to write complex numbers in exponential form. They write numbers in rectangular form. This two-page worksheet contains seven multi-step problems.
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Worksheet
Curated OER

Properties of Exponential Functions

For Students 10th - 11th
In this algebra worksheet, students graph exponential equations and use the formula to translate the graph on a coordinate plane. There are 3 word problems.
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Lesson Plan
Curated OER

Pi

For Teachers 6th
Sixth graders read the book "Sir Cumference and Knights of the Round Table" to introduce them to the concept of Pi. As a class, they discover where Pi originated and define the terms circumference, radius and diameter. To end the...
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eBook
Old Dominion University

Introduction to Calculus

For Teachers 11th - Higher Ed Standards
This heady calculus text covers the subjects of differential and integral calculus with rigorous detail, culminating in a chapter of physics and engineering applications. A particular emphasis on classic proof meshes with modern graphs,...
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Worksheet
Curated OER

More on Tessellations

For Students 10th
In this tessellations worksheet, 10th graders solve 3 different word problems that include creating various tessellations. First, they group pentagons around a vertex so the angles add up to 360 and determine whether the pentagons can...
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Lesson Plan
Curated OER

Geometry and Tony Smith Sculpture

For Teachers 6th - 8th
Learners respond to Tony Smith's sculpture as art and brainstorm about math concepts inherent in his work. They create a sculpture with polyhedra nets, calculate the cost of covering sculpture in gold, and write an exhibit label for...
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Lesson Plan
Curated OER

Faces, Vertices, Edges

For Teachers 9th - 10th
Learners identify the parts of three dimensional objects. In this geometry lesson, students find the number of faces, edges and vertices. They differentiate between prisms and polyhedra.
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Lesson Plan
Curated OER

Worksheet 19-Spring 1996

For Teachers Higher Ed
In this math worksheet, pupils begin with the Maclaurin series and prove De Moivre's Theorem. They use the De Moivre Theorem to solve four problems. Students apply these theorems to explain why a flock of geese will fly in an uneven...
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Lesson Plan
Curated OER

e, pi, and Exponential Functions

For Teachers 11th - 12th
Students investigate e, pi and exponents. In this calculus lesson, students define constants and non-constants using, pi, e and exponents as an example. They use the TI to work the problems in this lesson.
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Worksheet
Curated OER

Worksheet 18 - Spring 1996

For Students 11th - Higher Ed
In this math instructional activity, students practice finding the function while practicing using the Taylor series. Then they compute the second integral by parts.

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