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Instructional Video11:47
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\n\"Proving\n\n
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\nPBS\n
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\nProving Pick's Theorem\n

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\n\nFor Students\n\n10th - Higher Ed\n
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\nPick up a resource on Pick's Theorem. Individuals watch a video explaining how to find the area of a polygon drawn on a lattice using Pick's Theorem. The film also shows a proof of the theorem using the Euler characteristic and algebra.\n
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Activity
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\n\"Solidly\n\n
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\nCurated OER\n
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\nSolidly Platonic\n

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\n\nFor Teachers\n\n9th - 12th\n\nStandards\n
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\nWhen 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.\n
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Worksheet
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\n\"A\n\n
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\nCurated OER\n
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\nA Model for the Spread of Disease\n

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\n\nFor Students\n\nHigher Ed\n
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\nIn this model learning exercise, students explore a real life scenario to determine the rate at which a disease may spread. They use Euler's Method and the SIR model to determine values at a given point in time. This two-page learning...\n
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Worksheet
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\n\"A\n\n
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\nCurated OER\n
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\nA Refined Cooling Model\n

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\n\nFor Students\n\nHigher Ed\n
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\nIn this cooling model worksheet, students approximate solutions using Euler's method. They approximate piecewise linear equations. This six-page worksheet contains approximately 15 problems.\n
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Worksheet
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\n\"Euler's\n\n
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\nCurated OER\n
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\nEuler's Method\n

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\n\nFor Students\n\nHigher Ed\n
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\nIn this Euler's method worksheet, students use Euler's method to determine one-second time intervals in a rate problem. They explore functions to estimate rate changes in small time intervals. This two-page worksheet contains...\n
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Worksheet
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\n\"Rate\n\n
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\nCurated OER\n
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\nRate Equation\n

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\n\nFor Students\n\n12th - Higher Ed\n
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\nIn this rate equation worksheet, students use Euler's method to estimate the value of rate equations. They use the piecewise linear function approximation to determine the solution of an initial value problem. This two-page worksheet...\n
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\n\"Practice\n\n
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\nCurated OER\n
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\nPractice Exam Part 1: Vocabulary\n

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\n\nFor Students\n\n4th - 6th\n
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\nIn 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.\n
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Lesson Plan
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\n\"Discovering\n\n
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\nCurated OER\n
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\nDiscovering Euler's Theorem\n

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\n\nFor Teachers\n\n9th - 10th\n
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\nStudents identify different parts of a prism and polyhedra. In this geometry lesson, students identify the number of faces, edges and sides of polygons. They solve problems by recognizing patterns.\n
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Lesson Plan
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\n\"Eulerian\n\n
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\nCurated OER\n
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\nEulerian Paths and Circuits\n

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\n\nFor Teachers\n\n9th - Higher Ed\n
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\nStudents explore the concept of euler paths and circuits. In this euler paths and circuits lesson, students discuss the bridges of Königsberg problem. Students discuss how to determine if an euler circuit exists. Students discuss the...\n
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Worksheet
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\n\"Math\n\n
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\nCurated OER\n
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\nMath Matching Worksheet\n

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\n\nFor Students\n\n9th - 12th\n
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\nIn this math worksheet, students match math vocabulary to definitions and then solve problems using Euler's theorem and Fleury's algorithm. Students complete 24 problems.\n
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Worksheet
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\n\"Polygons\n\n
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\nCurated OER\n
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\nPolygons and Vertices\n

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\n\nFor Students\n\n9th - 12th\n
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\nIn this geometry worksheet, students 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.\n
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Interactive
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\n\"Euler\n\n
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\nCurated OER\n
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\nEuler Fortune Problem\n

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\n\nFor Students\n\n10th - 12th\n
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\nIn this problem solving worksheet, students solve for the amount of the fortune a father starts with before he divides it among his children, given a set of clues.  Students must also solve for how many children the money is divided...\n
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Worksheet
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\n\"Introduction\n\n
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\nCurated OER\n
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\nIntroduction to Mathematical Modeling\n

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\n\nFor Students\n\nHigher Ed\n
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\nIn this mathematical modeling worksheet, students answer two essay questions. They describe Newton's Law of Cooling by describing and constructing a model and answering seven essay questions about the process.\n
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\n\"Newton's\n\n
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\nCurated OER\n
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\nNewton's Law of Cooling\n

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\n\nFor Students\n\nHigher Ed\n
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\nIn this Newton's Law of Cooling worksheet, students complete an essay format write up of a convection model. They write the purpose and assumptions of their lab. Students complete three rate of change problems. They describe a model in...\n
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\n\"Variables\n\n
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\nCurated OER\n
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\nVariables and Slopes\n

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\n\nFor Students\n\n7th - 10th\n
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\nIn this variable and slopes worksheet, students practice a warm-up activity involving variables V and X and using Euler's Method to solve a value problem.\n
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Lesson Plan
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\n\"The\n\n
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\nThe Notorious Four-Color Problem\n

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\n\nFor Teachers\n\n9th - 12th\n\nStandards\n
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\nTake 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...\n
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Instructional Video13:04
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\n\"Basic\n\n
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\nKhan Academy\n
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\nBasic Complex Analysis\n

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\n\nFor Students\n\n10th - 12th\n
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\nThis video gives an excellent overview of the different representations of a complex number. First, Sal reviews a pictorial representation of a complex number as an Argand diagram, then shows how to find the modulus and the argument of a...\n
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Worksheet
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\n\"Challenge\n\n
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\nCurated OER\n
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\nChallenge Discussion Sheet 9\n

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\n\nFor Students\n\nHigher Ed\n
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\nIn this limits worksheet, students evaluate five limits using limit definitions. They solve differential equations by isolating one variable. Students determine the dimensions of a rectangle inscribed below the graph of a curve.\n
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Lesson Plan
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\n\"The\n\n
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\nThe Number \"e\"\n

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\n\nFor Teachers\n\nHigher Ed\n
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\nIn this college level mathematics worksheet, students explore the number e and graph functions involving e. The two page worksheet contains thirty-two problems. Answers are included.\n
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\n\"Exponential\n\n
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\nCurated OER\n
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\nExponential Equations and Functions\n

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\n\nFor Teachers\n\nHigher Ed\n
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\nIn this college level Pre-Calculus worksheet, students solve problems involving exponential functions.  Students determine the domain, range, y-intercept and asymptotes of exponential functions. The three page worksheet contains...\n
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Worksheet
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\n\"Countdown\n\n
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\nCurated OER\n
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\nCountdown Challenge: Platonic Solids - Part I\n

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\n\nFor Students\n\n7th - 8th\n
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\nUse 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...\n
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Handout
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\n\"Exponential\n\n
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\nMt. San Antonio Collage\n
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\nExponential Growth and Decay\n

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\n\nFor Students\n\n9th - 12th\n\nStandards\n
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\nStart with the basics and move up the exponential ladder to master a variety of problem-solving and application problems. The problems are heavy on exponential growth and decay, compound interest, and natural log.\n \n
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Lesson Plan
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\n\"Introduction\n\n
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\nIntroduction to Polyhedra\n

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\n\nFor Teachers\n\n9th - 11th\n
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\nStudents 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.\n
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Handout
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\n\"Interest\n\n
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\nWest Contra Costa Unified School District\n
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\nInterest and the Number “e”\n

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\n\nFor Students\n\n9th - 12th\n\nStandards\n
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\nMake 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,...\n
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