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\n\"The\n\n
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\nCurated OER\n
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\nThe Golden Students\n

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\n\nFor Teachers\n\n6th - 12th\n
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\nScholars view the video, \"Donald Duck in Mathmagic Land,\" and discuss examples in nature which have proportions of the golden ratio. They measure and record different body lengths from a worksheet and convert the ratios to equivalent...\n
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\n\"Golden\n\n
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\nTexas Instruments\n
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\nGolden Ratio Lab\n

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\n\nFor Teachers\n\n9th - 12th\n\nStandards\n
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\nLearners investigate the Golden Ratio in this algebra I or geometry instructional activity. They explore the Golden Ratio as the conduct an experiment in which they collect various measurement from their team members and find the...\n
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\n\"Class\n\n
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\nCurated OER\n
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\nClass of Gold\n

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\n\nFor Teachers\n\n6th - 9th\n
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\nHow can you see a number in nature? Here, learners discover both Fibonacci numbers and the golden ratio by exploring a number of different resources.  Note: Some of the resources are older and may be missing some of the links, but...\n
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Unit Plan
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\n\"Fibonacci\n\n
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\nRadford University\n
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\nFibonacci is All Around\n

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\n\nFor Teachers\n\n9th - 12th\n\nStandards\n
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\nOne ratio to rule them all. Young mathematicians investigate the Fibonacci sequence and the Golden Ratio. To begin the first lesson, they use a spreadsheet to see how the Fibonacci sequence gives the Golden Ratio. The second lesson...\n
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\n\"Are\n\n
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\nK20 LEARN\n
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\nAre We Golden?\n

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\n\nFor Teachers\n\n6th - 7th\n\nStandards\n
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\nLead your class on a search for precious bones. Using a presentation, the class investigates the golden ratio in art and nature. Groups of pupils measure specific bones and find the average ratio for the class. To further cement the...\n
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\n\"The\n\n
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\nCurated OER\n
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\nThe Golden Ratio\n

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\n\nFor Teachers\n\n7th\n
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\nSeventh graders investigate a ratio found in nature and in numerous pieces of artwork throughout history. The lesson is cross-curricular and builds a sense of appreciation of design for students.\n
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\n\"Start\n\n
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\nDick Blick Art Materials\n
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\nStart with a Circle...\n

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\n\nFor Students\n\nK - 12th\n
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\nThe Golden Ratio. The Divine Proportion. Yup. It's math and art blended into one colorful activity. Young artists combine colored tissue paper circles and parts of circles to create geometric patterns. As a bonus, kids get to figure out...\n
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\n\"Discovering\n\n
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\nTeach Engineering\n
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\nDiscovering Phi: The Golden Ratio\n

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\n\nFor Teachers\n\n6th - 8th\n\nStandards\n
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\nFe, phi, fo, fum. This activity leads pairs to find the ratio of consecutive terms of the Fibonacci sequence. The pairs find that the Fibonacci sequence can be found in many places. A discussion with the class shows that the ratios...\n
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\n\"As\n\n
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\nAs Good As Gold\n

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\n\nFor Teachers\n\n5th - 10th\n
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\nStudents find examples of the Golden Ratio on the human body through measurement. Additionally, students learn about the use of the Golden Ratio and the Golden Rectangle in art and architecture. A very interesting lesson for the students!\n
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\n\"Using\n\n
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\nCurated OER\n
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\nUsing Ratios\n

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\n\nFor Teachers\n\n8th - 10th\n
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\nStudents study the Golden Ratio and its relationship to Renaissance artists. After exploring proportions and ratios used by Renaissance artists, students create a mix of ten variations of color paint, and record the ratios of primary...\n
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\n\"I\n\n
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\nI Am Golden\n

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\n\nFor Teachers\n\n6th - 8th\n
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\nStudents become familiar with patterns, the Fibonacci Sequence, and the Golden Ratio. They see how many places these occur. They have practical applications for using the calculator and making charts to extend patterns.\n
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PPT
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\n\"Alice\n\n
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\nCurated OER\n
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\nAlice in Fractalland\n

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\n\nFor Teachers\n\n4th - 8th\n\nStandards\n
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\nTake your class on a field trip to Fractalland where they'll learn all about number and shape patterns. Based on Disney's movie Alice in Wonderland, this resource takes young mathematicians on an adventure as they explore patterns in...\n
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\n\"The\n\n
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\nCurated OER\n
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\nThe Golden Rectangle\n

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\n\nFor Teachers\n\n6th - 8th\n
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\nStudents explore the concept of the golden ratio. In this golden ratio lesson, students measure objects to determine if their measurements fit the golden ratio. Students calculate the average measurements of the class.\n
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\n\"Are\n\n
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\nCurated OER\n
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\nAre You a Golden Ratio?\n

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\n\nFor Teachers\n\n6th - 8th\n
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\nStudents explore the concept of the golden ratio in nature and architectural design. They discuss examples such as petals on a sunflower and the Parthenon. In small groups they take turns measuring their body parts to find a golden ratio.\n
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\n\""How\n\n
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\n\"How Divine Is My Proportion?\"\n

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\n\nFor Teachers\n\n8th\n
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\nEighth graders explore the concept of the divine proportion/golden ratio. In this Fibonacci Sequence exploratory lesson, 8th graders measure the length and width of various objects to see which items have a divine proportion. Students...\n
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\n\"There's\n\n
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\nThere's Gold in Them Thar Ratios\n

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\n\nFor Teachers\n\n7th - 10th\n
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\nStudents draw a model of the bunny problem which generates the Fibonacci Sequence, spirals generated from golden rectangles and golden triangles; identify the golden ratio in the human body, and find the Fibonacci numbers in nature.\n
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Worksheet
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\n\"What\n\n
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\nCurated OER\n
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\nWhat Number Differs from its Reciprocal by 1?\n

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\n\nFor Students\n\n10th - Higher Ed\n
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\nIn this reciprocal worksheet, students identify the number that differs from its reciprocal by 1.  The significance of this number is that it is the golden ratio.  The solution to the problem is provided.\n
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\n\"Golden\n\n
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\nGolden Ratio of the Human Body\n

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\n\nFor Teachers\n\n9th - 12th\n
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\nStudents calculate the ratio of the height of the body to the height of the navel. They discover that the ratios are all approximately equal.\n
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\n\"The\n\n
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\nThe Golden Ratio\n

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\n\nFor Teachers\n\n9th - 11th\n
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\nStudents solve problems using ratios and proportions. In this algebra lesson, students verify proportions, solve for the unknown and use real life scenario to model proportion.\n
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\n\"Amazing\n\n
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\nAmazing Fibonacci\n

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\n\nFor Teachers\n\n8th - 12th\n
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\nStudents integrate the patterns of Fibonacci into music. In this geometry lesson, students apply the concepts of recursion, pattern and Phi or Golden Ratio to composing and playing music on various instruments. They lesson is co-taught...\n
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Activity
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\n\"Authentic\n\n
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\nWake Forest University\n
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\nAuthentic Activities for Connecting Mathematics to the Real World\n

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\n\nFor Students\n\n6th - 12th\n\nStandards\n
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\nCheck out the handout from a presentation that contains a collection of high school algebra projects connecting a variety of mathematics to the real world. Activities range from simple probabilities to calculus. The activities...\n
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\n\"Scientific\n\n
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\nChapman University\n
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\nScientific Alphabet Chart - Get to Know Your Greek Alphabet\n

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\n\nFor Teachers\n\n9th - Higher Ed\n
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\nGreek alphabet letters are used to represent words or values in science and math. Keep a list on hand to refer to while working through calculus or physics problems.\n
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\nTeach Engineering\n
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\nThe Fibonacci Sequence and Robots\n

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\n\nFor Students\n\n6th - 8th\n\nStandards\n
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\nWhat better way to introduce the idea of a sequence than with robots! An educational lesson explains the classic Fibonacci sequence before pupils build and program a robot to move. Additionally, the lesson challenges individuals to...\n
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\n\"Least\n\n
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\nLeast Squares Fit Line\n

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\n\nFor Teachers\n\n7th - 8th\n
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\nPractice makes perfect! Learners estimate the least squares fit line for a set of data. They understand error involved in least squares fit lines, and solve application problems using least square fit lines.\n
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