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Illustrative Mathematics

Hexagonal Pattern of Beehives

For Teachers 9th - 12th Standards
Young geometers and biologists investigate the math of nature in an activity that is just the bee's knees. Participants will study the tessellations of hexagons in a beehive, along with the natural rationale behind the specific shape....
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Other

University of Surrey: The Fibonacci Number Sequence

For Students 9th - 10th
This resource provides extensive information on the Fibonacci number sequence. It has numerous formulas and examples.
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Other

Mathman: The Fibonacci Numbers, Pineapples, Sunflowers, and the Golden Mean

For Students 9th - 10th
Here is an exercise to do using a pineapple to explore Fibonacci numbers. Then find the ratios of larger to smaller of each consecutive pair of Fibonacci numbers and graph them to find out the sequence.
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TeachEngineering

Teach Engineering: The Fibonacci Sequence & Robots

For Teachers 6th - 8th
Using the LEGO NXT robotics kit, students construct and program robots to illustrate and explore the Fibonacci sequence. Within teams, students are assigned roles: group leader, chassis builder, arm builder, chief programmer, and...
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Ministry of Education and Universities of the Region of Murcia (Spain)

Ministerio De Educacion Y Ciencia: Sucesion De Fibonacci

For Students 9th - 10th
In Spanish. This unit is about Fibonacci numbers, some of its most interesting properties and their occurrence both in nature and art.
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National Council of Teachers of Mathematics

The Math Forum: Ask Dr. Math: Fibonacci Sequence

For Students 9th - 10th
This site from the Math Forum explains the explicit formula for fibonacci numbers.
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University of Cambridge

University of Cambridge: Nrich: 1 Step 2 Step, Fibonacci

For Students 3rd - 8th Standards
See if you can find the patterns on the staircase. Mr. Fibonacci would be so proud to know you found the solution. You can check your solution right at this nifty one-page website.
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Annenberg Foundation

Annenberg Learner: Part C: Fibonacci Numbers

For Students 9th - 10th
Look at an interesting application of ratios that demonstrates the amazing patterns that emerge when we examine mathematics. The Fibonacci numbers are found in art, music, and nature.
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Texas Instruments

Texas Instruments: Numb3 Rs: It All Started With a Pair of Rabbits

For Teachers 9th - 10th
Based off of the hit television show NUMB3RS, this lesson introduces students to the set of Fibonacci numbers and shows how this set is present in many aspects of nature. Through the lesson, students explore the first 13 elements in the...
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Texas Instruments

Texas Instruments: Class of Gold

For Teachers 6th - 8th
Students investigate Fibonacci numbers and the ratios of successive Fibonacci numbers.
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Math Is Fun

Math Is Fun: Golden Ratio

For Students 9th - 10th
A clear explanation, with drawings and examples, of the golden ratio. The examples demonstrate the beauty of mathematics, such as how two Fibonacci numbers can approximate the golden ratio, and why the golden ratio can be called the...
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TeachEngineering

Teach Engineering: Discovering Phi: The Golden Ratio

For Teachers 6th - 8th
Students discover the mathematical constant phi, the golden ratio, through hands-on activities. They measure dimensions of "natural objects"--a star, a nautilus shell and human hand bones--and calculate ratios of the measured values,...
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University of Cambridge

University of Cambridge: Nrich: Gnomon 1

For Students 3rd - 8th Standards
This interactive activity gives you an opportunity to explore a specific number pattern named the "Fibonacci sequence." See what other patterns you can discover while you manipulate the blocks. There is a "Printable Page" link if you...
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Texas Instruments

Texas Instruments: At a Snail's Pace for the Ti 73 Explorer

For Teachers 6th - 8th
It is hard to imagine a way to mathematically describe a spiral. Spirals are commonly seen in nature. There are a number of different types of spirals. Some interesting examples include the spiral arrangements of scales in pine cones,...
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Texas Instruments

Texas Instruments: Sequences

For Teachers 9th - 10th
Students learn how to graph the first n terms of a sequence, how to set the window and how to evaluate the nth term of a sequence. They also explore the Fibonacci sequence and Web plots.
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Texas Instruments

Texas Instruments: Numb3 Rs: Pythagorean Triples

For Teachers 9th - 10th Standards
Based off of the hit television show NUMB3RS, this lesson has students explore the notion of Pythagorean triples, the "traditional" method for finding Pythagorean triples, and a method to find triples which utilizes the Fibonacci...
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Cut the Knot

Cut the Knot: Lattice Multiplication

For Students 9th - 10th Standards
Have you heard of the 13th century mathematician, Leondardo Fibonacci? See examples of his concept of a lattice multiplication algorithm. Several example problems, including an interactive one where students can change the factors, are...
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Ministry of Education and Universities of the Region of Murcia (Spain)

Ministerio De Educacion Y Ciencia: Sucesiones Y Progresiones

For Students 9th - 10th Standards
In Spanish. This unit introduces the concept of succession focusing on the study of arithmetic, geometric and Fibonacci.
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Math Is Fun

Math Is Fun: Pascal's Triangle

For Students 9th - 10th
A detailed explanation of Pascal's trianlge, with lots of examples and patterns described.
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Ministry of Education and Employment of Spain

Red Escolar: Juega Con Sucesiones

For Students 3rd - 8th
In Spanish. Find out about patterns and number sequences and read about some of Fibonacci tricks.
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Wolfram Research

Wolfram Math World: Golden Ratio

For Students 9th - 10th
Math World explains the Golden Ratio, gives the formula for finding the irrational number, and expresses this value as an infinite series. Also defines and represents the Ratio geometrically, its relationship to the Fibonacci numbers,...
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Other

Who Was Fibonacci?: Roman Numerals

For Students 5th - 8th
Gives a short introduction to Roman numerals. Explains how to add, subtract, and multiply Roman numerals.
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University of Ottawa (Canada)

University of Ottawa: Linear Algebra Close to Earth

For Students 9th - 10th
The author of this site endeavours to explain how linear algebra has many applications in a wide range of disciplines, to help students see its uses in the real world.
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Wolfram Research

Wolfram Math World: Inverse Tangent

For Students 9th - 10th Standards
This site is all about inverse tangents. The site includes a definition, color graphs, formulas, and many links to related terms.

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