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Mathematical Quilts in a Radical Way

Mathematical Quilts in a Radical Way. Objectives. The students will investigate the mathematical patterns found in quilts. The students will investigate special right triangles through measurement and the use of the Pythagorean Theorem.

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Mathematical Quilts in a Radical Way

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  1. Mathematical Quiltsin aRadical Way Kathleen M. SyllaSummmer Institute 2007

  2. Objectives • The students will investigate the mathematical patterns found in quilts. • The students will investigate special right triangles through measurement and the use of the Pythagorean Theorem. • The students will investigate special right triangles using radicals. Kathleen M. Sylla Summmer Institute 2007

  3. Friendship Star Quilt Kathleen M. Sylla Summmer Institute 2007

  4. In a Radical Way Pythagoras of Samos lived from about 569 BC to about 475 BC Kathleen M. Sylla Summmer Institute 2007

  5. In a Radical Way Pythagoras was a Greek philosopher who made important developments in mathematics, astronomy, and the theory of music. The theorem now known as Pythagoras's theorem was known to the Babylonians 1000 years earlier but he may have been the first to prove it. Kathleen M. Sylla Summmer Institute 2007

  6. Pythagorean Theorem • Building squares on the sides of a right triangle. • Pythagoras' Theorem states that the sum of (the areas of) two small squares equals (the area of) the big one. • In algebraic terms, • a2+ b2 = c2 • where c is the hypotenuse while a and b are the legs of the triangle. Kathleen M. Sylla Summmer Institute 2007

  7. Let’s Investigate Quilt Kathleen M. Sylla Summmer Institute 2007

  8. A Second Look Kathleen M. Sylla Summmer Institute 2007

  9. What is the length of the hypotenuse? 45, 45, 90 Kathleen M. SyllaSummmer Institute 2007

  10. Square Root of 2 • The square root of 2 is the length of the hypotenuse (longest side) of a right triangle whose other two sides are each one unit long. • The square root of 2 has the approximate value 1.41421356 Kathleen M. Sylla Summmer Institute 2007

  11. More Quilts GeoGebra Kathleen M. Sylla Summmer Institute 2007

  12. 30, 60, 90 60 30 30 2 60 60 1 1 Kathleen M. Sylla Summmer Institute 2007

  13. More Quilts Kathleen M. Sylla Summmer Institute 2007

  14. Behold Quilt What is the ratio of the area of the white square to whole square? What is the side length of the white square? What are the length of the legs of the triangles? Behold Kathleen M. Sylla Summmer Institute 2007

  15. Making New Designs Kathleen M. Sylla Summmer Institute 2007

  16. Kathleen M. Sylla Summmer Institute 2007

  17. Behold a Bigger Quilt Kathleen M. Sylla Summmer Institute 2007

  18. Lets make a Quilt • Open to Geogebra Kathleen M. Sylla Summmer Institute 2007

  19. Sunshine State Standards • Number Sense, Concepts and Operations Benchmarks • MA.A.1.4.4 Students apply their understanding that numbers can be represented in a variety of equivalent forms. • MA.A.3.4.3 Students evaluate the hypotenuse and leg length of a triangle using the 45,45,90 degree Triangle Theorem. • Geometry and Spatial Sense Benchmark • MA.C.1.4.1 Students understand and prove the properties of 45, 45, 90 and 30, 60, 90 degree triangles. Kathleen M. Sylla Summmer Institute 2007

  20. Algebra- Prentice Hall • Introduce inSection 10-3 • Finding and Estimating Square Roots • 11-1 Simplifying Radicals • 11-2 The Pythagorean Theorem • 11-4 Operation with Radical Expressions • 11-5 Solving Radical Equations Kathleen M. Sylla Summmer Institute 2007

  21. Geometry Lesson • Geometry, Prentice Hall • Section 7-3 • Special Right Triangle Kathleen M. Sylla Summmer Institute 2007

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