Mathematical Quilts in a Radical Way

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Mathematical Quilts in a Radical Way 11/21/2018 Kathleen M. Sylla Summmer Institute 2007

Kathleen M. Sylla Summmer Institute 2007 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. 11/21/2018 Kathleen M. Sylla Summmer Institute 2007

Kathleen M. Sylla Summmer Institute 2007 Friendship Star Quilt 11/21/2018 Kathleen M. Sylla Summmer Institute 2007

Kathleen M. Sylla Summmer Institute 2007 In a Radical Way Pythagoras of Samos lived from about 569 BC to about 475 BC 11/21/2018 Kathleen M. Sylla Summmer Institute 2007

Kathleen M. Sylla Summmer Institute 2007 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. 11/21/2018 Kathleen M. Sylla Summmer Institute 2007

Kathleen M. Sylla Summmer Institute 2007 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. 11/21/2018 Kathleen M. Sylla Summmer Institute 2007

Kathleen M. Sylla Summmer Institute 2007 Let’s Investigate Quilt 11/21/2018 Kathleen M. Sylla Summmer Institute 2007

Kathleen M. Sylla Summmer Institute 2007 A Second Look 11/21/2018 Kathleen M. Sylla Summmer Institute 2007

What is the length of the hypotenuse? 45, 45, 90 11/21/2018 Kathleen M. Sylla Summmer Institute 2007

Kathleen M. Sylla Summmer Institute 2007 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 11/21/2018 Kathleen M. Sylla Summmer Institute 2007

Kathleen M. Sylla Summmer Institute 2007 More Quilts GeoGebra 11/21/2018 Kathleen M. Sylla Summmer Institute 2007

Kathleen M. Sylla Summmer Institute 2007 30, 60, 90 60 30 30 2 60 60 1 1 11/21/2018 Kathleen M. Sylla Summmer Institute 2007

Kathleen M. Sylla Summmer Institute 2007 More Quilts 11/21/2018 Kathleen M. Sylla Summmer Institute 2007

Kathleen M. Sylla Summmer Institute 2007 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? 11/21/2018 Behold Kathleen M. Sylla Summmer Institute 2007

Kathleen M. Sylla Summmer Institute 2007 Making New Designs 11/21/2018 Kathleen M. Sylla Summmer Institute 2007

Kathleen M. Sylla Summmer Institute 2007 11/21/2018 Kathleen M. Sylla Summmer Institute 2007

Kathleen M. Sylla Summmer Institute 2007 Behold a Bigger Quilt 11/21/2018 Kathleen M. Sylla Summmer Institute 2007

Kathleen M. Sylla Summmer Institute 2007 Lets make a Quilt Open to Geogebra 11/21/2018 Kathleen M. Sylla Summmer Institute 2007

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. 11/21/2018 Kathleen M. Sylla Summmer Institute 2007

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 11/21/2018 Kathleen M. Sylla Summmer Institute 2007

Kathleen M. Sylla Summmer Institute 2007 Geometry Lesson Geometry, Prentice Hall Section 7-3 Special Right Triangle 11/21/2018 Kathleen M. Sylla Summmer Institute 2007