1. Mathematical Quilts in a Radical Way
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Kathleen M. Sylla Summmer Institute 2007

2. 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

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

4. 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

5. 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

6. 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

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

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

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

10. 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
11/21/2018
Kathleen M. Sylla Summmer Institute 2007

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

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

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

14. 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?
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Behold
Kathleen M. Sylla Summmer Institute 2007

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

16. Kathleen M. Sylla Summmer Institute 2007
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Kathleen M. Sylla Summmer Institute 2007

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

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

19. Sunshine State Standards
Number Sense, Concepts and Operations Benchmarks
MA.A Students apply their understanding that numbers can be represented in a variety of equivalent forms.
MA.A 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 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

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

21. 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