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Nspired Flower Power
Travis Bower
Dos Pueblos High School
Santa Barbara Unified School District
tbower@dphs.org
Subject Area:
Math, Arts
Grade Level/s:
Grades 8-12
Project Description:
Students find the area of the shaded region by three main methods:
1) Estimation (by hand and by tech)
2) Inner Square (by hand and by tech)
3) Equilateral Triangle (by hand and by tech)
4) As an extension, Integral Calculus (by hand and by tech)
How it works:
Students are presented with the problem of finding the area of a geometric object with scant explanation or hints. It is printed multiple times on a half sheet. They are expected to grapple with it over a period of time. Since finding a solution is not immediately obvious, a series of scaffolded hints are provided for three different solution routes. These are given in class and also online. EDU2.0 offers a means to hide/show the graduated hints. Students are encouraged to keep all of their attempts as a record of their pursuit. One hint might be to shade as many different combinations as possible. These can then be displayed under a document camera to promote some classroom hybridization. Even though this project is largely individual, there is some collaboration. They are to seek the solution by traditional methods and using dynamic geometry software.
Project Materials:
HYPERLINK "https://sites.google.com/a/sbsdk12.org/tbower/nspired-flower-power" https://sites.google.com/a/sbsdk12.org/tbower/nspired-flower-power
Assessment:
Students turn in work done by hand on paper. They can also scan it and submit via EDU2.0. They are to retain all of their rough drafts. Students submit the tech screenshots via EDU2.0. The rubric is on EDU and students see their score for each category. Periodically I circulate and glance at their progress. I also provide encouragement. There is a multiple choice assessment.
Standards:
Common Core Standards 8/2010
Make sense of problems and persevere in solving them.
Use dynamic geometry software to enrich problems.
California 12/1997
Students solve problems involving the perimeter, circumference, and area of common geometric figures.
Students perform basic constructions with a straightedge and compass.
Students use angle and side relationships in problems with special right triangles, such as 30, 60, and 90 triangles and 45, 45, and 90 triangles.
Estimated Number of Class Periods for Students To Complete Unit:
Four class periods
Software or Materials Used:
The TI Nspire handheld and computer software work very well for this project. Geometer s Sketchpad ($$) and GeoGebra (free) could also be used. Students will also use a compass and graph paper. The convenience of Nspire is compelling. Students can use the handheld in class and follow along. They can use their computer at home, which affords a bigger screen and mouse. They can post screenshots on a class webpage. I use http://edu20.org/ as my LMS (learning management system). Some students may opt to send a digital copy of their paper work via camera or scanner.
Keywords:
Nspire, geometer s sketchpad, geogebra, area project, geometry project, dynamic geometry software, estimation, exact, sector, law of cosines, triangle, area, persevere, edu, approximation.
The Students:
This project is primarily for Geometry Honors students. It can also be scaffolded (give hints along the way) for a wider audience. Students will need access to the Internet via a computer. Prerequisites include facility with the Nspire graphing calculator.
Overall Value:
Nspired Flower Power is a great cumulative project. It incorporates the gamut of ancient technology (compass) to modern dynamic geometry in a handheld device. The problem is tantalizing and presents a significant challenge with several methods of solving it. Furthermore, it can be individualized to promote collaboration by varying the lengths of the square s sides. A spreadsheet (on computer or Nspire) quickly generates the correct approximations.
Tips for the Teacher:
Using edu2.0 I post all the directions screenshots, screencasts, rubrics and hints. This is particularly helpful for absent students or those who need to see the process again. Try to google the solution; I have eschewed posting solutions.
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