Transcript Ms. Lisa Herron

The Triangle World
Using GeoGebra
National Council of Teachers of Mathematics
St. Louis, MO – The America’s Center
October 28, 2011
Ms. Lisa Herron
Cypress Bay High
School
Weston, Florida
Dr. Joseph M. Furner
Florida Atlantic
University
Jupiter, Florida
Copyright 2011 Carol A. Marinas, Joseph M. Furner, Ana Escuder, Lisa Herron
Mrs. Ana Escuder
Florida Atlantic
University
Boca Raton, Florida
Concrete Representational Abstract
The CRA Model
1. Start with the Concrete
using hands-on
manipulatives
2. Move to Representational
models in diagrams
3. Lastly, connect to the
Abstract symbolism where
student understand and
function at an abstract level
completely
Copyright 2011 Carol A. Marinas, Joseph M. Furner, Ana Escuder, Lisa Herron
Geoboard
The Concrete
A Geoboard is a board covered in a grid
of pegs that is used to construct
geometric shapes and explore their
relationships.
Copyright 2011 Carol A. Marinas, Joseph M. Furner, Ana Escuder, Lisa Herron
Virtual Web Sites
The Representational
• National Library of Virtual Manipulatives
• National Council of Teachers of Mathematics
• Cut the Knot
• Other Resources
Copyright 2011 Carol A. Marinas, Joseph M. Furner, Ana Escuder,
Lisa Herron
GeoGebra
Helping with the Abstract
GeoGebra is free and multi-platform dynamic
mathematics software for all levels of education
that joins geometry, algebra, tables, graphing,
statistics and calculus in one easy-to-use package.
http://www.geogebra.org/cms/en/info
Copyright 2011 Carol A. Marinas, Joseph M. Furner, Ana Escuder, Lisa Herron
Having Fun with GeoGebra
Old Post Office District
Union Station
Copyright 2011 Carol A. Marinas, Joseph M. Furner, Ana Escuder, Lisa Herron
Triangle
Definition: A three-sided polygon
Link to GeoGebra: Triangle
Copyright 2011 Carol A. Marinas, Joseph M. Furner, Ana Escuder, Lisa Herron
Right Triangle –
Triangle with a right angle
Link to GeoGebra: Right Triangle
Copyright 2011 Carol A. Marinas, Joseph M. Furner, Ana Escuder, Lisa Herron
Equiangular Triangle –
Triangle with equal angles
Link to GeoGebra: Equiangular Triangle
Copyright 2011 Carol A. Marinas, Joseph M. Furner, Ana Escuder, Lisa Herron
Equilateral Triangle –
Triangle with equal sides
Link to GeoGebra: Equilateral Triangle
Copyright 2011 Carol A. Marinas, Joseph M. Furner, Ana Escuder, Lisa Herron
Isosceles Triangle –
Triangle with 2 sides equal
Link to GeoGebra: Isosceles Triangle
Copyright 2011 Carol A. Marinas, Joseph M. Furner, Ana Escuder, Lisa Herron
Standards on Triangles
Common Core Math Standards 6-8
http://www.corestandards.org/
Grades 6
6.G.1. Find the area of right triangles, other triangles, special quadrilaterals,
and polygons by composing into rectangles or decomposing into
triangles and other shapes; apply these techniques in the context of
solving real-world and mathematical problems.
6.G.3. Draw polygons in the coordinate plane given coordinates for the
vertices; use coordinates to find the length of a side joining points with
the same first coordinate or the same second coordinate. Apply these
techniques in the context of solving real-world and mathematical
problems.
Copyright 2011 Carol A. Marinas, Joseph M. Furner, Ana Escuder, Lisa Herron
Standards on Triangles
Common Core Math Standards 6-8
http://www.corestandards.org/
Grades 7
7.G.2. Draw (freehand, with ruler and protractor, and with technology)
geometric shapes with given conditions. Focus on constructing
triangles from three measures of angles or sides, noticing when the
conditions determine a unique triangle, more than one triangle, or no
triangle.
7.G.6. Solve real-world and mathematical problems involving area, volume
and surface area of two- and three-dimensional objects composed of
triangles, quadrilaterals, polygons, cubes, and right prisms.
Copyright 2011 Carol A. Marinas, Joseph M. Furner, Ana Escuder, Lisa Herron
Standards on Triangles
Common Core Math Standards 6-8 at:
http://www.corestandards.org/
Grades 8
8.G.5. Use informal arguments to establish facts about the angle sum and
exterior angle of triangles, about the angles created when parallel lines
are cut by a transversal, and the angle-angle criterion for similarity of
triangles. For example, arrange three copies of the same triangle so
that the sum of the three angles appears to form a line, and give an
argument in terms of transversals why this is so.
8.G.6. Explain a proof of the Pythagorean Theorem and its converse.
8.G.7. Apply the Pythagorean Theorem to determine unknown side lengths in
right triangles in real-world and mathematical problems in two and
three dimensions.
Copyright 2011 Carol A. Marinas, Joseph M. Furner, Ana Escuder, Lisa Herron
So why should we use GeoGebra?
A Summary
•
•
•
•
Free download. Go to geogebra.org
Up and coming dynamic teaching tool in schools.
User-friendly for students and teachers.
Great connect from the hands-on Geoboards to
virtual Geoboards to something a more abstract.
• Provides many resources and teaching tools at its
wiki for educators at: http://wiki.geogebra.org/en
• Can even be used for primary-aged students.
Copyright 2011 Carol A. Marinas, Joseph M. Furner, Ana Escuder, Lisa Herron
Thanks for coming
to our Presentation!
PowerPoint and Data Files: http://matharoundus.com/geogebra
Contact Information:
Ms. Lisa Herron
(Cypress Bay High School) [email protected]
Dr. Joseph M. Furner (Florida Atlantic University) [email protected]
Mrs. Ana Escuder (Florida Atlantic University) [email protected]
Copyright 2011 Carol A. Marinas, Joseph M. Furner, Ana Escuder, Lisa Herron