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Dynamic Project-Based Math: Investigations with GeoGebra

Transform your instruction of middle school mathematics using field-tested problems and investigations for engaging students in the study of geometry and algebra, using the free and open-source software, GeoGebra.

Andrew Hammons

on 10 October 2014

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Transcript of Dynamic Project-Based Math: Investigations with GeoGebra

All devices, start here:

Joshua Circle Elementary, Hesperia Unified School District
South Conference, Palm Springs [Session 838]
Transform your instruction of middle school mathematics using field-tested problems and investigations for engaging students in the study of geometry and algebra, using the free and open-source software, GeoGebra.
GeoGebra Institute of California
Dr. Agnes Tuska
Mr. Andrew Hammons
Professor, Credential Advisor
GeoGebra Institute of California
California State University, Fresno - Department of Mathematics
California Mathematics Council
Dr. Agnes Tuska
Mr. Andrew Hammons
Who's in the audience?
Why Use GeoGebra?
GeoGebra on Tablets...
As we begin, you may want to install GeoGebra on your notebook or tablet computer!
Twitter Stream
We'll monitor your questions, feedback, and any answers you provide during our survey questions!
Introduction to GeoGebra!
GeoGebra Resources
Principles to Actions:
An Urgent Agenda for School
Public Comment Draft
September 25, 2013

GeoGebra (www.geogebra.org) is free dynamic mathematics software for all levels of education that brings together geometry, algebra, spreadsheets, graphing, statistics and calculus in one easy-to-use package.

Interactive learning, teaching and evaluation resources created with GeoGebra can be shared and used by everyone at www.geogebratube.org.

GeoGebra is the world’s favorite dynamic mathematics software, has received numerous educational software awards, and supports STEM education and innovations in teaching and learning worldwide.

Join us. Dynamic Mathematics for Everyone.

• Free to use software for learning, teaching and evaluation
• Fully interactive, easy-to-use interface with many powerful features
• Access to an ever-expanding pool of resources at www.geogebratube.org
• Available in many languages
• A fun way to really see and experience mathematics and science
• Adaptable to any curriculum or project
• Used by millions of people around the world
The GeoGebra software is free and open source; we are free to use it, give it away to others, and customize it to fit our unique needs!
"So first,
five symptoms that you're doing math reasoning wrong in your classroom
. One is
a lack of initiative
your students don't self-start. You finish your lecture block and immediately you have five hands going up asking you to re-explain the entire thing at their desks.
Students lack perseverance
. They
lack retention
; you find yourself re-explaining concepts three months later, wholesale. There's
an aversion to word problems
, which describes 99 percent of my students. And then
the other one percent is eagerly looking for the formula to apply
in that situation. This is really destructive."

--Dan Meyer

Introduction to GeoGebra
Common Core GeoGebra on Tablets!
Who's in the audience?
Who has only heard of GeoGebra before?
Who teaches 5th or 6th grade?
How many teach 7th or 8th grade?
How many teach 9th grade?
Please take the time to complete your survey form thoroughly.
Also, feel free to share feedback, questions, and GGb requests on Twitter! ( #GeoGebraCMC )
Thank you!
Who has used GeoGebra before? To what extent?
Dr. Agnes Tuska
Mr. Andrew Hammons
Markus Hohenwarter talking about GeoGebra

“… we want to make mathematics easy to
understand …”

“… we want to show them [students] how much we
think that math is useful and something interesting, exciting; something that you
can grab; something natural and surrounding us everywhere …”

“ … [GeoGebra] is very visual; they [students] can play with mathematics; they can
grab things; they can drag a point around; they can just experiment with
mathematics and in that way hopefully get a better understanding of what it’s all
The mission of the GeoGebra project is to empower students and teachers at all levels to learn and teach mathematics with our easy-to-use and freely available software and interactive materials.
Tally the results!
“GeoGebra was created by Markus Hohenwarter in 2001/2002 as part of his master's thesis in mathematics education and computer science
at the University of Salzburg in Austria. … GeoGebra won several international awards, including the European and German educational software awards, and was translated by math instructors and teachers
all over the world to more than 25 languages.” – from the Journal of Online Mathematics and Its Applications, Volume 7 (2007).

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.
CCSS.Math.Content.6.G.A.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.
CCSS.Math.Content.7.G.A.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.
CCSS.Math.Content.7.G.B.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
CCSS.Math.Content.7.G.B.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.
CCSS.Math.Content.8.EE.B.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
3 Acts Defined - Dan Meyer
Act One

Introduce the central conflict of your story/task clearly, visually, viscerally, using as few words as possible.
Act Two

The protagonist/student overcomes obstacles, looks for resources, and develops new tools.
Act Three

Resolve the conflict and set up a sequel/extension.
Fun things were going to try.
All of your notes, diagrams, questions, creations, etc., left on your table at the end of our session will be photographed and compiled to be shared via our website.
We're going to attempt to adequately monitor a Twitter stream for #GeoGebraCMC to monitor your feedback, input, and questions.
We're going to allow time for the exchange of ideas between session members to build ownership in the take-away of CCSS investigations and guided learning opportunities.
Why Use GeoGebra?
Full transcript