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Mathematics Lesson Incorporating GeoGebra
Nevin Werner
William Paterson University
Dr. An
Grade: 5th
Topic(s):

Introduction to geometry
o Angles- obtuse, acute, and right
o Perpendicular Lines
o Parallel Lines

Classification and construction of 2D shapes
o Angle properties
o Side properties
o Parts of a shape- vertices and sides
Student Learning Outcomes (SWBAT):

Identify acute, obtuse, and right angles based upon an angles degree measurement

Construct perpendicular and parallel lines and identify them in quadrilaterals

Construct various quadrilaterals and make comparison and contrast statements to
understand a square is a rectangle, rhombus, parallelogram, and quadrilateral.
Standards:

Common Core State Standards
o 5.G.B.3- Understand that attributes belonging to a category of two-dimensional
figures also belong to all subcategories of that category. For example, all
rectangles have four right angles and squares are rectangles, so all squares have
four right angles.
o 5.G.B.4- Classify two-dimensional figures in a hierarchy based on properties.

ISTE Standards
o 1. Creativity and innovation

A. Apply existing knowledge to generate new ideas, products, or
processes.

C. Use models and simulations to explore complex systems and issues.

D. Identify trends and forecast possibilities
o 3. Research and information fluency

D. Process data and report results
o 4. Critical thinking, problem solving, and decision making

C. Collect and analyze data to identify solutions and/or make informed
decisions.
TPACK Framework:
Using GeoGebra, the students will be given the opportunity to investigate the properties
of lines, angles, and polygons. They will look for commonalities and differences to understand
the basics of geometry by using the software, rather than being explicitly taught the material.
GeoGebra will be the guiding factor of this lesson and not just an “add on”. The focus will be for
students to explore the properties of parallel and perpendicular lines and acute, obtuse, and right
angles. Then, using these angles and lines they created, students will create quadrilaterals and
compare and contrast them. To model how to use the program, the teacher will showcase how to
create lines, angles, and measure them using the algebra components of the program.
The rest of the lesson will allow students to independently or with a peer complete the
rest of the activities. GeoGebra was chosen for this lesson since it is a free Google application
and it enables students to interact with their constructions to manipulate the side and angle length
easily and efficiently.
Materials:

25 x Chromebooks
o GeoGebra added to all student Google accounts

1 x SMARTboard
Procedures:
Prior to using GeoGebra, students have been exposed to additional online learning
mathematics software and websites, such as ThinkCentral, Tenmarks, National Library of Virtual
Manipulatives, NCTM, and Khan Academy. These digital tools have allowed students to interact
more with their mathematics learning through modeling, construction, and manipulation. In my
classroom, I incorporate technology daily to support my learners with differentiation. These tools
enable me to create assignments relevant to their learning progression and evaluate their
understanding. Other than using mathematics digital tools, I also provide weekly sessions in
coding using Code.org and creating an online community on my class website and Google
Classroom. Students post blog entries and responses to classmate remarks on a weekly basis and
complete assignments, such as Webquests and online reflections.
To prepare students for this lesson, I would first allow a small period of time (10 minutes
or so) for the students to interact with the software freely. This time is important so they can get
accustom to the tools and features, and also experiment. Allowing experimentation time
encourages creativity, increases engagement, and opens a dialogue about the features. Students
tend to use this time to share with their classmates anything they find interesting, which provides
opportunities for peer learning and collaboration. After this short experimentation time, I would
then model how to use particular features required for the lesson, such as line creation, line
measurement, angle measurement, parallel and perpendicular lines, different views (grid and
coordinate grid), and enabling the algebra input table + view.
Once the students are used to these features, we would construct a pair of parallel lines.
Students would be asked to label the points then manipulate the lines to see how they move away
and towards each other. Students will then make the conjecture that parallel lines never intersect
and are always the same distance from each other (Appendix A). Then, students will repeat this
process for perpendicular lines (Appendix B), but measure the bisecting angle to notice it is 90o,
a right angle.
After the line properties have been established, students will then create their first shape,
a square. They will use the point and line segment tool to construct a square. Then, turn on the
grid and algebra view to measure the side lengths. After, students will also measure the interior
angles and draw parallel and perpendicular lines over the sides to see if they are parallel or
perpendicular. Using the checklist (Appendix C), they will check off the properties of the square.
Students will then manipulate the side lengths to create the other shapes on the checklist
and classify their properties for side length, angle length, and perpendicular or parallel sides. At
the end of the lesson, students will share their checklists with the class to make generalizations
about which shapes belong in the same family (e.g. a square is a quadrilateral, parallelogram,
rhombus, and rectangle).
Assessment:
Students will be assessed on their checklist and also on a digital exit ticket created using
socrative.com. This exit ticket includes multiple choice, open ended, and true or false questions
about the quadrilaterals the students created in the lesson. It is out of 3-points to monitor
progress and determine RTI groupings.
Exit Ticket Questions:
1. True or False: A rectangle is a parallelogram.
2. True or False: A square is a rhombus.
3. True of False: All parallelograms are squares.
4. True or False: All squares are rectangles.
5. Describe how a kite is not a parallelogram.
6. Look at the picture below. How would you classify this shape? Select all that apply.
a. Quadrilateral
b. Paralleogram
c. Rhombus
d. Square
e. Rectangle
f. Trapezoid
g. Kite
APPENDIX A
PARALLEL LINES
APPENDIX B
PERPENDICULAR LINES
APPENDIX C
QUADRILATERAL CHECKLIST
APPENDIX D
QUADRILATERALS