making sense of geometry in grades 3–5 classrooms
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Making Sense of Geometry in Grades 3–5 Classrooms. Marcia Torgrude K-12 Math Specialist Technology and Innovation in Education [email protected] http://mtorgrude.tie.wikispaces.net. Penny Smith SD Math Curriculum Director SD Department of Education [email protected]. - PowerPoint PPT PresentationTRANSCRIPT
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Making Sense of Geometry in Grades 3–5 Classrooms
Marcia TorgrudeK-12 Math Specialist
Technology and Innovation in [email protected]
http://mtorgrude.tie.wikispaces.net
Penny SmithSD Math Curriculum DirectorSD Department of Education
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Prior Knowledge
•When did you learn about geometry ?•What did you learn?•Do you remember working with shapes? •How and when do you teach geometry now?
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van Hiele Levels of Geometric Thought
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K-12 Geometry StandardsFour Common Goals
• Shapes and properties –study of the properties of shapes in both two and three dimensions, as well as a study of the relationships built on properties.
• Transformation - study of translations, reflections, and rotations (slides, flips, and turns) and the study of symmetry.
• Location –coordinate geometry or other ways of specifying how objects are located in the plane or in space.
• Visualization –recognition of shapes in the environment, developing relationships between two and three dimensional objects, and the ability to draw and recognize objects from different perspectives.
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Shapes Game• Partners – determine who goes first• Place a pattern block in the shape• Continue taking turns placing the pattern blocks• The last one to fill the shape with a pattern
block is the winner• What did you learn?• What strategy might you use the next time?
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Online Shapes Activities
• Patch Tool - http://illuminations.nctm.org/ActivityDetail.aspx?ID=27
• Shape Tool - http://illuminations.nctm.org/ActivityDetail.aspx?ID=35
• Geometric Solids - http://illuminations.nctm.org/ActivityDetail.aspx?ID=70
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Shapes Game Purpose
• Increases spacial sense – moving from visualization to analysis (van Hiele levels)
• Transformation - translations, reflections, and rotations
• Visualization – the ability to draw and recognize objects from different perspectives
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Grandfather Tang’s Story
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Grandfather Tang’s Purpose
• Increases spacial sense – moving from visualization to analysis (van Hiele levels)
• Transformation - translations, reflections, and rotations
• Visualization – the ability to draw and recognize objects from different perspectives
• Connects Literature to Geometry
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Trianquad Activity
• Work in pairs• Go through the cards one at a time, look at
the diagrams, and try to determine the attributes of a trianquad, refining your definition as you work.
• Note: a Trianquad is a fictional shape.
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Trianquad Purpose• Geometry is a definition-heavy content area.• Teachers often think they must provide definitions, or
have students look up definitions, prior to doing activities.
• Definitions can be developed through various hands-on activities –developing versus telling
• Move students’ thoughts from analysis to informal deduction of van Hiele’s levels of geometric thought.
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Trianquad Big Ideas• Definitions do NOT have to come first• Definitions can be derived from activities• The teacher labels the students’ thinking with
the correct word (definition): For example, when students are discussing “corners” of polygons in the context of an activity, the teacher might say, “Mathematicians call that a vertex.”
• Definitions need to be precise (cover all possibilities)
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Geoboard ActivityGrowing and Shrinking
• Make this shape on your geoboard. • Keep the perimeter the same and
make the area smaller.• Keep the perimeter the same and
make the area larger.• Keep the area the same and make
the perimeter smaller.• Keep the area the same and make
the perimeter larger.• Online Geoboard
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Geoboard Activity Purpose• Area and perimeter are continually a sense of confusion for students• Finding a relationship between area and perimeter and deepen their
understanding of each• Measurement and Geometry strands support one another to build
understanding• Shape and Properties - Best device for drawing 2-dimensional shapes• Location – ways of specifying how objects are located in the plane or in space.• Visualization –recognition of shapes in the environment, developing
relationships between two and three dimensional objects, and the ability to draw and recognize objects from different perspectives.
• Junior Architects - http://illuminations.nctm.org/LessonDetail.aspx?ID=U172
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Revisit Common Goals
• Shapes and properties – Trianquad– Shapes Game– Grandfather Tang’s Story– Geoboard – Area and Perimeter
• Transformation – Shapes Game– Grandfather Tang’s Story
• Location - Geoboard- Area and Perimeter• Visualization- All of the activities
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van Hiele Levels of Geometric Thought
Trianquad
Geoboard
Grandfather Tang
Shapes Game
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Make Sense of Geometry in K-5
Give your students the experiences they need to
succeed at the high school and college levels
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Bibliography• Grandfather Tang’s Story, a Tale Told with Tangrams, Ann Tompert,
Crown Publishers Inc. New York, 1990• Developing Number Concepts Books 1, 2, 3, and Planning Guide, Kathy
Richardson1999• Developing Mathematics with Pattern Blocks, Dr. Paul Swan and Geoff
White, Didax, 2006• Teaching Student-Centered Mathematics, John A. Van de Walle, 2006
and 2010• http://www.deltasee.org/CTC/Activity%2026%20Tangrams.pdf• http://www.users.muohio.edu/harpersr/conferences/Harper&Driskell_N
CTM_2005.pdf