Making Sense of Geometry in Grades 3–5 Classrooms

Making Sense of Geometry in Grades 3–5 Classrooms Marcia Torgrude K-12 Math Specialist Technology and Innovation in Education mtorgrude@tie.net http://mtorgrude.tie.wikispaces.net Penny Smith SD Math Curriculum Director SD Department of Education Penny.smith@state.sd.us

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?

van Hiele Levels of Geometric Thought

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.

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?

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

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

Grandfather Tang’s Story

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

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.

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.

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)

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

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

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

van Hiele Levels of Geometric Thought Geoboard Trianquad Grandfather Tang Shapes Game

Make Sense of Geometry in K-5 Give your students the experiences they need to succeed at the high school and college levels http://mtorgrude.tie.wikispaces.net

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_NCTM_2005.pdf

Making Sense of Geometry in Grades 3–5 Classrooms