Learning Links
Sonar / Quilting / Cartography / Interior Design / Archaeology / Architecture / Computer Graphics / Graphic Design / Perspective / Auto-CAD / Clothing Design / Radar / Air Traffic Control / Fractals / Solar Systems / Dance / Topographic Maps / Molecular Models
Related Concepts
Regular and Irregular Figures in Various Dimensions / Coordinate Systems / Geometry / Congruence / Symmetry / Spatial Visualization / Spatial Representation / Similarity / Orientator / Vectors / Fractals
Demonstrators should be read from top to bottom, but need not be demonstrated sequentially.
Elementary Demonstrators
• Demonstrate the spatial relationship of two objects (e.g., inside/outside, between).
• Describe, model, draw, sort, classify, and compare shapes.
• Explore, identify, and classify similar plane and solid figures in various orientations.
• Extend and create geometric patterns using concrete and pictorial models and recognize their use in the real world.
• Investigate and predict the results of combining, subdividing, and changing shapes.
• Translate 3-dimensional objects to 2- dimensional drawings and vice versa.
• Explore symmetry, translations (slides), reflections (flips), and rotations (turns).
• Describe relationships among points, lines, segments, and angles.
Middle School Demonstrators
• Use attributes to classify and analyze regular and irregular figures in 2 and 3 dimensions.
• Use a coordinate system to define and locate position.
• Investigate symmetry, similarity, and congruence using concrete models and drawing.
• Explore, describe, and draw transformations.
• Visualize different representations of 2 and 3-dimensional geometric figures.
High School Demonstrators
• Interpret and draw 3-dimensional figures.
• Apply congruence and similarity relationships in real-world situations.
• Represent and solve problem situations with geometric models and properties.
• Apply transformations and vectors to solve problems and represent physical phenomena.
• Compare, contrast, and translate among synthetic, coordinate, and transformational geometry.
• Explore and investigate the dimensionality of fractal objects.
• Verify conjectures about geometric objects using deduction (van Hiele Level 3).
Sample Teaching/Assessment Strategies
Collaborative Process: Cooperative Learning / Community-Based Instruction: Field Studies / Graphic Organizers: Graphic Representations / Problem Solving: Inquiry, Creative Problem Solving, Future Problem Solving, Formulating Models / Technology/Tools: Computers, Manipulatives, Multimedia, Video Production
These sample strategies offer ideas and are not meant to limit teacher resourcefulness. More strategies are found in the resource section.
Ideas for Incorporating Community Resources
• Visit the geological survey department in your community and observe how maps are made.
• Do a community field study led by a local architect/construction worker/carpenter. Identify geometric properties and shapes used in the construction of buildings.
• Invite a local quilt maker to discuss repetition of patterns. Create class designs.
Core Concept - Space and Dimensionality
Sample Elementary Activities
• Build 3-dimensional shapes using toothpicks and gum drops. Discuss the relationship between the line segments and angles. PE, P
• Fold paper cutouts of various shapes (e.g. geometric shapes, leaves, snowflakes) to discover lines of symmetry. PE
• Construct a building with cubes. Then draw the building from all views (front, top, back, right side, and left side) on graph paper. PE, P
• Create a large square using a geoboard. Subdivide the square into as many squares as possible and record the number of squares. PE
• Construct a regular or irregular polygon on a geoboard and let another student construct the congruent shape in a slide (translation), turn (rotation), or flip (reflection) on his/her geoboard. Extend to movements made by characters on Nintendo games (Super Mario Brothers, Tetris). PE, P
• Create a repeating pattern with pattern blocks to cover an area such as quilt square, wrapping paper, or wallpaper. PE
• Make as many shapes as possible with 2 tangram pieces, 3 pieces, 4 pieces, and up to 7 pieces. PE
• Explore the properties of a planar shape using measuring instruments and list as many as you can. PE, OE
Applications Across the Curriculum
Language Arts
· Describe the rotation of an object. OE, P
· Tell a story about what life might be like if there were only two dimensions. OE, P
Science
· Construct a scale model of an organism. PE
· Build or draw a model of the entire shell of an animal after observing a shell fragment. OE
Social Studies
· Find examples of familiar geometric shapes in the built/physical environment. Create a histogram showing the frequency in which shapes occur. PE, OE
Arts and Humanities
· Use triangle pieces to construct a design with a repeating pattern. Use markers to find new triangles created by overlapping. PE, OE
Practical Living
· Construct environmental mobiles using geometric shapes to depict recyclable items, conservation practices, and pollution control. PE
Vocational Education
· Rearrange furniture in a playhouse to be used by different numbers of children. PE
· Create a floor design with parquet blocks. PE
Sample Middle School Activities
• Construct models of the five platonic solids and investigate relationships among the numbers of edges, faces, and vertices. PE, P
• Draw 2-dimensional top, front, and side views to represent a 3-dimensional object. Reverse the process to draw a 3-dimensional representation based on top, side, and front views. Use isometric dot paper. PE, P
• Draw or build a 2 or 3-dimensional model using oral or written instructions provided by another student. OE
• Work in cooperative groups with school cameras to take a series of photographs as the photographer rotates 360 degrees. Shuffle photos. Have other groups reassemble photos in order and locate position of photographer. PE, P
• Draw a portion of a map on graph paper, locate two points, X and Y, and write a set of directions from Point X to Point Y. PE, P
• Build a simple kaleidoscope to show rotations and reflections. PE, P
• Draw a checkerboard from both 1- and 2-point perspective. PE, P
• Design a tile floor or quilt using simple tessellations. PE, P
• Show that lines are parallel by synthetic geometry (congruent alternate interior angles) and coordinate geometry (equal slopes). Write a comparison of the two methods. OE, P
Applications Across the Curriculum
Language Arts
· Keep a "geometry journal." Cut out interesting shapes and designs and list places they might be found in the real world. P
Science
· Compare and contrast geometric shapes of crystal forms grown in the classroom such as salt, alum, and sugar. PE, P
Social Studies
· Construct a model of an invention which would make a positive contribution to the American economy. PE, OE, P
· Develop a variety of maps depicting the school grounds (e.g., political, 3-dimensional relief map). PE, P
Arts and Humanities
· Draw your school building using 2-point perspective. PE, P
Practical Living
· Design a student activity area to best utilize existing areas. OE, P
· Enlarge a diagram of the body system using a grid method (physical wellness). OE
Vocational Education
· Draw a topographic map of a sloping area. PE, P
· Use a computer graphics program to design a brochure or invitation. PE, P
Sample High School Activities
• Estimate the height of the school flagpole using similar triangles, the height of a student, and relative lengths of shadows. PE
• Use vector analysis to determine the effect of wind shear on an airplane's actual track over ground. OE, P
• Design a computer program to draw a fractal. Use design on a T-shirt. PE, P
• Construct an Escher-type tessellation. PE
• Build a prism using cubes and find the surface area. Rearrange the same set of cubes into another shape and find the surface area. Discuss reasons why one shape could be more economical to build than another. PE
• Draw a coordinate system on a parking lot or football field; assign all students a different x value; students stand along the x-axis, and teacher calls out an equation in y-intercept form; students walk to y value to represent the graph. PE
Applications Across the Curriculum
Variations on a theme: Sculpture
Language Arts
· Describe a famous piece of statuary in terms of space and dimensionality. PE, OE, P
Science
· Design a packaging system to transport a particularly fragile sculpture. PE, P
Social Studies
· Trace the historical development of representations of the human form in sculpture with regard to size and proportion. P
Arts and Humanities
· Create a sculpture from a 2-dimensional subject. PE, P
Practical Living
· Design a display for a variety of sculptures. PE, P
Vocational Education
· Design a sculpture garden. PE