Mathematics 8 -
Shape and Space (3-D Objects and 2-D Shapes)

This sub-organizer contains the following sections:
Prescribed Learning Outcomes
Suggested Extensions
Suggested Instructional Strategies
Suggested Assessment Strategies
Recommended Learning Resources

In order to prepare students to link angle measures and the properties of parallel lines to the classification and properties of quadrilaterals, it is expected that students will:

• identify, investigate, and classify quadrilaterals, regular polygons, and circles according to their properties

SUGGESTED EXTENSIONS

To extend students' understanding of 3-D objects and 2-D shapes, they could:

• build 3-D objects from a variety of representations (e.g., nets, skeletons)

SUGGESTED INSTRUCTIONAL STRATEGIES

Disciplines such as architecture, engineering, graphic design, cartography, drawing, and sculpting all incorporate geometric principles. An understanding of linear and spatial visualization is valuable for students to develop their artistic and aesthetic expression.

• Display examples of Escher art on the overhead (or as a handout). Have students discuss the representations of 3-D space on 2-D space and the transformations through tessellations. Ask students to research other patterns of the same type (e.g., in Greek, Moorish, or Islamic mosaics).
• Using large sheets of graph paper, have students draw and cut out a rhombus, square, kite, parallelogram, rectangle, trapezoid, and dart. By folding the shapes, students can discover and chart the properties of diagonals, sides, and angles.
• Have students create a chart or concept map organizing and displaying the various quadrilaterals classified by their properties.
• Ask students to create "find-the-polygon" puzzles (like "find-the-word" puzzles), in which they hide polygons within matrixes of lines and provide "lists" of the polygons for other students to find.
• Have students work with origami to discover various ways to manipulate 2-D shapes and to consider their applications. (e.g., What is the result when you fold a square diagonally?) Invite students to organize a contest for tessellation artwork for an upcoming school event or holiday.
• Ask students to research BC Aboriginal beading or weaving designs and represent them on grids. They could then design and apply their own patterns based on the designs researched (using actual textiles or computer simulations).
• Ask students to investigate the relationship between tessellations and quilting. (e.g., Marjorie Rice applied her knowledge of quilting to solve a difficult tessellation problem.)
• Have students construct 3-D models from nets and skeletons (e.g., using straws, balsa wood, toothpicks, construction paper, clay, marshmallows, or jujubes).
  

SUGGESTED ASSESSMENT STRATEGIES

An understanding of related terminology and the ability to recognize and classify geometric shapes help students use their understanding of shape and space to solve problems and describe the world around them.

Question

• Ask students to explain the reasons behind their classification of quadrilaterals, circles, and polygons.

Collect

• Have students design covers for their mathematics textbooks, portfolios, or displays on bulletin boards, incorporating all types of quadrilaterals, polygons, and circles. Do they use all possible types? Can they identify the types when asked? Does it follow a theme?
• Ask students to prepare notes for a friend who has been out of town and had to miss class. Students should describe the properties of different types of quadrilaterals, regular polygons, and circles. Diagrams can be used to clarify their descriptions. Use the following criteria to evaluate students' work. Check for:
  • clarity and logic of descriptions
  • accuracy of descriptions
  • appropriate classification of quadrilaterals, regular polygons, and circles
  • effective use of examples and diagrams
  Provide feedback to students to help them correct their mistakes.
• Provide students with a 6 x 6 square with 36 points. Have them connect the points in as many ways as possible to produce as many different quadrilaterals as they can. Have students classify their results by looking for patterns of similarity. Can they justify their classifications? As students work, circulate through the classroom and ask questions about lines of symmetry and classification.
• Ask students to draw nets (and cut them out) of various 3-D shapes and have them explain why certain nets will not work, even though they have the requisite faces.
  

RECOMMENDED LEARNING RESOURCES

Print Materials

• Interactions (Level 8)
• MATHPOWER 8, Western Edition
  

Multimedia

• The Geometer's Sketchpad
  
• The Learning Equation Mathematics 8 (TLE)
• Math Tools
• Mathematics 8 (Distance Education Package)
• Minds on Math 8, Revised Edition
• Understanding Math Series
  

CD-ROM

• Geometry Blaster
  
• Mathville VIP
  
• Mirror Symmetry
  

© Copyright 2001. All Rights Reserved. BC MOE Standards Department.
Maintained by: Mathematics Coordinator
Revised: September 1, 2001

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