Mathematics 8 -
Shape and Space (Transformations)

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 analyse design problems and architectural drawings using the properties of scaling and proportion, it is expected that students will:

• represent, analyse, and describe enlargements and reductions
• draw and interpret scale diagrams

SUGGESTED EXTENSIONS

To extend students' understanding of transformations, they could:

• represent, analyse, and describe colouring problems
• describe, analyse, and solve network problems (e.g., bus routes, a telephone exchange)

SUGGESTED INSTRUCTIONAL STRATEGIES

Knowledge of transformational geometry is essential for students to understand much of what they see in graphic representations.

• Using dynamic geometry software, demonstrate the rate of change as scaling is applied to 2-D and 3-D objects.
• Have students compare the difference in areas of small, medium, and large pizzas. Ask them to construct a graph to represent the relationships between the diameter and the area for each size. What generalizations can they make for these relationships?
• Divide the class into groups. Have each group investigate a real-world application of enlargement and reduction (e.g., how a knitting or sewing pattern is adjusted for size, map scales) and report to the class.
• Provide students copies of maps of BC that identify Aboriginal language groups. Have students colour the regions so that they use the minimum number of colours and adjoining regions do not use the same colour.
• Suggest that students find examples of bus and airplane routes, truck routes, and telephone routes. Have them work in pairs to create and answer questions related to the networks or to design their own networks showing the most efficient paper route in their neighbourhood.
  

SUGGESTED ASSESSMENT STRATEGIES

Assessment is based on students' ability to demonstrate their understanding of the ideas and procedures they have learned by drawing, building, and discussing.

Question

• Determine if students can identify places outside school where enlargements, reductions, and scale diagrams (and networks) are used.

Collect

• Give students a scale drawing of a 2-D or 3-D object. Ask them to produce a second scaled drawing by doubling the dimensions of the first and then construct a model of the object that is four times its original dimensions. Ask students to describe the effect that the enlargements have had on surface area and volume. Use the same activity to have students demonstrate their understanding of reductions.
  • Are students' enlargements and reductions made to scale and accurate?
  • Can students describe the methods they use to enlarge or reduce the original drawings?
  • Can students move between 2-D and 3-D representations?
• Determine if students can predict the most efficient method of getting from point A to point B in their school. Give students a map of the school and a list of Grade 8 teachers, specifying their room locations. Ask students to predict the most and least efficient timetables possible for moving from room to room in terms of the distance travelled in the school.
• Ask students to bring material about networks and use it to design questions for other students to solve. Evaluate the complexity of the questions and the accuracy of students' solutions to their own and other' s questions.
  

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
  
BC MOE

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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