Mathematics 8 -
Shape and Space (Measurement)

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 apply indirect measurement procedures to solve problems
generalize measurement patterns and procedures and solve problems involving area and perimeter, it is expected that students will:

• use the Pythagorean relationship to calculate the measure of the third side of a right triangle, given the other two sides in 2-D applications
• describe patterns and generalize the relationships by determining the areas and perimeters of quadrilaterals and the areas and circumferences of circles
• estimate and calculate the area of composite figures

SUGGESTED EXTENSIONS

To extend students' understanding of measurement, they could:

• estimate, measure, and calculate the surface area and volume of any right prism or cylinder
• estimate, measure, and calculate the surface areas of composite 3-D objects
• estimate, measure, and calculate the volume of composite 3-D objects

SUGGESTED INSTRUCTIONAL STRATEGIES

The Pythagorean relationship is pervasive in mathematics and critical to the concept of indirect measurement. To facilitate students' understanding, use hands-on activities with physical objects. The ability to conceptualize and apply measurement formulae for 2-D shapes is best developed using hands-on activities.

• Demonstrate the Pythagorean relationship using concrete examples such as dissection puzzles, area constructions, and student-generated illustrations.
• Divide a piece of rope or string into 12 equal lengths by placing tape on 11 spots. Ask three students to hold the rope in a way that constructs a triangle with a right angle (each student represents a vertex; one student holds the two ends of the rope together). Students should discover that there is only one solution. Discuss:
  • Can any other right triangle be made?
  • Does 3, 4, 5 always result in a right triangle?
  • What are the applications?
  • What is the history of this method?
• Encourage student to research the Pythagorean relationship in a variety of contexts, such as:
  • the history of the relationship in various cultures
  • how trades people determine right angles in their trade
  • how Aboriginal people ensured that their longhouses were square
• Provide students with a variety of composite shapes and have them estimate the perimeter and area of each. Then have students check their guesses using suitable software such as dynamic geometry software, Computer Assisted Drafting (CAD), or Geographic Information Systems (GIS).
• Ask students to estimate the perimeters, areas, surface areas, and volumes of composite shapes and objects (e.g., concrete building blocks, Roman windows, desks) and then measure, calculate, and compare their estimates. Have students write in their journals to reflect on the differences between their estimates and the actual measurements. Were their estimates closer for one type of measurement than for another?
  

SUGGESTED ASSESSMENT STRATEGIES

By demonstrating an ability to apply the Pythagorean relationship, students show that they have the foundation for learning many of the procedures and relationships they will encounter in algebra and geometry. Assessment also focusses on students' abilities to develop ideas about measurement and apply them to practical situations.

Question

• Ask students to illustrate the Pythagorean relationship with concrete materials and diagrams. Are their illustrations accurate? Can they explain the relationship?

Collect

• Have students create simple blueprints of their dream homes, specifying the measurements of each room and calculating the areas and perimeters. Can students explain why it is important to know these measurements if they are going to build a house? Ask students to exchange their projects with other students and evaluate each other' s work using the following criteria:
  • Are the measurements realistic?
  • Based on the measurements students have supplied, are the calculations of area and perimeter accurate?

Collect and review students' blueprints and the corrections and comments made by their peers, and provide feedback.

Observe

• As students make estimates and measurements of the area, surface area, perimeter, and volume of composite shapes or objects, observe:
  • Do students select the most appropriate measurement scale?
  • Do students select the appropriate units for the answer?
  • Do their estimates approximate the measurements?
  • Do they identify the various shapes that make up the composite figures before they make their estimates?
  • Do they recognize that the non-included space must be subtracted?
  • Can they identify reasons why their estimates might be off?
    

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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