Applications of Mathematics 11 -
Shape and Space (Measurement)

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

PRESCRIBED LEARNING OUTCOMES

It is expected that students will:

• demonstrate an understanding of scale factors, and their interrelationship with the dimensions of similar shapes and objects.
• use measuring devices to make estimates and to perform calculations in solving problems.

It is expected that students will:

• enlarge or reduce a dimensioned object, according to a specified scale
• calculate maximum and minimum values, using tolerances, for lengths, areas and volumes
• solve problems involving percentage error when input variables are expressed with percentage errors
• design an appropriate measuring process or device to solve a problem

SUGGESTED INSTRUCTIONAL STRATEGIES

Understanding the concept of scale, including the implications of tolerances and errors involved, is important in many jobs and projects that require accuracy and precision in measurement. Knowledge of measurement processes transcends many fields.

• Demonstrate the concept of tolerance, using a high-quality machined mechanical component and a low-quality mechanical component.
• Discuss the effect of absolute error and percentage error when comparing the quality of machines.
• Have students compare the errors generated when a number of small values are added to those generated when fewer but larger amounts are added.
• To bring relevant labs and experiences into the classroom, consult with science teachers for current applications of error in measurements and with shop teachers regarding precision of tools.
• Have students investigate applications of scale, including:
  • enlargement techniques for artists
  • metal tooling machines making small parts from larger initial diagrams
  • blueprints produced with Computer Aided Design programs
  • links to trigonometry and similar triangles
• Have students analyse the difference in accuracy when measuring using:
  • an Erlenmeyer flask
  • a volumetric flask
  • a graduated cylinder Discuss effects the shape of each has on the measuring error.
• Provide students with opportunities to use various methods of showing scale (e.g., the linear scale, the ratio method, the statement method, the scale factor method). Encourage students to become efficient and confident at making conversions and determining scale factors and ratios.
• Have each student select a scale and use it to make a scale diagram of the classroom.
• Provide a number of small items such as thumbtacks, paper clips, or stickers, and have each student make an enlargement scale diagram of one item. As a class, discuss differences in how selected scales are stated.

SUGGESTED ASSESSMENT STRATEGIES

Assessment should centre on students’ ability to calculate errors as well as the development of an intuitive understanding of how much error is allowed and how much error will be introduced by various measurement procedures.

Observe

• Assign projects that involve 3-D scales and observe the extent to which students:
  • use appropriate ratios and scale
  • can use connecting blocks to build an object from an orthographic diagram

Question

• Have students critique different methods used in making scale diagrams and suggest changes in procedures.
• Analyse situations when percent accuracy is more favorable than absolute accuracy.
• Have students suggest methods of minimizing various types of errors in measurement.

Collect/Observe

• Have students make a list of various devices used for measuring a particular attribute (e.g., length) and rank them in terms of their precision.
• Have students sort a list of questions according to which would require absolute error and which would require percent error to solve
• Have students list various measuring devices used in other shop or science courses at your school. In small groups have students discuss the precision of each tool. Ask students to:
  • give examples of projects which might require two or more measuring tools
  • explain how the precision of their measurements are affected when two or more tools are used

Peer/Assessment

• Have students perform a simple physics lab (such as rolling a marble down a ramp) and do the calculations to find the marble’s average velocity. Have students calculate all experimental error and share their findings with peers. Groups can switch calculations and check each other’s work

RECOMMENDED LEARNING RESOURCES

Print Materials

• Applied Mathematics 11, Western Canadian Edition

Software

• The Geometer's Sketchpad

CD-ROM

• Geometry Blaster

© 2000 Copyright. All Rights Reserved. Curriculum Branch.
Maintained by: Mathematics Coordinator
Revised: November 30, 2000

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