Measurement Unit Outline

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					                           Applications of Mathematics 11
                             Measurement Unit Outline
                                      Chapter 7

General Specific Learning Outcomes:
    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.

Specific Prescribed Learning Outcomes:
    Enlarge or reduce a dimensioned object, according to a specified scale
Notes:
    This specific outcome builds on outcomes in Applications of Mathematics 10.
    Proportion and ratio competency is a requirement.
    Students should be comfortable with measuring tools.
    Students have to be able to read and interpret scales.
    3-D manipulatives will be very helpful in this section.
    Proportion and ratio competency is a requirement.
    Conversion skills within a system of measurement are required.
    The processes of estimation and visualization are emphasized in this outcome.
    Vocabulary distinctions are less important than the concepts themselves; e.g., the
       distinction between scale and scale factor.
    Isometric dot or line paper would assist students in drawing 3-D objects.
Acceptable Standard:
    read and interpret scale drawings
    enlarge or reduce 1-D or 2-D drawings
    enlarge or reduce simple shapes in 3-D, using orthographic drawings.
Standard of Excellence:
    enlarge or reduce complex/hidden shapes in 3-D, using orthographic drawings.

      Calculate maximum and minimum values, using tolerances, for lengths,
       areas and volumes.
Notes:
    This specific outcome builds on outcomes in Applications of Mathematics 10.
    Students have been introduced to the concept of the precision of a measuring
       instrument in Applications of Mathematics 10.
    Plus and minus tolerances only apply to measured quantities; e.g., length, mass,
       capacity.
Acceptable Standard:
    calculate maximum and minimum values, using measured tolerances in
       routine/familiar problems
    calculate the sum or difference of two measurements, including measurement
       errors.
Standard of Excellence:
    calculate maximum and minimum values, using measured tolerances in non-
      routine/unfamiliar problems
    calculate the sum or difference of more than two measurements, including
      measurement errors.

      Solve problems involving percentage error when input variables are
       expressed with percentage errors.
Notes:
    This specific outcome builds on outcomes in Applications of Mathematics 10.
    Students can relate their understanding of measurement error, from the previous
       specific outcome, to percentage error.
Acceptable Standard:
    convert between tolerances and percentage error
    solve simple problems involving tolerance and percentage error.
Standard of Excellence:
    solve complex/multi-step problems involving tolerance and percentage error.

    Design an appropriate measuring process or device to solve a problem.
Notes:
    This specific outcome lends itself to project work.
    This specific outcome should be linked to the other specific outcomes in this
       topic.
    The focus should be on different measuring strategies, rather than on the design of
       a device.
    Design of measuring devices is more aligned with the standard of excellence.
Acceptable Standard:
    select an appropriate process to solve a measurement problem
    analyze the scale of a measuring instrument
    design a measuring instrument, with guidance.
Standard of Excellence:
    design an appropriate process to solve a measurement problem
    design and analyze the scale of a measuring device
    design a measuring instrument independently.
                                    Lesson Sequence

Day 1 – Tutorial 7.1 – Enlarging and Reducing in Two Dimensions
    Define scale drawing and scale factor.
    Define scale and they ways to represent scale: statement, rate, ratio, and linear
       scale.
    Go through Investigation 1 on page 360
    Go through Example on page 361
    Go through Discussing the Ideas #5 – 6
    Assignment: Page 363 #1 – 5

Day 2 – Tutorial 7.2 – Diagrams of Three-Dimensional Objects
    Need cube blocks and grid dot paper for this lesson
    Define pictorial diagram and orthographic diagram
    Discuss the features of orthographic diagrams (broken lines, solid lines, etc.)
    Go through Activities #1 – 4 on attached handout with class.
    Go through Example 1 on page 367
    Can use attached “Matching Exercise” handout as an overhead.
    Assignment: Page 370 #1 – 2

Day 3 – Tutorial 7.3 – The Uncertainty of a Measurement
    Need a class set of rulers
    Read through measurement standards paragraphs on page 372.
    Discuss uncertainty of measurements
    Define measurement error, uncertainty, and precision.
    Look at picture on page 373 with class. Discuss the precision of the ruler, the
       bolt’s measurement, the uncertainty of the measurement, and the minimum and
       maximum measurements of the bolt.
    Go through Investigation 1 on page 374
    Do not do Investigation 2 – too hard!
    Do not discuss the two points on page 375.
    Go through Examples 1 and 2 on page 376.
    Assignment: Page 378 #1, 2abc, 3, 5 – 7

Day 4 – Quiz

Day 5 – Tutorial 7.4 – Percentage Error
    Review precision and accuracy from Applications of Math 10
    Go through “Practise Your Prior Skills” #1 – 4 on page 382.
    Go through Example 1 on page 382.
    Read through paragraphs after the example on page 383
    Define relative error, percentage error and introduce the formula for percentage
       error.
    Go through Examples 2 and 3 on page 384
    Assignment: Page 385 #1 – 7
Day 6 – Tutorial 7.5 – Applications of Percentage Error
    Go through attached handout with class.
    Assignment: Attached worksheet

Day 7 – Tutorial 7.6 – Applying Tolerances
    Read through paragraphs on page 394
    Define tolerance range and tolerance interval
    Go through Examples 1 and 2. Example 3 is quite difficult. Can use questions
       from exercises or extra practice CD for more examples
    Assignment: Page 398 #1 – 6

Day 8 and 9 – Project
    Use attached worksheets to go through Tree Volume Project. You will need
       TREEVOL program from the Teacher’s Resource Manual CD.
    Do Part 1 on Day 8 and Part 2 on Day 9

Day 9 – Review
    Use attached review handout for students to complete during class.

Day 10 – Unit Exam

				
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