The Measurement Standard

1
The Measurement Standard

• Principles and Standards for School Mathematics
• National Council of Teachers of Mathematics
• 2000

2
Instructional programs from pre-kindergarten
through grade 12 should enable all students to

• Understand measurable attributes of objects and
  the units, systems, and processes of
  measurement.
• Apply appropriate techniques, tools, and
  formulas to determine measurements

3
Why Teach Measurement?

• It provides many applications to everyday life.
• It can be used to help learn other mathematics.
• It can be related to other areas of the school
  curriculum.
• It involves the students in active learning.
• It can be approached through problem solving.

2 inch
4
How to Teach Measurement
2 inch

• Children must measure frequently and often,
  preferably on real problems.
• Children should encounter activity-oriented
  measurement situations by doing and experimenting
  rather than passively observing.
• Instructional planning should emphasize the
  important ideas of measurement that transfer or
  work across measurement systems.

5
The Measurement Process

• I. Identify the attribute by comparing objects
• A. Perceptually
• B. Directly
• C. Indirectly through a reference
• II. Choose a unit
• A. Arbitrary
• B. Standard

6
The Measurement Process

• III. Compare the object to the unit
• IV. Find the number of units
• A. Counting
• B. Using instruments
• C. Using formulas
• V. Report the number of units

7
Stack the rods on a table so that the longest
rests on the table and others are on top in order
from longest to the shortest. Find the surface
area of the structure that could be painted
without moving any rods.
8
One possible solution

• Explanation I put two together. Each large
  face is 10 by 11 or 110. This takes care of the
  front and back. The side is 10 and the top is
  10, so the surface area is 130 square units.

9
Early Calendars

• Why does February have only 28 days ?
• Here is a calendar showing the number of days in
  each month during the Roman era.
•  
• J F M A M J J A S O
  N D
• 31 29 31 30 31 30 31 30 31 30
  31 30
•  
• Describe any patterns you see.
• How is this calendar different from our current
  calendar?

10
Early Calendars

• The emperor Augustus changed the calendar twice.
  Here is the first change.
•  
• J F M A M J J A S O
  N D
• 31 28 31 30 31 30 31 31 31 30
  31 30
•  
• Here is the second change.
•  
• J F M A M J J A S O
  N D
• 31 28 31 30 31 30 31 30 30 31
  30 31