Transcript Length in the Customary System

Length in the Customary
System
By Harry Marshall
Summary
• Accompaniment to Glencoe’s Mathematics:
Applications and Concepts Course 1
• Chapter 12 Measurement
• Lesson 12-1 Length in the Customary System
• 6th Grade Mathematics Enrichment
Sunshine State Standards
MA.B.1.3.3-1, MA.B.1.3.3-2, MA.B.1.3.3-3,
MA.B.2.3.1-1, MA.B.2.3.1-2, MA.B.2.3.2-1,
MA.B.3.3.1-1, MA.B.3.3.1-3, MA.B.3.3.1-4,
MA.B.4.3.1-2, MA.B.4.3.2-1, MA.B.4.3.2-2,
MA.B.4.3.2-3
Prerequisite Skills and Supplies
• Basic Understanding of Computers
• Internet Access
• Familiarity with concepts of customary
measurement, area, perimeter, and scales
• Standard Six-Inch Ruler
Objective
• To provide students with practical
experience in measurement without the
need for manipulatives, rulers, or other
costly classroom supplies.
Key Terms
• Customary measure (compare to metric)
• Length
• Diameter
• Radius
• Area
• Perimeter
• Pi
Historical Background
• The system for measuring length in the
United States' customary system is based
on the inch, foot, yard, and mile, which are
the only four customary length
measurements in everyday use.
Wikipedia
Web Address
http://www.geogebra.org/en/upload/files/MS
P/HarryMarshall/CustomaryLength.html
Click to Activate
Drag the Ruler to Measure the
Shapes to the Nearest Half,
Quarter, or Eighth Inch
Questions
1. What is the length of the base of the
triangle?
2. What is the length of the side(s) of the
square? perimeter? area?
3. What is the diameter of the circle?
radius? perimeter? area?
Beyond the Basics
• 1. Is one inch on the virtual ruler = one
standard inch?
2. If not, what is the scale (or relationship)
between the virtual ruler and an actual
ruler?
3. Will everyone attempting this exercise
reach the same conclusion for the scale?
4. Why or why not?
In the Real World
• Architecture
• Blueprints
• Graphic Design
• Computer Animation
Instructional methods
Teacher-centered approaches
• Vocabulary, key concepts, and real-life tieins to the lesson should be instrumented
by the teacher prior to the students
completing the online activity.
• Following the activity, the teacher should
summarize and discuss the results with
the students.
Instructional methods
Student-centered approaches
• Discovery Learning
• Simulation
• Problem-based learning, inquiry, and
discussion
Key Questions
• Compare / Contrast customary measurement
with metric measurement.
• Name professions that use the skills you are
using here.
• Will items you measure in the real world always
measure exactly to the nearest half, quarter, or
eighth inch?
• What effect would using a ruler that is divided
into sixteenths of an inch have on the
measurement of real objects?
• For aeronautical engineers, are sixteenths of an
inch precise enough?
Answer Key
1. What is the length of the base of the
triangle? 1 ¾ inches
2. What is the length of the side(s) of the
square? 1 5/8 inches; perimeter? 6 ½
inches; area? 2 41/64 inches
3. What is the diameter of the circle? 2 ¼
inches; radius? 1 1/8 inches; perimeter?
7.07 inches or 2 ¼ Pi inches; area? 3.98
inches or 1/64 Pi inches
Beyond the Basics
1. 1. Is one inch on the virtual ruler = one
standard inch? Answers may vary.
2. If not, what is the scale (or relationship)
between the virtual ruler and an actual ruler?
Answers may vary.
3. Will everyone attempting this exercise reach
the same conclusion for the scale? No
4. Why or why not? Because of differences in
monitor size and resolution, the ruler may
appear larger or smaller than an actual ruler.
Assessment
• The answers to the questions are to be
turned in and graded by the teacher and
returned to the students with feedback.
• A participation grade can also be given for
the class discussion.
Students with Disabilities
• Teacher-presented material via an LCD
projector
• Call up a few students to measure the
objects
• Implement the follow-up questions as
group work or a class project/ discussion
Supplemental activities lesson
• To include measurement of real objects,
such as a pencil, comb, toothbrush,
television remote control, etc.
Connections
(Other Material)
• Integrates measurement, perimeter, area,
and scale while providing the teacher with
an inexpensive practicum and the student
with practical measurement drills.
• Can be used as a review for multiplying
decimals, fractions, and algebra sections
since it draws upon all these skills.
• Could serve as an introduction to the
Geogebra software used to create it.
Connections
(Other Classes)
• Science
-Figure out to actual length of an insect’s
thorax using a ruler and a scale on from a
magnified image.
• Social studies
- Find the distance between two locations
on a map.