Concepts of Measurement
Informal Units, Standard Units, and
Estimation
The Goal of the Teacher
Help students understand what it
means
to measure length, volume, weight, and area!
The BIG Ideas
• Measurement involves a comparison of an attribute with a unit
that has the same attribute.
• Meaningful measurement and estimation of measurements
depend on a personal familiarity with the unit of measure being
used.
• Estimation of measures help students increase familiarity with
units, prevent errors and aid in the meaningful use of
measurement.
• Understanding how measurement instruments work.
The 3 Steps of Measurement
1. Decide on the attribute to be measured
2. Select a unit that has that attribute
3. Compare the units, by filling, covering, matching,
or
some other method, with the attribute of the object
being meaurement.
Plan for Instruction
1. Understand the attribute to be measured
2. Understand filling, covering, matching, or making other
comparisons of an attribute with informal measuring units
3. Students will use common measuring tools with
understanding and flexibility
WHY USE INFORMAL UNITS?
• Easier to focus directly on the attribute being measured.
• Keeps the size of the numbers reasonable.
• In K-3 a discussion of inches, feet, centimeters, etc., can
obscure what it means to measure.
• Provides the rationale for standard units.
• It's gosh darn fun!!
Assessment
Can the student pick the best unit to measure with?
Does the student overlap their units or measure in a crooked
line?
Can the student tell which is longer when measuring two
objects?
How does the student go about measuring?
LENGTH
•
•
•
•
•
giant footprints
rope
paper clips
straws
cubes
Have students measure with one unit and then another to make a
comparison.
• Meaure the length of your desk with paper clips. Now with
straws. What do you notice about these two numbers?
AREA
chips, pennies, beans, one inch color tiles, cardboard
squares, or newspaper
Cut up one shape and re-arange it to show the area is the same
Fill a space with cut pieces of paper (lends itself to the area
algorithim)
Give students two shapes. Which has the greater area? Fold or cut
in any way to find out.
Volume and Capacity
beans
coins
styrophome peanuts
rice
water
plastic caps
cups and jars
TIME
slow drip bottles
pendulum swing
one handed clock
elapsed time on a number line
Weight and Mass
Two-pan balance
Rubber-band (spring) scale
ANGULAR MEASURE
wedges
protractor made from wax paper
protractor made with hand drawn units
Comparison Activities
• Comparison activities help students focus on the attribute
being measured.
• During these activities emphasis approximate language!
• Many measurements don't come out even, so
"approximate" language is especially useful for children.
The desk is about 10 blue rods long
The chair is less than five pencils high
Comparison Activities That Work Well!
K-3
Length:
Area:
Begin by comparing two or
more lengths
*important to understand
attribute first
Compare lengths that aren't
straight lines
Rearranging shapes doesn't
affect area!
Use comparison to
demonstrate (Act. 8.8)
Comparison Activvities K-3
Volume and Capacity:
• Start with comparing
capacities
• Compare capacity using
different containers
• Volumes of solid objects
can be a difficult concept
to comprehend.
Weight and Mass:
• Use simple activities to
start. Hold out two
objects in hands.
• Use approximate
language
• Move into using balance
pans and spring scales
Comparison Activities For 3-5
Length:
• Students should have a
good grasp on
understanding the
attribute of length by this
age, but need to continue
working with units of
length.
Area:
• Work on distinguishing
between size and shape,
length and width.
• Comparing rectangles
with different lengths and
widths (Act. 9.3)
• Tanagram Areas (Act.
9.4)
Comparison Con't 3-5
Volume & Capacity:
Measuring Angles:
• Capacity Line-up (Act.
9.9)
• Compare angles by
overlapping
• Displacement activities
for volume
• Use a cut-out angle as an
informal unit to measure
other angles
• Box Comparison-Cubic
Units (Act. 9.10)
• make a wax paper
protractor
Standard Units of Measurement:
Instructional Goals
1. Familiarity with the unit
2. Ability to select an
appropriate measure
3. Knowledge of a few
important relationships
between units
Standard Units of Measurement
• Students must develop a familiarity with standard units of
measurement!
• Students must learn appropriate relationships between
standard units of measurement!
• Use standard units once measuring concepts are in
place!
The Ruler!!!
Informal Units to Standard Units:
How Does This Work?
Standard Customary Units
LENGTH: inch, foot, yard, mile
AREA: square inch, square foot, square yard
VOLUME: cubic inch, cubic foot, cubic yard
CAPACITY: ounce*, teaspoon, tablespoon, cup, quart, gallon
WEIGHT: ounce*, pound, ton
Standard Metric Units
LENGTH: millimeter, centimeter, meter, kilometer
AREA: square centimeter, square meter
VOLUME: Cubic centimeter, cubic meter
CAPACITY: mililiter, liter
WEIGHT: gram, kilogram, metric ton
Estimation and Measurement
K-3
• Meaningful measurement and estimation of measurements
depend on a personal familiarity with the unit of measure being
used.
• Estimations of measures and the development of personal
benchmarks for frequently used units of measure help students
increase their familiarity with units, prevent errors in
measurements, and aid in the meaningful use of measurements.
Estimation and Measurement
3-5
• Estimation helps students think about the attribute being
measured and the measuring process.
• Estimation provides intrinsic motivation.
• Estimation can help build familiarity with units when
standard units are being used.
• Using benchmarks in estimation promotes multiplacative
reasoning.
How do we do this?
*Students need to have a familiarity with measurement units
and what units apply to different types of measurement.
!Have students estimate a measure before they make it!
Benefits:
1. Helps students focus on the attribute being measured and
the measurement process
2. It can be used as an intrinsic motivator
3. Helps develop a familiarity of the unit
Estimating Measures
WE USE ESTIMATIONS ALL THE TIME!!!
Four Strategies:
1.Develop and use benchmarks
2.Use "Chunking"when appropriate
3.Use subdivisions
4.Iterate a unit mentally or physically
Tips for Teaching Estimation
• Start by using specific approach
• Discuss with students how estimates were made, what
techniques did they use
• Accept a range of estimates
• Have students give a range of measures: Real life
practicallity & approximation
• Use estimations on a regular basis.
Estimate Exercises
• Don't have to be ellaborate
• "Quik Estimation" (Act. 9.17)
• "Estimation Scavenger Hunt" (Act. 9.18)
• "E-M-E Sequence" (9.19)