STANDARD 9 - MEASUREMENT
All students will develop an understanding of and will use
measurement to describe and analyze phenomena.
Standard 9 - Measurement - Grades 3-4
Students can develop a strong understanding of measurement and
measurement systems from consistent experiences in classroom
activities where a variety of manipulatives and technology are used.
The key components of this understanding, as identified in the K12
Overview, are: the concept of a measurement unit; standard
measurement units; connections to other mathematical areas and to
other disciplines; indirect measurement; and, for older
students, measurement error and degree of
Students in grades 3 and 4 continue to encounter measurement
situations in their daily lives and in their schoolwork. They
investigate how much weight different structures will support or make
a model of the solar system in science class, they make maps in social
studies, and they read and discuss stories in which people measure
objects. Measurement continues to provide opportunities for making
mathematical connections among subject areas.
Measurement also helps students make connections within
mathematics. For example, as students begin to develop their
understanding of fraction concepts, they extend their understanding of
measurement to include fractions of units as well. Measurement is
interwoven with developing understanding of the geometric concepts of
perimeter, area, and volume. Furthermore, students develop their
estimation skills as they develop their understanding of
Students also continue to learn about more attributes of objects
that can be measured. In addition to length, distance, capacity,
weight, area, volume, time, and temperature, they now are able to
discuss the size of angles and the speed of a car or a bike. Students
begin to make more indirect measurements as well. For example,
they will measure a desk to find out whether it will fit through a
door, or measure how far a toy car goes in a minute and divide to find
its speed in feet per second.
The emphasis in these grades is on building on the students'
earlier experience with non-standard units and their developing
concept of measurement unit to the use of more sophisticated
standard units of measurement. They solidify their
understanding of the basic units introduced in the earlier grades and
begin to use fractional units. Students use half-inches,
quarter-inches, and eighths of an inch, for example, in measuring the
lengths of objects. Students also begin to use some of the larger
units: miles, kilometers, and tons.
Some students may begin to discover formulas to help count units.
For example, students may use shortcuts to find out how many squares
cover a rectangle, multiplying the number of rows times the number of
squares in each row. Or they may find the distance around an object
by measuring each side and then adding the measures.
In summary, in grades 3 and 4, it is important that all students
get extensive hands-on experience with measuring the properties of a
variety of physical objects. They will learn to measure by actually
doing so with an appropriate measuring instrument.
Standard 9 - Measurement - Grades 3-4
Indicators and Activities
The cumulative progress indicators for grade 4 appear below in
boldface type. Each indicator is followed by activities which
illustrate how it can be addressed in the classroom in grades 3 and
Building upon knowledge and skills gained in the preceding grades,
experiences in grades 3-4 will be such that all students:
1. Use and describe measures of length, distance,
capacity, weight, area, volume, time, and temperature.
- Students find out how many inches long their hand is. The
class then generates a graph showing the results.
- Students use rulers to measure the length of the
room in feet and inches and then in metric units.
- Students move thermometers to different parts of the
school, recording the temperature at each location. For example, it
may be hot in the cafeteria and cold in the gym. They learn to
identify appropriate reference points on both Celsius and Fahrenheit
scales (e.g., 30 degrees Centigrade is a hot day).
- Students investigate truth-in-packaging by reading labels,
estimating weights, and then using balances to weigh foods.
- Students investigate how many cups in a pint, how many
pints in a quart, and how many quarts in a gallon by making lemonade
and filling various sizes of containers.
- Students make their own rulers, marking off intervals equal
in length to one centimeter.
- Students estimate and measure the distance around an object
using a length of string which they then measure with centimeter
- Students conduct experiments using timers: how many
times can you bounce a ball, clap your hands, or blink your
eyes in one minute? They discuss how many times each would occur
in 10 minutes, in an hour, or in a day, if they continued at the same
rate, and why their answers might be different.
- Students measure all sorts of performances in
their physical education class: the time it takes to run 100 meters,
the length of a long jump in inches, and the length of a softball
throw in meters.
- Students read Time to . . . by Bruce
McMillan. In this book about a farm boy and his daily activities,
clock faces are always there to remind the reader what time it
- Students use calculators to help them find out how many
days old they are.
- When going on a field trip, students determine how much
time they will have available at a museum by considering when they
will arrive and when they must leave.
- Students use cubes to fill rectangular boxes of various
sizes as they explore the concept of volume.
2. Compare and order objects according to some measurable
- Students compare the areas of different leaves and order
them from smallest to largest. They use a variety of strategies; some
students cover the leaves with centimeter cubes, others make a copy of
the leaf on grid paper, and still others just "eyeball" it.
They discuss the different strategies used, comparing their advantages
- Students bring in a variety of cereal boxes from home and
estimate their order from smallest volume to largest volume. They
then check their accuracy by filling the boxes with cubic inch blocks,
with cubic centimeter blocks, and with sand, and discuss the reasons
for the differences in their results.
- Students build bridges using straws and pipe cleaners,
estimate how many round metal washers their bridge will hold, and then
place the washers on their bridge until it buckles or breaks. They
compare different types of bridges to determine what type is
- Students estimate and then weigh objects, putting them in
order from heaviest to lightest.
3. Recognize the need for a uniform unit of
- Students measure the length of their classroom using their
paces and compare their results. They discuss what would happen if the
teacher measured the room with his or her pace.
- Students read and study the illustrations in the
book Long, Short, High, Low, Thin, Wide by James Fey. There
are many activities in this attractive book that take the students
through an historical account of the development of standard
4. Develop and use personal referents for standard units
of measure (such as the width of a finger to approximate a
- Students identify parts of their body that are the same
length as ten centimeters and use them to measure the length of their
- Students find things in their environment that weigh about
- Students use a meter stick to identify a personal
referent which is approximately a meter. For example, for one child it
may be an armspan, for another it might be the distance between a
kneecap and the top of the head.
- Students measure the length of their pace in inches and use
that information, along with a measurement of the length of the room
in paces, to find the length of the room in inches.
5. Select and use appropriate standard and
non-standard units of measurement to solve real-life
- Students decide what units they should use to measure the
weight of a textbook.
- Students discuss what units they should use to measure the
length of the hallway outside their classroom.
- Students write about how they might measure the distance
from the cafeteria to their classroom or the area of the gym.
- A nice approach to assessment of students'
skills with this topic is to make a list of items that they can
measure, such as the length of a piece of notebook paper, the weight
of a teacher, the amount of water a bucket can hold, and the distance
between Trenton and Newark, and ask them to name a measurement unit
with which it would be appropriate to measure the given item. They
discuss their choice of unit, estimate the measure of each item, and
then actually measure it and compare it to their estimate and to the
results of other students.
6. Understand and incorporate estimation and
repeated measures in measurement activities.
- Students read and laugh
about the pictures in Counting on Frank by Rod Clement. Frank
is a dog whose young owner, challenged by his father to use his brain,
estimates and imagines all sorts of measurements leading to some
pretty silly situations. Possible extensions are plentiful and easy
to devise. As an openended assessment followup to the story, the
teacher asks each of the students to make a
"CountingonFranklike" estimate of how many of something
(television, little sister, car, dog) would fit into their bedroom and
to draw a picture showing all of them there.
- Students estimate the weight of various objects in grams
and then use a balance scale to check the accuracy of their
- Students estimate the weight of, and then weigh the
contents of a box of animal crackers, graphing their results and
comparing them to the weights indicated on the packages.
Clement, Rod. Counting on Frank. Milwaukee, WI: Gareth
Stevens Publishing, 1991.
Fey, James. Long, Short, High, Low, Thin, Wide. New
York, NY: Thomas Y. Crowell Publishers, 1971.
McMillan, Bruce. Time to . . . Lothrop, Lee and
Burton, G., et al. Curriculum and Evaluation Standards for
School Mathematics: Addenda Series:
ThirdGrade Book. Reston, VA: National Council of
Teachers of Mathematics, 1992.
The Framework will be available at this site during
Spring 1997. In time, we hope to post additional resources
relating to this standard, such as grade-specific activities submitted
by New Jersey teachers, and to provide a forum to discuss the