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 precision.

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 measurement.

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.

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 4.

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 cubes.

• 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 is.

• 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 attribute.

• 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 and disadvantages.

• 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 strongest.

• Students estimate and then weigh objects, putting them in order from heaviest to lightest.

3. Recognize the need for a uniform unit of measure.

• 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 units.

4. Develop and use personal referents for standard units of measure (such as the width of a finger to approximate a centimeter).

• Students identify parts of their body that are the same length as ten centimeters and use them to measure the length of their pencil.

• Students find things in their environment that weigh about an ounce.

• 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 problems.

• 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 measurements.

• 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.

References

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 Shepard, 1986.

General reference

Burton, G., et al. Curriculum and Evaluation Standards for School Mathematics: Addenda Series: ThirdGrade Book. Reston, VA: National Council of Teachers of Mathematics, 1992.

One-Line Resources

http://dimacs.rutgers.edu/archive/nj_math_coalition/framework.html/

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 Mathematics Standards.