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Name: Pamela
Status: other
Grade: 6-8
Location: CA
Country: USA
Date: Fall 2009

Hi. I am writing a 6th-grade science book, and I am currently working on a chapter on atoms, elements, and compounds. My question relates to the definitions of matter and mass. In my research, I have found that matter is defined in terms of mass and mass is defined in terms of matter. Specifically, matter is defined as "anything that has mass and takes up space," while mass is defined as "the amount of matter in an object." If I substitute the definition of mass into the definition of matter, I get: matter is anything that has an amount of matter and takes up space. This does not make sense. Can you please provide me with definitions of matter and mass that are not mutually dependent on one another and that will make sense to 6th-grade students? Any clarification that you can provide will be greatly appreciated.

Hi Pam,

Operationally, as a chemist I think of ordinary matter as "anything made of atoms" although I am hardly an authoritative source.

In "General Chemistry", 9th edition by D.D. Ebbing and S.D. Gammon (Houghton Mifflin & Co, Boston/NY, 2007), matter is defined as "whatever occupies space and can be perceived by our senses." I think that is kind of vague, and I do not like the use of perception in the definition. Still, might be okay for sixth graders. Also, mass is defined as "the quantity of matter in a material." I do not love that either because of its lack of clarity. What is meant by quantity?

In "Chemistry: The Molecular Science", 3rd edition by J.W. Moore et. al. (Brooks-Cole/Thomson, Belmont CA, 2008) matter is defined as "anything that has mass and occupies space" while mass is defined as "a measure of an object's resistance to acceleration." These definitions are both correct and useful, but the definition of mass might possibly be a tough one for a sixth grader because you have to define acceleration and other Newtonian physics concepts. Still, it avoids the circular problem that you bought up.

Mass is, in reality, a deeper concept than described here because of its equivalence with energy (according to Einstein's theory of relativity). However I have ignored this important complication because it is completely outside of the scope of your question (I am stating this for the benefit of Internet kibitzers out there who may be reading this in the future).

good luck!
dr. topper

Hi Pamela,

We need to emphasize that mass is a *measure of the amount* of matter, while matter is simply a label, a name, for things that take up space. So using the substitution you applied, we can say that mass is a measure of the amount of material in a particular object.

To my mind, rather than having these things defined for the students, it might be better as an exercise where the students define it for themselves. There are many little exercises that can guide students to their own definitions and they do not need to be hung up on a particular wording.

Greg (Roberto Gregorius)
Canisius College

Matter is the material, the physical "stuff". Mass is the measurement of the amount of material present. Mass is a number.

It is like seeing cows. The matter is cow. All cows are made up of cow.

A cow's mass is how much cow there is. Not all cows mass the same, but all are made up of matter called cow.

R. W. "Bob" Avakian
B.S. Earth Sciences; M.S. Geophysics
Oklahoma State Univ. Inst. of Technology

When you get down into these fundamental concepts it is easy to get trapped in circular definitions -- some would say inevitable. The reference "Handbook of Mass Measurement" gives a definition attributed to Condon & Odishaw in "Handbook of Physics": "The property of a body by which it requires force to change its state of motion is called inertia, and mass is the numerical measure of this property." In short, it is the resistance to a change in motion. Paraphrasing Richard Feynman's "Lectures on Physics" Vol. 1, Chapter 9, Section 1: Inertia is how hard it is to change the direction of motion of an object. Mass is the quantitative measure of inertia. Surprisingly, the "AIP Physics Desk Reference" 3rd edition does not even bother to give any definition. The references above also take up the definition of matter.

Vince Calder

One way to define mass is to refer to Newton's Second Law of Motion. It states that the acceleration produced by a particular force acting on a body is directly proportional to the magnitude of the force and inversely proportional to the mass of the body. Mass is the measure of an object's inertia. Mass is the ratio of an applied force to the resulting acceleration. That is: mass = (applied force)/(acceleration). While the weight of an object is different if you are on the earth or the moon, the mass is the same. That is, a given force applied to an object will result in the same acceleration whether on the earth or the moon.

David S. Kupperman


I would define mass as the amount of matter and I would define matter as anything that is made up of atoms (or protons, neutrons or electrons). I think these definitions always work but I have always disliked the definition of mass. It is such a vital concept and yet very difficult to measure directly. We either have to do through weight or else through inertia in some other way. Hmmmmmm...

Best wishes,

Tom Collins

Hi Pamela,

I think your question probes one of the basic premises of science. "Science" is a way of explaining and classifying observations. Science attempts to observe, describe, and classify what is, but does not attempt to explain why something is so. So science, and scientific terms, are fundamentally operational in nature. This is very different than the more symbolic/axiomatic approach you seem to be implying.

The concept of mass comes from the observation that some objects require more force to move than others. What is the property that makes one object require more force to move than another? Science calls it "mass". Objects that have more "mass" require a greater force to accelerate at a given rate. "Mass" can be observed by many means, including how an object responds to a gravitational field. I would shy away from the definition of mass as "the amount of matter in an object" because it is the forces that you are observing, not the matter itself (again, referring back to the operational definition). We can compare observations and quantify them, but it is important to be clear about what you are observing, and what you are inferring from the observation. The more successive inferences you make, the more risk there is in introducing error.

I also would challenge the common definition "having mass and taking up space." This is OK in some basic contexts (and is probably just fine for the vast majority of junior-high subjects), but over the past several decades, new discoveries in quantum physics have shown this definition can be inadequate. There is much information on this subject on the Internet, and various standards organizations have adopted different strategies on how to address the issue. These are certainly outside the scope of a 6-8th grade text book, so I will not go into detail here.

The bottom line is that I think scientific terms are better when operationally defined. Students should understand what the meaning and source of these properties/quantities are -- and not rely on memorizing symbolic definitions. This is partly because operational definitions tend to avoid the confusions that are concerning you, but more importantly because science is founded on observation.

Hope this helps,

Burr Zimmerman

Oh - I love all this discussion, but let's simplify somewhat for a junior high or middle school student. Weight is a measurement in response to gravity for most of us. An object has weight due to the gravitational pull on it. It would weight a great deal less on the moon, for example, since the gravitational pull is less. A spring scale measures weight. The idea of weightlessness comes from the lack of gravity pulling on an object or gravity being equal on all sides.

The same object can be measured in comparison to known objects by mass. The mass never changes (well, I have to be somewhat careful here). Using a instrument that compares the mass of objects to known objects will have the same mass whether on the moon or the earth. Gravity is not a factor in this measurement.

Steve Sample

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