labcdrommass.html

Measuring Mass
(ISBN 0-7872-4108-3, primary): In this investigation the children learn how to use the equal arm balance, to get a feel for the values of masses for some everyday objects, start to use the proper units for mass, and, most importantly, understand that mass is a variable that one must consider alongside length, area, and volume. The children use a variety of standard masses and repeated addition or simple multiplication to determine the masses of five different objects which they choose from a wide variety set up by you. Addition, subtraction, and even the idea of a remainder come into play as the children determine the mass difference between objects, how many of one light object it takes to balance a heavy one, etc. These predictions are checked out on the balance. The children can literally see balanced mathematical equations right on the equal arm balance.

Mass vs. Shape
(ISBN 0-7872-4109-1, primary & intermediate): This investigation is another attack on the misconception that the mass of an object depends upon its shape. The children measure the mass of a piece of clay using an equal arm balance and standard masses. They then change the shape of the clay four times, measuring its mass each time. We are sure they will all agree that changing the shape does not change the mass. In a sense, the investigation parallels Volume vs. Shape, but the results of the two investigations are not to be confused. Mass and volume are different variables. It just so happens that neither changes when you change the shape of the object. Using standard masses allows us to have the children carry out problem-solving activities involving the concepts of addition, subtraction, multiplication, and division. It is important that the children are challenged by multistep problems if they are to develop their intellectual skills. Mass vs. Shape is a good beginning.

Ordering Six Masses
(ISBN 0-7872-4110-5, primary & intermediate): As a follow-up to our earlier Ordering Four Masses investigation, we add a new layer of confusion for the children by challenging them to order six masses using only the equal arm balance and pair-wide comparisons. The two new objects have different shapes and are made of different materials but have the same mass. Although the logistics are more complicated, the basic idea is still the same, to confront the children early on with the fact that mass is independent of shape, size, and materials.

Balancing Games
(ISBN 0-7872-4111-3, intermediate): The investigation is designed to introduce the children to the concept of mass. The idea is to balance a given number of set A masses against a given number of set B masses. The number of set A is the manipulated variable, the number of set B is the responding variable. The only trick in the investigation is that one must choose the individual members of sets A and B so that a whole number of one will balance a whole number of the other. The game is played twice with the same A but different B’s. The result of either game is a linear relationship between A and B that passes through (0,0). Besides interpolation and extrapolation, Balancing Games is a simple yet wonderful tool for developing proportional reasoning skills. We also give the children a chance to work on common denominators. But underlying all of this is that we are balancing masses, the amount of matter, in very different looking objects. It is this property of mass that allows us to play the game.

Mass vs. Number
(ISBN 0-7872-4112-1, intermediate): Mass vs. Number was the brainchild of one of our TIMS teachers. It just so happened that the school had a lot of new erasers, so the teacher decided to have the children find the relationship between the number of erasers (the manipulated variable) and their mass (the responding variable). Since then we have done the investigation with new chalk, new pencils, paper clips, marbles, and spheres of all sizes. The nice linear relationship between number and mass means we can ask lots of interpolation, extrapolation, and proportional reasoning questions. And we do. The investigation has an extremely important practical application. The knowledge that the number of identical objects is proportional to their mass means that we have a powerful way of “counting” large numbers of like objects by finding their total mass.

Can You Stop This?
(ISBN 0-7872-4113-X, intermediate & middle): The students roll first one, then two, and finally three steel spheres down a ramp and into a slider and measure how far the slider travels (D). The students determine the mass of the steel spheres (M), and plot M vs. D, where M is the manipulated variable and D is the responding variable. The children use the linear relationship between M and D to predict the mass of a mystery sphere by how far it pushes the slider. Questions involving proportional reasoning are explored in the comprehension section as well as applications of these ideas to out-of-control cars and boats. This investigation is an introduction to the internal properties of mass.

Mass vs. Volume
(ISBN 0-7872-4114-8, intermediate & middle): About 2000 years ago, King Hieron of Syracuse asked Archimedes to determine whether his new gold crown had been adulterated with silver. When Archimedes discovered how to do this, he was so excited he ran through the streets shouting “Eureka, I have found it.” Although we shall be more restrained, we shall find it too—the remarkable relationship between mass and volume that allowed Archimedes to learn that the crown was not pure gold. Using the equal arm balance and a graduated cylinder, the children find the relationship between mass and volume for three different-sized spheres of steel and three of plastic. The result is a different straight line curve through (0,0) for each material. Using this simple but important relationship, the children make predictions using proportions, learn about the concept of density, and explore the composition of the Earth’s crust. Archimedes would be pleased.

Taste of TIMS
(ISBN 0-7872-4115-6, intermediate & middle): The students bring a sandwich to class ready for eating. The sandwich must be eaten whole, not sliced in two, no matter what etiquette dictates. The children measure the initial mass of the sandwich, and then at lunch they take one bite (N = 1) and measure the mass of the sandwich (M), then take another bite (N = 2) and measure M, and then 2 bites (N = 4) and measure M. They plot M vs. N and predict what M would be for N = 6, and what N would be to finish the sandwich. Predictions are checked (eaten) and percent differences calculated. Other variables that may affect the slope of the M vs. N curve are explored. The experiment is a good example of a curve that does not pass through (0,0) and that has a negative slope.

Candle Burning III: Part I—Mass vs. Time
(ISBN 0-7872-4116-4, intermediate & middle): With a burning candle on one of the balance pans, the students study the rate at which the candle loses mass. The relationship between the mass of the candle (M) and time (t) will have a negative slope and so the ideas behind the analysis of this investigation carry over from Taste of TIMS. We use the negative slope of the M vs. t relationship and proportional reasoning to make predictions on how long the candle will burn; we explore grocery stores to check that prediction; and we study some of the first candles, over 40,000 years old, and predict how long they would have burned. We conclude Part I by comparing the burning times of different types of candles and try to understand why their mass loss rates might be different.

Candle Burning III: Part II—Combustion & Chemistry
(ISBN 0-7872-4117-2, intermediate & middle): In Part II the students use their results of Part I to continue the study of chemistry and combustion that they began in Candle Burning I and continued in Candle Burning II. They do some model building of chemical systems and use a conservation law to determine the mass of the combustion products and then the mass and volume of oxygen used by the burning candle. This leads to a discussion of the human metabolic process. They learn how much mass they would lose if they stopped eating, how many calories a day they need to stay healthy, and even learn a little about artificial respiration. Part II is composed of eleven questions along with written background materials. You may want to have the children use the library for more information on atoms and molecules or you may want to stick with the materials in the lab write-up augmented by the information presented in the Teacher Lab Discussions. The lab makes liberal use of proportional reasoning.

Sink and Float
(ISBN 0-7872-4118-0, middle): The mass and volume of single samples of various materials are found and plotted as in Mass vs. Volume. Lines are then drawn through (0,0) and each data point. Then the mass and volume of a sample of water are found so that the M/V line for water can be plotted on the same graph. It is found that materials with M/V lines below the line for water will float in water. Materials with M/V lines above the line for water will sink. This investigation has an upper grade extension that discusses density and leads to building boats out of materials that sink.

Hung Out to Dry
(ISBN 0-7872-4119-9, intermediate & middle): Evaporation is an extremely important tool of nature. Water evaporates from your skin, from leaves of plants, from cups of water (see the TIMS investigations Evaporation I and Evaporation II), from oceans, lakes, and rivers, from laundry hung out to dry. The evaporation process helps regulate body temperature, promotes salination of salt water, dries up lakes and rivers in hot summers, and cools us after a dip in the water on a hot day. Using the equal arm balance, the children look at evaporation of water from towels by studying the mass of the towel vs. time, they try to understand the crucial role surface area plays in the evaporation process, they study problems involving negative slopes, they think about fair ways to report their data, and lastly, we give them an opportunity to extend the experiment to different types of towels, to sponges, and to different temperature conditions.

TIMS Laboratory Investigations

Mass