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Learning Math Home
Measurement Session 3: Measurement Systems
Session 3 Part A Part B Homework
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Session 3 Materials:

Session 3, Part B:
Metric Units

In This Part: Length | Liquid Volume | Mass | Reasoning With Balance Scales

Whereas weight measures the gravitational force that is exerted on an object, mass measures how much of something there is; thus, mass is closely related to volume. The weight of an object can change depending on its location (e.g., on the Earth or on the Moon), but the mass of the object (how much of it there is) always stays the same.

Mass and weight are often confused, because our two systems of measurement use different terms. In the metric system, kilograms and grams are measures of mass, but in the U.S. customary system, ounces and pounds are measures of weight. When using the metric system, we should really state that we are measuring mass, saying, for example "I have a mass of 60 kg" rather than "I weigh 60 kg," but this goes against convention. Throughout this course, we will use both terms (but regardless of the term we use, mass is what we'll be finding!). Note 10

The base unit of mass is the kilogram (kg). In the 1790s, a kilogram was defined as the mass of 1 L (cubic decimeter, or dm3) of water:

Though that definition has changed somewhat with time, here is a definition that is close enough for ordinary purposes: There are 1,000 g in 1 kg, and 1,000 g occupy a volume of 1,000 cm3, or 1 L. Therefore, 1 g of water weighs the same as 1 cm3 of water and occupies 1 mL of space. In other words, for water:

1,000 g = 1 kg = 1,000 cm3 = 1 dm3 = 1 L
1 g = 1 cm3 = 1 mL

Kilograms are used to weigh just about everything but very light objects (which are weighed in grams) and very heavy objects (which are weighed using metric tons). A gram is almost exactly the weight of a dollar bill. A metric ton is equivalent to 1,000 kg (so it can also be thought of as a megagram) and should not be confused with the common American ton in the U.S. customary system. In fact, the metric ton is often referred to by its French and German name, tonne, to distinguish it as a metric measure. Most cars have a mass of between 1 and 2 tonnes; a large diesel freight locomotive has a mass of approximately 165 tonnes.

As with metric lengths, it is useful to establish benchmarks for metric mass measures.


Problem B9



Using the centimeter grid paper (PDF), build a cubic decimeter. What is its capacity? What is its weight if filled with water?


What is the capacity and weight of 1 cm3?

Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
How many cubic centimeters are there in a cubic decimeter?   Close Tip


Problem B10


Some people use balance scales like the one illustrated above, and some people use spring scales like a typical grocery or bathroom scale. How are the two different?

Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
Think about how they work and whether they measure weight or mass.    Close Tip


Problem B11


Look around the room you're in now, and find one or more objects that you estimate has each of the masses listed below. If a scale is available, use it to measure each object to corroborate your estimates. If a scale is not available, select some food products (with very light wrappers) such as candy bars and cereal. Estimate their mass and compare your estimate to the mass indicated on the product. Note 11


1 g


100 g


500 g


1 kg


Problem B12


Take an empty plastic liter bottle and weigh it. Then fill the bottle with very cold water and weigh it again. What do you notice about the weight of the liter of water? Explain your findings.

video thumbnail

Video Segment
Watch the participants as they measure the mass of a 1 Liter bottle filled with water. They are surprised to discover that it's a little more than 1 kg. This is not what they expected, so they contemplate possible explanations of their result.

Can you think of any other possible reasons that would explain why the bottle weighs more than a kilogram?

If you are using a VCR, you can find this segment on the session video approximately 19 minutes and 20 seconds after the Annenberg Media logo.



Problem B13


How will filling the liter bottle with something other than water -- for example, juice, yogurt, or sand -- affect the mass? Explain.

Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
Think about the relationship between mass and volume. Can two substances have the same volume but different mass?   Close Tip


Problem B14


Estimate the mass of a newborn baby, a fifth grader, an adult woman, and an adult man. If possible, use scales to gather your data. Note 12

Next > Part B (Continued): Reasoning With Balance Scales

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