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Learning Math Home
Measurement Session 1: Notes
Session 1 Part A Part B Part C Part D Homework
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Session 1 Materials:

A B C 


Notes for Session 1, Part B

Note 3

Prior to measuring these attributes, it is important to consider what type of unit should be used. Children frequently have a difficult time choosing appropriate units of measure. For example, they often try to measure area using linear units (centimeters), or volume using two-dimensional units (square centimeters). Reflect on your own knowledge of metric units of measure. Does your knowledge of and familiarity with metric units have anything to do with your ability to choose an appropriate unit?

<< back to Part B: Which Rock Is the Largest?


Note 4

The following equivalencies may be helpful: 1 cm2 = 4(0.5 cm2), and 1 cm2 = 16(0.25 cm2). In order to visualize these relationships (e.g., that four 0.5 cm squares cover the same amount of space as 1 cm2), draw the 0.5 cm squares on 1 cm2. Reflect on or discuss why the average of the inner and outer measures is the approximate surface area and not the exact surface area.

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Note 5

The relationship between cubic centimeters and milliliters (1 cm3 = 1 mL) and, accordingly, between cubic decimeters and liters (1 dm3 = 1 L) will be explored further in Session 3.

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Note 6

This method works best with a beaker marked in milliliters. Other containers may not have adequate markings for you to determine the volume of water displaced when you submerge the rock. If you don't have such a beaker, you could fill the container to the top, measure the amount of water that overflows when you submerge the rock, and then pour the overflow into more precisely marked measuring devices.

Since spilled water can be messy, you might try using a solid material instead, such as fine sand or rice. Fill a container to the top with sand, place your rock in the container, collect the overflowing sand, and then measure the amount that overflowed.

<< back to Part B: Which Rock Is the Largest?


Note 7

In this session, we are using the common term "weight," even though we are technically finding the mass of the rock. The difference between the terms is discussed in detail in Session 3.

Also, many teachers have not had the opportunity to study different types of scales, chiefly because scales are not standard equipment in classrooms. To do a hands-on version of this activity, you'll need a two-pan balance and a three-arm balance. Using the two-pan balance, you can compare an object on one pan to a set number of weights on the other pan, adjusting the weights until the pans are level (or balanced). The three-arm balance has weights built into the instrument. You may be able to borrow scales from colleagues in middle or high school science departments. Try to use the best scales your school system has available. Be sure that the scales have been "balanced" prior to using them.

<< back to Part B: Which Rock Is the Largest?


Note 8

Some people may consider the weight of the rock to be an exact amount, perhaps because it is more difficult to think about using smaller and smaller units to measure weight. But is weight ever exact? Reflect on or discuss this problem as a group.

<< back to Part B: Which Rock Is the Largest?


Note 9

If you and your colleagues are working in several small groups, try to decide which group has the largest rock. Unless the rocks are very different, though, this might not be a simple task. The term "largest" is not an absolute and has many meanings, depending on the circumstances and the judgement of those involved with the decision-making process. Ultimately, you may choose to use a combination of measures, such as those that are discussed in the homework.

<< back to Part B: Which Rock Is the Largest?


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