# Crystals in Science, Math and Technology

## Making Measurement Simple: The Metric System

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## Lesson Plan #3

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Objective
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To understand the size of an atom

To multiply and divide by powers of ten To practice estimation

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Materials needed
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Film “Powers of Ten” (available from the central A.V. office)

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Procedure
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- 1. Review the fact that the metric base unit of length is the meter and show the meter stick so there a concrete display of size.
- 2. Discuss the concept of atoms so that students are aware that everything is made up of atoms. This might lead to discussions of the states of matter or similar things.
- 3. Show the film “Powers of Ten” and discuss.
- 4. Discuss the fact that, in metrics, different units result from multiplying or dividing by powers of ten. Thus a meter divided by ten equals a decimeter which divided by ten equals a centimeter and so on. So, if a meter divided into a thousand parts equals a millimeter, then a millimeter divided into 10 million parts is roughly the size of an atom; or mathematically an atom equals

_____1m____ | or | ___1mm__ | 10,000,000,000 | 10,000,000 |

- ____ If the concept of negative powers of ten has been introduced, then it can be shown as 10 m or 10 mm. Remind students that when numbers are expressed as powers of ten and multiplied or divided, the exponents are simply added or subtracted.
- 5. Moving on to a concrete representation of the relative sizes, suppose that a grain of sand is i mm long. Then in the length of 1 grain of sand there would be 10,000,000 atoms or 10
^{ 7 }. But, because the grain of sand also has width and height, it would be 10^{ 7 }wide and 10^{ 7 }high. Knowing that volume equals length times width times height (v=lwh) then 10^{ 7 }10^{ 7 }10^{ 7 }=10^{ 21 }or 1,000,000,000,000,000,000,000 atoms in a grain of sand. This should give students the idea of just how miniscule an atom is. Another way to say it would be to figure a trip to the sun. If the sun is roughly 100,000,000 km away, how far would a journey equal to the length of 1 atom be? (100,000,000 km = 10^{ 8 }km = 10^{ 11 }m divided by 10^{ 10 }which is the number of atoms in a meter gives us 10^{ 1 }or 10 meters in our journey to the sun.)- ____ ____ A possible assignment might be to have students think of other situations which might lend themselves to estimation, powers of ten and the atom.