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Force of Gravity

Mathematics Standards
Mathematical Connections
Mathematics as Reasoning

Science Standards
History and Nature of Science
Science as Inquiry
Unifying Concepts and Processes

Newton's discovery of the universal nature of the force of gravity was remarkable. To take the familiar force that makes an apple fall to Earth and be able to recognize it as the same force that keeps the planets on their quiet and predictable paths represents one of the major achievements of human intellectual endeavor. This ability to see beyond the obvious and familiar is the mark of a true visionary. Sir Issac Newton's pioneering work epitomizes this quality.

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Proportionality

Mathematics Standards
Algebra
  Computation and Estimation
  Functions
Mathematics as Communication
  Number and Number Relationships
  Patterns and Functions

Science Standards
Unifying Concepts and Processes

F is proportional to m1 times m2 over r squared   indicates proportionality

F = G times m1m2 over r squared    indicates equality

G time m1m2 over r squared    is an expression

F = G time m1m2 over r squared    is an equation

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Mass

Mathematics Standards
Algebra
Mathematical Connections
Mathematics as Communication
  Measurement

Science Standards
Science and Technology
Science as Inquiry
Unifying Concepts and Processes

The internationally recognized Systeme International (Sl) is a system of measurement units. The Sl units for length (meter) and mass (kg) are taken from the metric system. Many dictionaries and mathematics and science textbooks provide conversion tables between the metric system and other systems of measurement. Units conversion is very important in all areas of life. For example in currency exchange, airplane navigation, and scientific research.

Units Conversion Examples
1 kg ~= 2.2lb      1 in = 2.54cm
1 liter ~= 1 qt      1 yd ~= 0.9 m

Questions for Discussion
  • What common objects have a mass of about 1 kg?
  • What are the dimensions of this sheet of paper in cm and inches?
  • How many liters are there in a gallon?
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Scientific Notation

Mathematics Standards
  Computation and Estimation
Mathematics as Communication
  Number and Number Relationships
  Number Systems and Number Theory

Science Standards
Science as Inquiry
Science in Personal and Social Perspectives
Unifying Concepts and Processes

Scientific notation makes it easier to read, write, and manipulate numbers with many digits. This is especially useful for making quick estimates and for indicating the number of significant figures.

Examples:
   0.001 = 10 -3
   10 = 10 1
   1000 = 10 3

Which is bigger, 6 x 10 -3 or 8 x 10 -4? 6 x 10 3 or 8 x 104 ? How much bigger?

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Scale

Mathematics Standards
Mathematical Connections
Mathematics as Reasoning

Science Standards
Science and Technology
Science as Inquiry
Unifying Concepts and Processes

Questions for Discussion
  • How does a scale work ?
  • What does a scale measure?
  • How many different kinds of scales can you list?
  • Do they need gravity for them to work?
  • Would you get different results on the Moon or Mars?
  • How can you measure the mass of an object in microgravity?
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