Chapter 2 Properties of Real Numbers

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Chapter 2 Properties of Real Numbers
The Bigger Picture - Positive and Negative
Numbers (, -, X, -- Graphing
Comparing Opposites Absolute Value) - Real
Life Applications of Negatives Losses,
Deficits, Low Temperatures, - Creating,
Simplifying, and Evaluating more complex,
but realistic Expressions and Matrices The
properties of real numbers will be used to solve
higher level algebraic problems, as well as
real-life problems such as finding velocity,
speed, and distance profit and loss for a
business the difference in stock market prices
averages or the balance of a loan.
The What and the Why

• Graph and Compare Real Numbers
• Organize data, including negative values, in
  such a way as to evaluate and determine specific
  answers or characteristics, e.g. coldest temp
  ever recorded.
• Find the Opposite and Absolute Value of a Real
  Number
• Using absolute values and opposite values allows
  us to assess in relative terms, regardless of the
  direction of the data, e.g. measuring speed and
  velocity
• Add Subtract Real Numbers
• Understanding the impact of mathematical
  operations on both positives and negative.
• Organizing, Adding, and Subtracting Data in a
  Matrix
• - Allows us to organize related data into a
  format for comparison both within, and to other
  similarly arranged data for the same categories

• Multiplying Real Numbers
• The principles of multiplying positive and
• negative numbers is a key component is
• understanding directional changes in may
  applications
• Use of Distributive Property
• - Being able to distribute a constant factor
  across multiple variables in an equation or
  algorithm
• Combine Like Terms
• - Key tool for simplifying expressions in order
  to more easily evaluate and solve them
• Divide Real Numbers
• - Dividing real numbers is a very common
  occurrence in many areas such as evaluation of
  stock price changes
• Express the likelihood of an event as a
  probability or as odds
• - Probability and statistics applications help us
  understand the likelihood of events from the
  weather, to poker hands, to the complexity of
  unlocking cures for diseases.

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Chapter 2 Properties of Real Numbers,
Helicopter Example
Helicopters are capable of vertical flight
flying straight up and down. Rotor blades
generate an upward force (lift) as they whirl
through the air. Mathematics provide a useful
way of distinguishing between upward and downward
motion. We can use positive numbers to measure
the velocity of upward motion and negative
numbers to measure the velocity of downward
motion.

• Questions for Discussion
• Has anyone ever flown in a Helicopter?
• What are some other real-life situations that you
  might represent with negative numbers?
• How could we describe the average speed and
  direction of the helicopter in the diagram if it
  travels the distance indicated in 15 seconds?

120 ft
180 ft