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
Multiplying 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.
-The principles of multiplying positive and
negative numbers is a key component is
understanding directional changes in may applications
Use of Distributive Property
Find the Opposite and Absolute Value of - Being able to “distribute” a constant factor across
multiple variables in an equation or algorithm
a Real Number
- Using absolute values and opposite values
Combine Like Terms
allows us to assess in relative terms, regardless of - Key tool for simplifying expressions in order to more
the direction of the data, e.g. measuring speed
easily evaluate and solve them
and velocity
Divide Real Numbers
Add & Subtract Real Numbers
- Dividing real numbers is a very common occurrence in
-Understanding the impact of mathematical
many areas such as evaluation of stock price changes
operations on both positives and negative.
Express the likelihood of an event as a
Organizing, Adding, and Subtracting
Data in a Matrix
probability or as “odds”
- Probability and statistics applications help us understand
- Allows us to organize related data into a format
the likelihood of events from the weather, to poker hands,
for comparison – both within, and to other similarly to the complexity of unlocking cures for diseases.
arranged data for the same categories
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:
1. Has anyone ever flown in a
Helicopter?
2. What are some other real-life
situations that you might represent
with negative numbers?
3. 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