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.

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