Topic 1: Real Numbers, Operations, and Basic Properties

Goals and Problem Sets Handout
 

Goal 1: Identify whether a number is real, rational, irrational, and/or an integer (1-3)
Optional extension: Also identify imaginary, whole, and/or natural numbers.

Goal 2: Demonstrate thorough knowledge of the order of operations, including grouping
symbols and the absolute value symbol (1-2 and 1-3)

Goal 3:  Add, subtract, multiply, and divide positive and negative rational numbers (emphasis on fractions, decimals, and mixed numbers).  Use these operations in expressions with absolute values and with multiple operations, following the order of operations.  (1-4, 1-5, and 1-6)

Goal 4:  Define subtraction as the inverse of addition; division as the inverse of multiplication.  Apply these definitions to simplify expressions. (1-4, 1-5, and 1-6)

Goal 5:  Recognize when the Distributive Property does and does not apply.

Goal 6:  Use the Distributive Property for multiplication, division, and factoring (1-7)

Goal 7: Add and subtract like terms; recognize addition and subtraction of like terms as an instance of the Distributive Property. (1-7)

Goal 8: Analyze how properties can be used when simplifying expressions:
• Know the definitions of key properties and the situations in which they apply
• Identify them and give examples. (1-8)

Topic Summary