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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.

Required tasks/resources Optional tasks/resources
Video: Classifications of Numbers (20 min) Textbook pp. 17 - 18
Problem set: 1-3 Part 1 Converting repeating decimals to fractions (Ask Dr. Math)
In-class activity: Classification of Numbers diagram Video: Does .999... equal 1?


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

Required tasks/resources  Optional tasks/resources
 Video:  Order of Operations (21 min)  Textbook pp. 9 - 12
 Problem Set: 1-2  Your notes/resources from 6th and 7th grade
Problem Set: 1-3 Part 2  Order of Operations online game
   Order of operations jigsaw puzzle
   Additional practice handouts
   "Exponents" and "Zero and Negative Exponents" GSP activities


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)

 Required tasks/resources  Optional tasks/resources
 Video: Addition and Subtraction (13 min) Textbook Lessons 1-4, 1-5, and 1-6
Problem Set: 1-4 Your notes/resources from 6th and 7th grade
Problem Set: 1-5 "Fractions in a Nutshell" handout
Video:  Multiplication and Division (24 min) "Decimals Review" handout
Problem Set 1-6  "Mixed Numbers Review" handout
  "Rational Addition and Subtraction" handout
   "Adding Integers" GSP activity
  "Subtracting Integers" GSP activity
  Video: Why is Negative times Negative Positive?
  Video: On Dividing by Zero


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)

 Required tasks/resources  Optional tasks/resources
 Video: The Distributive Property (aka Disobeying the Order of Operations) (15 min) Textbook Lesson 1-7
In-class game: To Distribute, or Not To Distribute? Algebra Battleship: The Distributive Property practice game
 Problem Set 1-7 Algebra Battleship: Like Terms, Distributive Property, and Evaluating (positive numbers only)


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)

 Required tasks/resources  Optional tasks/resources
 Video: More Properties (14 min) Textbook Lesson 1-8
 Problem Set 1-8 "Proof Practice" handout
Algebraic Properties Review Sheet "Using Number Properties" handout
 "Properties Practice" handout "Practice 1-8" handout

"The Commutative Property" and
"The Associative Property" GSP activities


Topic Summary

 Required tasks/resources

Article: 8 Tips for Studying Smarter

Problem Set:  Chapter Test Assignment

 Optional tasks/resources