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MAT 156 Topics for UNIT #3
5-3, 5-4, 5-5, 6-1, 6-2, 6-3
Printable PDF version

*My Animated Flash tutorials available are listed as blue web-page links (more are currently being created, so check back!)
*Red links are to other websites, like the Virtual Manipulative Library (use the back button on your browser to get back to this website)

5-3: Divisibility:

• Definition “a divides b” (glossary)
• Theorem 4-1
• Theorem 4-2
• Divisibility rules for 2, 3, 4, 5, 6, 7 (not in book), 8, 9, 10, 11 (divisibility tests)
• Be able to use 0 (zero) correctly and give examples of when it does and does not work (a divides b)

5-4: Prime numbers:

• Definition (glossary) ( Sieve of Eratosthenes )
• Decide whether a number is prime (*largest prime needed to test? THM 4-6) (prime test)
  

5-4: Composite numbers:

• Definition (glossary)
• Factoring composite numbers (not prime factorization)
  • visually ( rectangles)
  • numerically
• Prime factorization (virtual) - tree or box method
• Fundamental Theorem of Arithmetic (glossary) (THM 4-3)
• THM 4-4
  

5-5: Greatest Common Factor (GCF = GCD: Greatest Common Divisor):

• Intersection of sets method
• Prime factorization method (venn diagram)
• Euclidean Algorithm method
• Be able to tell what it is used for

5-5: Least Common Multiple (LCM = LCD: Least Common Denominator):

• Intersection of sets method
• Prime factorization method (venn diagram)
• Euclidean Algorithm method
• Be able to tell what it is used for

6-1: Introduction to Fractions:

• Set of rational numbers
• Difference between rational numbers and fractions
• Numerator
• Denominator
• Represent a particular fraction (draw a picture using circles or rectangles & shading)
• Equivalent fractions ( definition and.interactive tutorials)
• Mixed numbers (tutorials in individual add/subtract sections)
• Improper fractions (be able to convert back and forth)
• Estimating the value of a fraction (and decide whether estimation is high or low)
• Fundamental Law of Fractions
• Simplifying fractions (using the Fundamental Law of Fractions)

6-2: Adding Fractions:

• Adding fractions –like and unlike denominators( visual and/or arithmetic)

6-2: Subtracting Fractions:

• Subtracting fractions
  • Visual (with borrowing)
  • Regrouping (borrowing)
  • Improper fractions
• Alternate Methods
• Up-the-hill
• Equal addition
• Negative numbers (expanded algorithm)

6-3: Multiplying Fractions:

• Multiplying fractions - Hyperstudio stacks
  
  • First number whole = "repeated addition"
  • second number whole = "part of a set "
  • Visual (circle pieces or rectangles = array) ( intro:1 fraction) (2 fractions) (polygons)
  • Multiplying Mixed numbers:
    • Change to improper
    • Expanded algorithm (vertical)
    • Distributive property (horizonal = FOIL)

6-3: Dividing Fractions:

• Dividing fractions - Hyperstudio stacks
  • Count elements (“size” of set)
  • Count sets (how many sets that size)(polygon model)