| Final Exam List of Topics June, 2009
Chapter 1 Problem Solving Problem solving � Polya�s 4 step process. Chapter 2 Sets, Numbers and Numerals 2.1 Sequence, mulitset, set, element, subset, proper subset, empty set, universal set, Venn diagrams, intersection, union, complement. 2.2 Number: cardinal #, ordinal #, identification #. measurement, unit, magnitude. Number vs. Numeral 2.3 Hindu-Arabic Numeration System, numeration systems (tally, grouping (Roman Numerals), multiplicative grouping (coins), and positional-base (Hindu-Arabic)), base, place-value, expanded form, numbers expressed in different bases. Arithmetic, data structures and Algorithms on data structures Chapter 3 Counting and The Natural Numbers Counting, �counting chant�, �skip counting�, �counting on�, one-to-one correspondence Ordination vs. Cardination 3.1 Addition and Subtraction Concrete, representational, and symbolic models. Addition: set model, number line model (a measurement model); Subtraction: set model, number line model, the �missing addend� metaphor (subtraction as the �inverse� operation of addition, the Jeopardy idea). 3.2 Multiplication and Division Multiplication: set model, array model, area model (a measurement model), repeated addition metaphor; Division: set model, repeated subtraction metaphor, the �missing factor� approach Chapter 4 Calculation, Algorithms, and Calculators 4.2 Roman numerals (not subtractive notation), the Roman Counting Table, the lattice method of multiplication, Egyptian multiplication and division by �duplation� Chapter 5 Number Theory 5.1 Divisibility : Divides, divisor, factor, multiple, prime, composite, Sieve of Eratosthenes, factor tree, Fundamental Theorem of Arithmetic. 5.2 GCD (or GCF) and LCM Finding GCD using the intersection method, the prime factorization method, the Euclidean algorithm, finding LCM. Chapter 6 Fractions 6.1 Fraction, numerator, denominator, rational number, proper and improper fractions, mixed numbers, set model, area model, number line model, fraction strips, simplest or lowest terms 6.2 Addition and Subtraction of Fractions Common denominator, least common denominator (LCD), addition and subtraction of fractions. Use of area models and fraction strips 6.3 Multiplication and Division of Fractions Multiplication: Area model (paper folding example) Chapter 7 Decimals 7.1 Expanded form, converting fractions to decimal form, converting decimal to fraction form, terminating decimals. 7.2 repeating and non-repeating decimals, rational and irrational numbers. Chapter 12 Geometry 12.1 The Van Hiele Theory of how children develop geometric concepts. |