I. Principles and Standards
II. Chapter 1 – Problem Solving
A) Polya's problem solving principles
B) Problem solving strategies
C) Gauss' insight
D) Pigeonhole principle
III.Chapter 2-Sets and Whole Numbers
A) Section 1 & 2
1) Three ways to describe sets
2) Venn Diagrams – what they are and how to use them to solve problems
3) Union, intersection, complement of sets
4) Empty set and universal set
5) Idea of “equivalent” sets
6) Definition of Natural Numbers and Whole Numbers
B) Sections 3 & 4
1) Models and properties of Whole Number addition and subtraction
2) Models and properties of Whole Number multiplication and division
3) The division algorithm
4) Working with exponents
IV. Chapter 3-Computations with Whole Numbers
A) Section 2
1) Working with different bases
i. Convert from base 10 to base 5 and vice versa
B) Section 3
1) Algorithms for addition /subtraction of whole numbers
i. How they are developed using mats, strips, units; place value cards, place
value
diagrams, etc.
2) Algorithms for multiplication/division of whole numbers
i. How they are developed
ii. Expanded notation
iii. Long division, short division, and scaffold method
V. Chapter 4-Number Theory
A) Sections 1 & 2
1) Prime, composite, unit numbers
2) Definition of “a divides b”, “a is a factor of b ”, “b is a multiple of a”
3) The statement of the Fundamental Theorem of Arithmetic
4) Finding prime factors
i. Tree method, short division
5) Prime product representation
6) Prime power representation
7) How many primes are there?
8) Divisibility tests for sums /differences, for 2, for 5, for 10, for products,
for 3, for 9, for
7, for 11, for 13, and for powers of 2
B) Section 3
1) Euclidean Algorithm
2) GCD and LCM
i. Finding by set intersection, prime-power representation, and Euclidean
Algorithm
VI. Chapter 5-Integers
A) Representing the integers with colored counters
B) Addition/subtraction of integers with colored counters
C) Clock Arithmetic
D) Just kidding
VII. Chapter 6-Fractions and Rational Numbers
A) Section 1
1) Models of fractions (and what three questions must each model answer)
2) Equivalent fractions & simplest form
3) Ideas of common denominator and least common denominator
4) Definition of the set of Rational Numbers
5) How to compare rational numbers
B) Sections 2 & 3
1) Addition/subtraction and multiplication/division of rational numbers
i. Know the procedure and the various models
2) The density property of the rational numbers
VIII. Chapter 7- Decimals and Real Numbers
A) Section 1
1) Representations of decimals (i.e., mats, strips, units, etc.)
2) Negative exponents
3) Multiplying and dividing by powers of 10
4) Terminating and nonterminating decimals
5) Repeating and non-repeating decimals
6) Converting decimals to fractions and fractions to decimals
7) Definition of the Rational Numbers
8) Ordering decimals
9) Definition of irrational numbers and of the Real Numbers
10) Examples of irrational numbers
11) Determining the rationality/irrationality of numbers
B) Section 2
1) Rounding decimals
2) Adding/subtracting and multiplying/dividing decimals
3) Decimal expansion of fractions
4) Scientific notation and significant digits
C) Section 3
1) Definition of Ratio and proportion
2) Finding ratios and condition for proportion
3) “constant of proportionality”
D) Section 4
1) Percent
i. Definition
ii. Decimal to percent and percent to decimal
iii. Solving problems
IX.Number Systems
A) Know the definitions of all the numbers systems that we've talked about
B) Know how they relate together via a Venn Diagram'
C) Explain which are subsets
D) Explain which are not subsets by using a counterexample
