MAT156 FALL2013

1. Understand the problem.

2. Devising a Plan.

3. Carrying out the plan.

4. Looking back. (Check!)

Arithmetic sequence

Geometric sequence

Fibonacci sequence

Hindu-Arabic Numeration System

Talley Numeration System

Egyptian Numeration System

Babylonian Numeration System

Mayan Numeration System

Roman Numeration System

Other Number Base System

One-to-One Correspondence

Equivalent Sets

Cardinal Numbers

Universal Set

Subsets

Set Intersection

Set Union

Set Difference

Numer Line (Measurement) Model

Ordering Whole Numbers

Addition Properties

Closure Property

Commutative Property

Associative Property

Identity Property

Basic Addition Facts

Counting on

Doubles

Making 10

Counting back

Addition Algorithms

Subtraction Algorithms

Equal-Addition Algorithms

Multiplication of Whole Numbers

Repeated-Addition Model

The Array and Area Model

Cartesian-Product Model

Properties of Whole Number Multiplication

Closure propery of multiplication of whole numbers

Commutative property of multiplication of whole numbers

Associative property of multiplication of whole numbers

Identity property of multiplication of whole numbers

Zero multiplication property of whole numbers

Distributive property of multiplication over addition and subtraction

Division of Whole Numbers

Set (Partition) model

Missing-Factor model

Repeated subtraction model

The Division Algorithm

Relating Multiplication and Division as Inverse Operation

Division by 0 or 1

n divided by 0 is undefined

0 divided by n=0

0 divided by 0 is undefined also

Order of Operation

Parenthesis, Exponents, Multiplication or Division, Addition or Subtraction

Multiplication Algorithms

Single digit number times two digit number

Multiplication with two-digit factors

Lattice multiplication

Division Algorithms

Functions as Rules

Functions as Machines

Functions as Equations

Functions as Arrow Diagrams

Functions as Tables and Ordered Pairs

Functions as Graphs

Sequences as Functions

Every function is a relation, but not every relatioin is a function.

Scientific Notation

Dividing Decimals

Mental Computations

Rounding Decimals

Estimating Decimal Computations

Rouding- off Errors

Division problem or solution to a multiplication problem

Partition, or part, of a whole such as Joe ate 1/2 of the pizza for lunch.

Ratio such as the ratio of girls to boys in the class was ten to twelve

Probability

Equivalent or Equal Fractions

Simplifying Fractions

Equality of Fractions

Ordering Rational Numbers

Denseness of Rational Numbers

Area Model

Number-line Model

Addition of Rational Numbers with like Denominators

Addition of Rational Numbers with unlike Denominators

Additive Inverse Property

Addition Property of Equality

Multiplicative Identity

Multiplicative Inverse (reciprocal)

Distributive Property of Multiplication Over Addition

Multiplication Property of Equality

Multiplication Property of Inequality

Multiplication Property of Zero

Chip Model for addition-Black chips are used to represent positive integers and negative integers are red.

Charged-Field Model- Similar to chips but used the positive (+) and negative (-) charges.

Number Line Model- Always start at zero and move line to first number, then go to second number.

Pattern Model- Addition of integers can also be motived by using patterns of addition of whole numbers.

Absolute Value-The distance between the point corresponding to an integer and 0 is the absolute value of the integer.

For every integer a, there exists a unique integer -a, the additive inverse of a.

Chip Model for Subtraction

Charged-Field Model for Subtraction

Number Line Model for Subtraction

Pattern Model for Subtraction

SubtractionUsing the Missing Addend Approach

Subtraction Using Adding the Opposite Approach

Properties of Subtraction

Patterns Model for Multiplication of integers-3(-2)=-6, 2(-2)=-4, 1(-2)=-2

Chip Model and Charged-Field Model for Multiplication

Number-Line Model

Properties of Integer Multiplication

The quotient of two negative integers, is a positive integer and the quotient of a positive and negative integer, is negative.

The order of operations: parenthesis, exponents, multiply/divide left to right/ add/subtract left to right.

If b l a, then b is a factor, or divisor, of a, and a is multiple of b.

Divisibility rules

Numbers in which there are only two factors or positive divisors. (ex) 2, 3, 5, 7

Numbers in which there are more than two factors or positive divisors. (ex) 4, 8, 12, 16

Factorization- Composite numbers can be expressed as product of two or more whole numbers greater than 1.

Prime factorization- factorization containing only prime numbers.

Factor Tree

Ladder Model

Number of Divisor

Colored Rods Method

The Intersection of Section Method

Prime Factorization Method

Calculator Method

Ladder Mehtod of Division by Primes Method

Number-Line Method

Colored Rods Method

Intersection of Sets Method

Prime factorization Method

Ladder Method or The division by Primes Method