MAT156 FALL2013

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Chapter.5 Integers

Greatest Common Divisor and Least Common Multiple

Least Common Multiple

Ladder Method or The division by Primes Method

Prime factorization Method

Intersection of Sets Method

Number-Line Method

Greatest Common Divisor (factor)

Ladder Mehtod of Division by Primes Method

Calculator Method

Prime Factorization Method

The Intersection of Section Method

Colored Rods Method

Prime and Composite Numbers

Prime Factorization

Number of Divisor

Ladder Model

Factor Tree

Prime factorization- factorization containing only prime numbers.

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

Composite Numbers

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

Prime Numbers

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

Divisibility

Divisibility rules

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

Multiplication and Division of Integers

Order of Integers

Order of Operations on Integers

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

Integer Division

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

Multiplication of Integers

Properties of Integer Multiplication

Number-Line Model

Chip Model and Charged-Field Model for Multiplication

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

Add and Subtract integers

Integer Subtraction

Properties of Subtraction

Subtraction Using Adding the Opposite Approach

SubtractionUsing the Missing Addend Approach

Pattern Model for Subtraction

Number Line Model for Subtraction

Charged-Field Model for Subtraction

Chip Model for Subtraction

Uniqueness of the Additive Inverse

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

Integer Addition

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

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

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

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

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

Chapter6. Rational Numbers

Division of Rational Numbers

Properties of Multiplication of Rational Numbers

Multiplication Property of Zero

Multiplication Property of Inequality

Multiplication Property of Equality

Distributive Property of Multiplication Over Addition

Multiplicative Inverse (reciprocal)

Multiplicative Identity

Properties of Addition for Rational Numbers

Addition Property of Equality

Additive Inverse Property

Mix Numbers

Estimation with Rational Numbers

Subtraction of Rantional Numbers

Addition of Rational Numbers

Addition of Rational Numbers with unlike Denominators

Addition of Rational Numbers with like Denominators

Number-line Model

Area Model

The sets of Rational Numbers

Denseness of Rational Numbers

Ordering Rational Numbers

Equality of Fractions

Simplifying Fractions

Equivalent or Equal Fractions

Uses of Rational Numbers

Probability

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

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

Division problem or solution to a multiplication problem

Chapter7. Decimals

Ordering Repeating Decimals

Repeating Decimals

Operations on Decimals

Algorithm for mulptiplying decimals

Rouding- off Errors

Estimating Decimal Computations

Rounding Decimals

Mental Computations

Dividing Decimals

Scientific Notation

Algorithm for addition and subtraction of terminating decimals

Ordering Terminating Decimals

Terminating Decimals

Chapter 4. Functions

Relations

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

Ways to represent functions

Sequences as Functions

Functions as Graphs

Functions as Tables and Ordered Pairs

Functions as Arrow Diagrams

Functions as Equations

Functions as Machines

Functions as Rules

Chapter3. Whole Numbers and Their Operations

Algorithms for Whole-Number Multiplication and Division

Division Algorithms

Multiplication Algorithms

Lattice multiplication

Multiplication with two-digit factors

Single digit number times two digit number

Multiplication and Division of Whole Numbers

Order of Operation

Parenthesis, Exponents, Multiplication or Division, Addition or Subtraction

Division by 0 or 1

0 divided by 0 is undefined also

0 divided by n=0

n divided by 0 is undefined

Relating Multiplication and Division as Inverse Operation

The Division Algorithm

Division of Whole Numbers

Repeated subtraction model

Missing-Factor model

Set (Partition) model

Properties of Whole Number Multiplication

Distributive property of multiplication over addition and subtraction

Zero multiplication property of whole numbers

Identity property of multiplication of whole numbers

Associative property of multiplication of whole numbers

Commutative property of multiplication of whole numbers

Closure propery of multiplication of whole numbers

Multiplication of Whole Numbers

Cartesian-Product Model

The Array and Area Model

Repeated-Addition Model

Algorithms

Equal-Addition Algorithms

Subtraction Algorithms

Addition Algorithms

Set model

Basic Addition Facts

Counting back

Making 10

Doubles

Counting on

Addition Properties

Identity Property

Associative Property

Commutative Property

Closure Property