Elementary Mathematics

Sequence: an oredered list of objects, events, or numbers which may be refered to as elements of the sequence, memers of the sequence or terms.Arithmatic Sequence: sequences of numbers with a common difference; example: -3,-1,1,3,5 (add 2)Geometric Sequence: sequences of number with a common ratio; example: 8,-4,2,-1 (divide by-2)Recurrence Relationship Sequence: a sequence in which the current term is dependent on the previous term(s); example: 15,3,12,-9,21,-30,51(subtract from previous term)

Types of Algorithms:The Standard AlgorithmPartial SumDenominate NumbersExpanded NotationLeft to Right AdditionScratch Addition MethodAny Column FirstLow Stress Addition

Addend: Any number being addedInverse Operation: An opposite operation (ex. addition and subtraction are inverse operations)

Three Major Models:Repeated Addition (Discrete)Repeated Addition (Continuous)Area Model

Multiplication Properties:Closure PropertyCommunative PropertyAssociative PropertyIdentity PropertyZero PropertyDistributive Property

Developmental Fraction Constructs:-Part-Whole: 2/3 of the class went on a field trip-Measure: For 5/8 use five 1/8 unit fractions to count or measure-Division: Sharing $10.00 with four people is 4/10 -Operators: 4/5 of 20 feet -> 4/5*20= 80/5 =16-Ratio: 1/4 can mean the probability is one in four.

Notes:-Writing and saying decimals(.12468 you would say twelve thousand, four hundred sixty-eight hundred-thousandTHS)-Using base ten blocks (: if a flat equals 1, then a long equals 1/10 and a unit equals 1/100 and a cube would equal ten. 1.4= one flat and 4 longs) ComparisonExpanding decimals (34.26 (3x10)+(4x1)+(2x 1/10)+(6x 1/100) )

Adding and subtracting decimals: Decimals line up with each other because they are always in the same place value spot.

Types of Strategies:Look for a PatternExamine a Related ProblemExamine a Simpler CaseMake a TableIdentify a SubgoalMake a DiagramUse Guess and CheckWork BackwardWrite an Equation

Types of Numeration Systems:Hindu-Arabic Numeration SystemTally Numeration SystemEgyptian Numeration SystemBabylonian Numeration SystemMayan Numeration SystemRoman Numeration SystemOther Number-base System

Subtraction Models:Take AwayMissing AddendComparison

Properties for addition do NOT apply to subtraction

The Two Major Models-Partition: Splitting a quantity into groups and determining the size of each groupMeasurement Model: Splitting a quantity into groups and finding the number of groups formed.

Properties for mltiplication do not work for division

Divisibility Tests-2: ones digit is 0,2,4,6, or 83: sums of digits is divisible by 34: the number formed by the last two digits is divisible by 45: ones digit is 0 or 56: the number is even and the sum of digits is divisible by 38: number formed by the last three digits is divisible by 89: sum of digits is divisible by 910: ones digit is 0

Notes:-The opposite of an integer is written as -a-Chip colors are a great manipulative to use for opposites of integers-The absolute value of something is its magnitude-The absolute value is the distance of the given number to zero-When adding a one negative to one positive is called a zero pair

Using a number line is a great way to see how division of fractions works.