Scientific Notation: Used when you have either a very large or small number. EX large: 93,000,000=9.3x10power of 7 EX small: 0.000078=7.8x10-power of 5.
Dividing decimals
Multiplying decimals
Subtracting decimals
Adding decimals
Dividing fractions
Multiplying fractions
Subtracting fractions
Adding fractions
Integers
Least Common Multiple
4. Ladder method
3. Prime factorization method
2. Intersection of Sets Method
1. Number line method
The least common multiple of a and b is the least natural number that is simultaneously a multiple of a and multiple of b.
Greatest Common Divisor
3. Ladder method
2.Prime factorization method
1. The intersection of Sets Method
The greatest common divisor of two natural numbers a and b is the greatest natural number that divides both a and b.
Composite numbers
Composite numbers are numbers that have more than 2 factors or positive divisors. ex. 4,6,8,9,10,12,14,15,16,18,20
Prime numbers
Prime numbers are numbers that only have 2 factos or positive divisors. ex. 2,3,5,7,11,13,17,19
Divisibility
A number is divisible by 11 if the sum of the digits in the places that are even powers of 10 minus the sum of the digits in the places that odd powers of 10 is divisible by 11. ex. 57,729,364,583
A number is divisible by 10 if the number ends with 0. ex. 200
A number is divisible by 9 if the sum of digits is divisible by 9. ex. 126
A number is divisible by 8 if the last 3 digits are divisible by 8. ex. 1,888
A number is divisible by 6 if the number is divisible by both 2 and 3. ex. 126
A number is divisible by 5 if the number ends with 0 or 5. ex. 205
A number is divisible by 4 if the last two digits are divisible by 4. ex 424
A number is divisible by 3 if the sum of the digits is divisible by 3. ex. 123
A number is divisible by 2 if the number ends with an even number. ex. 202
Integer Division
Divide and positive and a negative the answer is negative
Divide a positive and a positive the answer is positive
Integer Multiplication
Multiply a positive and a negative the answer is negative
Multiply a positive and a positive the answer is positive
Integer Subtraction
Missing addends
Adding opposites: "Keep change change"
3. Pattern model for subtraction
Integer Addition
Identity property
Associative property
Communitive property
Closure property
3. Absolute value
2. Number line
1. Chip model
Operations
Properties
Zero multiplication: Any number multiplied by 0 is 0 2x0=0
Identity: Any number multiplied by 1 is the same number 2x1=2
Closure: The set of whole numbers is closed under multiplication.
Commutaive: a+b=b+a
Associative: a+(b+c)=(a+b)+c
Distributive: a(b+c) =ab+ac
Order of Long Division
Correct/Circle
Bring Down
Check
Subtract
Multiply
Divide
Order of Operation
Subtraction
Addition
Multiplication
Division
Exponents
Parenthesis
Teaching Addition and Subtraction Facts
Countin by Doubles
Counting by 10s
Counting Backwards
Fact Family
Number Line
Counting On
Numbers Blocks
Functions
Arrow diagram
Make a graph
Make table
The rule
Ordered pairs
Vocabulary
Relations: A set of input and output values. Usually represented in ordered pairs.
Function: A relation in which every input value is paired with exactly one output value.
Division: The operation of dividing multiple numbers into each other.
Addition: The opperation of adding two or more numbers.
Subtraction: The operation of taking away/subtracting two or more numbers.
Multiplication: An operation that gives the total number when you join two or more numbers
Product: The result of multiplying two or more numbers
Difference: The result of subtracting one number from another.
Quotient: The answer after dividing one number into another
Divisor: A number by which another number is to be divided
Dividend: A number divided by another
Sum: Total number after adding two or more numbers
Addends: Numbers added together
Sets
Cartesian Pruducts
For any sets A and B, the Cartesian produce of A and B, is the set of all ordered pairs such that the first componet of each pair is an element of A and the second componet of each is an element of B.
Properties of Set Opperations
1. Associative Property 2. Distributive Property
Set Difference
The colplement of A relative to B, is the set of all elements in B that are not in A.
Set Union
The union of two sets A and B, is the set of all elements in A or B.
Set Intersection
The intersection of two sets, A and B, is the set of all elements common to both A and B.
Subset
B is a subset of A, if every element of B is an element of A.
Universal Set
Universal set denoted U, is the set that contains all the elements being considered in a discussion. A Venn diagram can be used to illustrate sets.
Cardinal Numbers
The cardinal number of a set denotes the number of elements in a set. ex. (a,b) (r,s),@,#) are equivalent to each other because they each have two elements in their set.
Equivalent Sets
Two sets A and B are equivalent, if and only if there exists a one-to-one correspondence between the sets.
One to One Correspondence
If the elements of sets P and S can be paired so that each element of P there is exactly one element of S, then the two sets P and S are considered one to one correspondence
Numeration Systems
Base Five
The following website gives a detailed description of base five
Roman Numeration System
l=1, V=5, X=10, L=50, C=100, D=500, M=1000
Tally Numberation System
This method uses single strokes or tally marks to represent each item being counted. ( l,ll,lll)
Hindu-Arabic
All numbers come from the 10 digits (0,1,2,3,4,5,6,7,8,9)
Problem Solving
Geometric Sequence
Each successive term of a geometic sequence is obtained from its predecessor by multiplying by a fixed number, the ratio. (Ratio can never =0) ex2,4,8,16,32...
Fibonacci Sequence
Sequence when the sum of the first two numbers becomes the third number, and so on. ex 1,1,2,3,5,8,13,21...
