Kelley Cannady Elementary Mathematics

Strategies for the addition of whole numbers include:Counting On: Counting one by one, starting from the larger number, until you reach your answerSet Model: Modeling disjoint numbers and combining themNumber Line Model: A strategy that visually draws it out and counts it on. Others to know: Doubles, Making 10, Counting BackWhole Number Addition Properties:Closure Property: The sum of two whole numbers exist and is a unique whole numberCommutative Property: "order property" a+b=b+aAssociative Property: (a+b)+c=a+(b+c)Identity Property: a+0=a Strategies for the Subtraction of Whole Numbers Include:Take Away Model: A visual way to see objects being taken awayMissing Addend: a-b=____ can be found by b+___=aComparison Model and Number Line Model are also includedFirst number must be bigger otherwise it will not equal a whole number.

Division:Dividend: A number that is divided by anotherDivisor: A number dividing another numberQuotient: The answer in a division problemInverse: ReversedPartition: DividingMultiplication:Factors: What's being multiplied togetherProduct: The answer in a multiplication problemMultiplication has the same properties as addition. These properties do not work for subtraction and division.Strategies for Modeling the Multiplication of Whole Numbers: Repeated-Addition Model: 4x3=4+4+4=12Array and Area Model: Draw a grid and count the points of intersection. Can be used for tiles and other area models.Cartesian Product Model: Create a Tree. Can be used for situations like how many outfits someone can wear. Whole Number Multiplication Properties: Closure Property: If a and b are whole numbers then axb is a whole unique numberCommutative Property: axb=bxaAssociative Property: (axb)xc=ax(cxb)Distributive Property: 5x(3+4)=5x7=5x3+5x4

Examples of Whole Number: {0,1,2,3,4,5,6,7,8.....}Cannot be a decimal, cannot be negativeOther Words to Know: Cardinal Number: A number representing a quantityBinary Operations: addition, subtraction, multiplication, and divisionDisjoint: Having nothing in commonFinite: a defined amountSet: A group of numbers...: "and the pattern continues">,<: greater than, less thanBasic addition facts: Those involving a single digit and a single digit

Divisibility:Definition: A set of rules that can quickly determine if one whole number is divisible by another.How To Tell If A Number is Divisible By:2: The last digit in a number is divisible by 2 ex:1743: The sum of the digits is divisible by 3 ex: 732 4: The last two digits in a number is divisible by 4 ex: 2205: The last digit is a 5 or a 0 ex: 2106: The number is divisible by both 2 and 3 ex: 7328: The last three digits are divisible by 89: The sum of the digits is divisible by 910: The last digit is 0

Prime and Composite Numbers:Prime Number Definition: Can only be divided into equally by itself and 1. Ex: 3,5,7,11,13,etc.Composite Number Definition: A whole number that can be divided equally by more numbers than itself and 1.

Greatest Common Divisor: Definition: The largest positive integer that divides each of the integers. Can be found using intersects model and prime factorizationLeast Common Multiple:Definition: The smallest number they can both divide equally into.Can also be found using intersects model and prime factorization

In the addition and subtraction of fractions, the denominator must be the same. Example: 1/3+1/9= 3/9+1/9=4/9

When Multiplying fractions you multiply the top by the top (multiply numerators together) and the bottom by the bottom (multiply denominators together) For example: 4/5*1/4= 4/20but the fraction must be simplified and it can be reduced to 1/5Dividing fractions is done by flipping the second number and multiplying it to the other fraction, for example: 4/5*2/7= 4/5*7/2=28/10 and can be reduced to 14/5

Definition of Probability: P(A)= Number of elements of A/Number of elements of S Or in other words; Number of times the event is likely to occur/Number of trials

Permutation: nPr= n!/(n-r)!This equation is used in a situation where order matters such as when choosing who wins 1st, 2nd, or 3rd place. The variable n is the total number of options available and the variable r is the number of things you're going to pick. The ! means that the number will be multiplied in descending order such as 4! is multiplied as 4*3*2*1Combination nCr= n!/r! (n-r)!The equation for combinations is when order does not matter such as when you are see how many different ways you can organize a group. The variable n is the total number of options available and the variable r is the number of things you're going to pick. The ! means that the number will be multiplied in descending order such as 4! is multiplied as 4*3*2*1

Finite Decimals- Are decimals that have a definite end. Examples of finite decimals include decimals such as .12433456 or .12 Theorem- fraction a/b can be written as a terminating decimal if, and only if, the prime factorization of the denominator contains no primes other than 2 or 5

Percent=per 100Percentage can be found by dividing the numerator by the denominatorfor example to find the percentage of 4/5 you would divide 5 into four and get .8 since percentages are not decimals, we would move the decimal twice to the right and get 80%There are many real life applications for percentage such as taxes and sales.

Repeating Decimals-will have a bar over the repeating digits and go on infinitely. Repeating digits are not very accurate so it is best to leave it in fraction form if at all possible. For example 1/3 in decimal for is .333......

Adding- When adding decimals the decimals should line up Subtracting- Same rule as addingMultiplying- When multiplying decimals need not line up but the final product should have the decimal moved the amount of spaces of both decimals added upDividing- when dividing, the decimal that is the divisor should have the decimal moved to the end. The dividend should then be given as many 0s to the end of the number that is equal to the number of decimal places moved.