Elementary Math

The first two days, the class went over the course syllabus and expectations. This includes expectations regarding the course overview, course objectives, grading scale, attendance policy,  ASU/MLFTC policies, course calendar and course communication methods. We then made a social contract in class where we would agree to what we would want our classroom policies to consist of and follow them. The class was assigned to make an introduction post. Introductions included making a poster with a personal introduction and some personal facts that would be uploaded in a discussion board. Then to respond to the person before and greet them in class.

Common Core Standards allow students to learn and understand content with a deeper meaning while building a foundation for advanced studies. These common standards for mathematical practice can be broken up into eight sections. Make sense of problems and persevere into solving them; understand solving complex problemsReason abstractly and quantitively; making sense and using quantitative reasoning Construct viable arguments and critique the reasoning of others; distinguish logic and reasoningModel with Mathematics: analyze mathematical results and reflectUse appropriate tools strategically: identify and use relevant math resources to solve problemsAttend to precision: communicate the meaning and definitions of math vocabulary Look for and make use of structure: look from multiple perspectivesLook for and express regularity in repeated reasoning: look for methods and repetitions

Numeration systems are a collection of properties and symbols agreed upon to represent numbers systematically. We use the Hindu-Arabic number system (0, 1, 2, 3...).Important vocabulary to understand number systems:Digit: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9Numeral: written symbol for digitsNumber: an arithmetical value, expressed by a word, symbol, or figure. Tally Numeration system: how many tally marks there are (teaches children how to count with tally marks in groups of five).Hindu-Arabic System: all numbers constructed from the 10 digits; 0,1,2,3,4,5,6,7,8,9. Place Values: Exponent is how many times to multiply the base power by itself. Base is the number being multiplied. Place values are based on the powers of ten. EX; 458 400 is hundreds place50 is the tenths place8 is the ones place 

Definitions: Natural Numbers: N = {1.2.3.4.5....,} Whole Numbers: W = {0,1,2,3,4,5...}Adding: pushing two amounts togetherAddend: the numbers being addedSum: is the result of addition (the answer) EX: 3 + 2 = 5 3 & 2 are the addends 5 is the sum Ordering whole numbers:> is greater than < is less than ≤ is less than or equal to ≥ is greater than or equal toIt is important to include is when stating less than or greater than as it makes a mathematical difference. EX: one is less than three -> 1<3one less than three -> 3-1 PROPERTIES OF ADDITION: Closure property of addition: if a & b are whole numbers, then a + b are whole numbers. EX: 5 + 3 = 8, whole # + whole # = unique whole number Commutative Property: if a & b are any whole numbers, then a + b = b + aEX: 4 + 2 = 2 + 4Associative Property of Addition: if a, b, and c are whole numbers then (a + b) + c = a + (b + c)EX: (3 + 6) + 1 = 3 + (6 + 1)Identity Property of Addition: there is a unique whole number 0, called the additive property, such that for any whole number a, a + 0 = 0 + aEX: 5 + 0 = 0 + 5Mastering Basic Addition Facts: DoublesDoubles +1: EX: 7 + 8 7 + 7 = 147 + 7 + 1 = 15 Doubles -1: EX: 7 + 88 + 8 = 168 + 8 - 1 = 15How making ten is useful: It makes it easier for students to understand a problem by apply basic addition facts to make sense of a problem and deconstruct one of the addends to make ten.

Subtraction Definitions: Subtraction: taking away something/ difference of two numbersMinuend: the part you start with Subtrahend: the part being taken away Difference: the result of subtraction EX: 5 - 3 = 2 5 is the minuend 3 is the subtrahend2 is the difference MODELING SUBTRACTION:-Take away model: showing the answer using chips, coins, cubes etc.,-Missing Addend Model: Word Problems that are missing a term in an addition sentence that includes at least one other addend and the sum. EX: There are 6 red circles in a set. How can we determine how many circles are hidden? -Comparison Model: Subtraction problem that finds out how much bigger or smaller one set is compared to another. EX: Sarah is 3 ft tall. Her older brother is 5 ft tall. How much taller is Sarah's brother? -Number line measurement model: Subtracts using counting logic. PROPERTIES OF SUBTRACTION: Closure property: works depending on the whole number EX: 3-1 YESAssociative Property of Subtraction: Does not work as (7-3) - 2 = 7 - (3-2) NOIdentity Property of Subtraction: Does hold true EX: 3-0=3 YESCommutative Property of Subtraction: Does not work as 3-1 = 1-3 NOFACT FAMILY: 3 + x = 7. x + 3=77 - x = 3, 7 - 3 = x Standard Algorithm: 344 - 159----------185 Equal Additions Algorithm: Does subtraction through regrouping. 344 + 1 = 345 + 40 = 385- 159 + 1= 160 + 40 = 200------------------------------------------                                       185 Counting Algorithm: Does subtraction through regrouping.344-159=159 + 1 = 160 + 100=260+40=300+44=3441+100+40+44=185

What is Multiplication? -Multiplication is a repetition of things/duplicates, repeated same size of groups of thingsFactor: the numbers being multipliedProduct: The result of multiplicationEX: 2 x 3 = 62 & 3 are the factors, 6 is the productWhat do the factors tell us?1st factor is how many groups2nd factor is what is in each group EX: 2 X 3 = 62 is the first factor, which is 2 groups 3 is the second factor, which is 3 in each group Representing Multiplication: 2 x 3 = 62 x 3 = 6, (2)3 = 6 ab(2)(3)= 6, 2(3)= 6 2xWays to Model multiplication: Groupings: EX: 2 x 3 2 groups of 3 - - -- - -3 x 2 3 groups of 2- -- -- -Repeated addition: EX: 4 + 4 + 4 = 12, 4 x 3 = 12Array model: organized objects arranged in rows and columns Area Model: Unit squares to fill in the spaceNumber line measurement model: using the number line to model multiplication in groups

PROPERTIES OF MULTIPLICATION: Closure Property of Multiplication: a x b = unique whole numberEX: 2 x 3 = 6Commutative Property of Multiplication: a x b = b x aEX: 2 x 3 = 3 x 2Associative Property of Multiplication: (a x b) x c = a x (b x c)EX: (2 x 3) x 4 = 2 x (3 x 4) Identity Property of Multiplication: a x 1 = a = 1 x a EX: 3 x 1 = 3 = 1 x 3Multiplication property of 0: a x 0 = 0 = 0 x aEX: 4 x 0 = 0 = 0 x 4 Distributive Property of Multiplication over Addition: EX: (47 x 97) + (47 x 3)47 (97 x 3)47 (100) = 4700

Division Vocabulary: Division: breaking a big group into smaller groups that are the same size; seeing how many times a number goes into another number Dividend: the amount you have being broken up Divisor: How what you have is being being shared/broken up Quotient: the result of division EX: 6 / 2 = 3 6 is the dividend, 2 is the divisor, 3 is the quotient Two types of word problems that can model division: 1) I have 6 cookies to share with my friend, how many cookies will each get? 6 / 2 = 3; 6 is the amount of cookies, 2 is how many people, 3 is the cookies per person2) I have 6 cookies to put in bags. Each bag holds two cookies. How many bags of cookies do I get?6 / 2 = 3; 6 is the amount of cookies, 2 is the cookies per bag, 3 is bags per person Partitive Model: fair sharingEX: Have 6, break up into 2 groups Quotative Model: subtraction of measurement have 6, break up into 2 in each group What properties does division have? Commutative property: Does Not WorkEX: 8 / 4 = 4 / 8 2 = 1/2 No Associative Property: Does Not Work EX: (8 / 4) / 2 = 8 / (4 / 2) No Identity Property: Does work EX: 6 / 1 = 61 x 6 = 6Distributive property: Only works when distributing divisor. Zero Property of Division: Division by 0 is undefined EX: 6/0 = undefinedTo change division to multiplication distributive property: 6/ ( 4 + 2) 6/1 x ( 1/4+2) = 6/6 = 1OR(6 + 4) /2(6 + 4) x 1/26 x 1/2 + 4 x 1/23 + 2 = 5

Multiplication & Division Fact Family: 2, 3, 6 6 / 2 = 3 6 / 3 = 22 x 3 = 6 3 x 2 = 6You can use fact families to solve. EX: 24 / X = 3 3 x X = 24 24 / 3 = XX x 3= 24 x = 8 Inverse Operations: Inverse operations undo math. Addition and Subtraction are Inverse Operations.EX: 6 + 2 = 8, 8 - 2= 6 Multiplication and Division are Inverse Operations. 6 x 2 = 12, 12 / 2= 6

Base 10 blocks, Area Model, & Standard Algorithm Area Model: EX: 4 x 23, 4 rows of 23 ---- ---- - - ----- ---- - - ----- ---- - - ----- ---- - - - Base 10 blocks: https://i.ytimg.com/vi/UDM47UetyA0/maxresdefault.jpgExpanded Algorithm: 4 x 2320 + 3 x 4---------- 12+ 80---------92Partial Products: 4 x 2323x 4------ 12+ 80 --------92Standard Algorithm: 4 x 2323x 4-------92

Base 10 blocks:Partitive & Quotative base ten models: https://i.ytimg.com/vi/xnXu-DXEAbQ/hqdefault.jpgExpanded Algorithm: 325 / 5 5 + 60 = 65----------5/ 3 2 5 -300----------- 25 - 25------------ 0Partial Quotients: 325 / 5 x 6 5---------------5/ 3 2 5 - 300------------- 25 - 25---------- 0Standard Algorithm: 325 / 5 x 6 5--------------5/ 3 2 5- 3 0 v--------------- 0 2 5 - 2 5 --------------- 0