Elementary Mathematics

Week 1:Numerals:numeral- Written symbol for the digitsnumber- an arithmetical value, expressed by a word, symbol, or figure.digit- 0,1,2,3,4,5,6,7,8,9roman numerals: (I, V, X, L, C, D, M)Hindu-arabic equivalent: (1,5,10,50,100,500,1000) ( Anything to the power of 0 is 1)

Week 2:Base 2 : 2^2, 2^2, 2^4, 2^8Base 5: (uses 1-5)5^0, 5^1, 5^2, 5^3, 5^4, 5^5Natural numbers:N=(1,2,3,4,5...) *Think about counting things in nature*Whole numbers:W=(0,1,2,3,4,5...)vocabulary for addition:Addend: The numbers being addedSum: Is the result of addition EX: 3+2=5Properties of Addition:Closer property: If a and b are whole #'s, then a+b is a whole # (5+3=8) *There is only one possible answer*Commutative property: If a and b are any whole #'s, then a=b= b+a (3+5= 5+3)Associative property: If a,b and c are whole #'s, then (a+b) + c= a+ (b+c) ( 3+4) + 5= 3+ (4+5)Identity property: There is a unique whole # 0, called the additive identity, such that for any whole # a,a+0=a=0+a (5+0=5=0+4)ordering whole numbers:> = is greater than < = is less than> = is greater than or equal to< = is less than or equal toalways make sure to put "is"

Week 3Subtraction Vocabulary:Minuend- The part you start withSubtrahend- The part being taken awaydifference- Is the result of subtraction Ex: 5 - 3 = 2Different models to help subtract are:take away modelmissing addend modelcomparison modelnumber line modelProperties of subtraction:Closure property- 3-2=1Commutative property- 3-1= 1-3Associative property- (7-3)-2 = 7- (3-2) This one cannot workIdentity property- 3-0=33 different algorithms:standard equal- additioncounting up Multiplication Vocabulary:Factor- The numbers being multipliedProduct- The result of multiplication Ex: 2 x 3 = 6In multiplication the first factor for example (in 2x 3) 2 is the 1st factor which means how many groups, then the 3 is the 2nd factor which means what is in each group.Properties of multiplication:closure property- a x b= Unique whole number (2x3=6)Commutative property- a x b=b x a ( 2x3 = 3x2 )Associative property- (a x b) = c = a x (b x c) / ( 2 x 3) = 4 = 2( 3 x 4)Identity property- a x 1 = a = 1 x a/ ❤️ x 1 = ❤️= 1 x ❤️Multiplication property- a x 0 = 0 = 0 x a

Week 4 Division vocabulary: Dividend- The amount you have that is being shared, divided upDivisor- How what you "have" is being shared, broken upQuotient- The result of division Ex: 6 ÷ 2 = 3There are 2 types of division:Partitive model: For sharing have 6, break up into 2 groupsQuotitive model: Subtraction or measurementProperties of division:Commutative property: 8 ÷ 4 = 4 ÷ 8 ( This cannot work)Associative property: (8 ÷ 4) ÷ 2 = 8÷(4÷2) (This can also not work)Identity property: 6 ÷ 1 = 6 ( 1 x 6 = 6)zero property of division:Division of 0 : Division by 0:0 ÷ 6 = 0 6 ÷ 0 = undefined6 x 0 = 0 0 x __undef__ = 6 0 ÷ 0 = undefined 0 x __Undef__= 0

Week 5Definition of a^n: If a, the base, and n, the exponenr, are whole #'s and n =/ 0 then.1.For every whole number a, and natural numbers m an n. Ex: (a^n)^n = d^n). 3^4)^2 = 3^4= 3x3x3x32.For every whole number a =/ 0, and natural numbers m and n. Ex: (a^m x a^n= a^m+n). 3^4 x 3^5 3^4+5 = 3^9 3^4 x 3^5 = 3^9 3x3x3x3 x 3x3x3x3x3 = 3^9 3.For whole numbers a and b and natural numbers n. Ex: a^n - b^n = (ab)^n. 3^4 x 2^4, 3x3x3x3 x 2x2x2x2 (3x2) (3x2) (3x2) (3x2) = (3x2)^4order of operations: parenthesis ()Exponents ( x )^bMultiplication ( x )Division ( ÷ )Addition (+)Subtract ( - )How would we explain odd numbers and even number to students:match pairs in boxes- odd if there are leftoversshare into two equal groupsmaking partners ( w/ students)any number that could be divided by 2- odd add if not whole #show on a number lineends in 0,2,4,6,8, its evenEven number: A number when divided by 2 has no remainderOdd number: A number when divided by 2 has a remainder of 1using 10 blocks for division:

Week 6Divisibility rules:6: A number is divisible by 6 if the number is divisible by 2 and 3. Ex: 3726. 3+7+2+6= 18(2 x 9 = 18) divisible by 2 = yes(3 x 6 = 18) divisible by 3 = yes7: No rule, Do division8: A number is divisible by 8 if the last 3 digits is a number that is divisible by 8 Ex: 2568 568 ÷ 8 = 71 --> 256815 is divisible by 8 9: A number is divisible by 9 if the sum of the digits is divisible by 9 Ex: 720936 7+2+0+9+3+6= 2727÷9= 3 --> 720936 is divisible by 910: A number is divisible by 10 if the units (ones) digit is divisible by 10 Ex: 67830 --> 0 ÷ 10= 0 67830 is divisible by 1011: A number is divisible by 11 if the sum of the odd power of 10 digits minus (-) the sum (+) of the even powers of 10 digits is divisible by 11Ex: 9482 (8+9) - (2+4)6-17= 11 ÷ 11= -1 --> 9482 is divisible by 11Fact Families:2 x 3 =6 54 x 6= x3 x 2=6 6 x 54= x6 ÷ 2=3 x ÷ 54= 66 ÷ 3= 2 x ÷ 6= 54dividend x= 324divisorquotientVocabulary:Factor: Number being multipliedmultiple: The result you get from multiplying a number by a whole number (integer)Divisor: The number being used to divide or a number that divides evenly into another numberDivisible: Can be divided by a number without a remainder

Week 7Prime number: Only has 2 factors, one and itself (have 2 rectangular models)ex: 7= factors are 1 & 7Composite number: have more than 2 factors (more than 2 rectangular models)ex: 24 = factors 1,2,3,4,6,8,12,24Square number: Perfect squares Numbers that have a square modelLength and width are the same number(odd number of rectangular model)Ex: 9 = 3x3 4 = 2x2Even numbers: All have 2 as a factorEx: 6 = factors are 1,2,3,6Odd numbers: Do not have 2 as a factorEx: 9 = factors are 1,3,9---------------------------------------------------------------------------------------------------------------------Factorization - Factoring A method of breaking numbers into factors.Prime FactorizationBreak a number into factors that are only prime numbers.Another method which is called The factor tree method:No matter how you make the tree or if you make the longest factor string, the answer is unique. (ONLY ONE ANSWER)Greatest common factors (GCF)Greatest common divisor (GCD)1) Intersection of sets method2) Prime factorization method3) Venn diagram method (GCF)1) Intersection of sets methodlist all the factors of each number circle all the common factorsGCF is the largest common factor2) Prime factorization methodFind the prime factorization of both numberscircle the common prime numbers multiply the common prime factors to find the GCF3) Venn diagram methodLeast common multiples:1) Intersection of sets method2) prime factorization method3) venn diagram method (LCM)1) Intersection of sets methodlisting some multiples of each number circle common multiples LCM is the smallest common multiple2) prime factorization methodFind the prime factorization of both numbers circle the most use of each prime number multiply the "most" prime factors to find the LCM3) venn diagram method

Week 14Dividend ÷ Divisor = Quotienttells us how much "stuff" we have tells us how we are going to break up the "stuff"a) size of each groupb) how many groupstells us the result of breaking up the "stuff" into groupsa) how many groupsb) size of the group

Week 13*Different ways to solve multiplying fractions with a whole number*Ex #1: 7/8 x 4801.) 480 ÷ 8 = 6060 x 7 = 420 2.) 7/8 x 480 = 7 x 480/8 = 7 x 60 = 4203.) 7/8 x 480/1 = 3360/8 = 420 Ex#2: 4 3/4 x 4801.) 4 3/4 x 480( 4x4 ) = 16 ( 16 + 3) = 19480 ÷ 4 = 12019 x 120 = 22802.) 4 x 480 = 1920 480 ÷ 4 = 120120 x 3 = 3601920 - 360 = 22803.) 4 3/4 x 480(4 + 3/4) x 4804 x 480 + 3/4 x 480 = 2280Ex #3: If you read the book 1 1/2 times, how many pages have you read?1.) 1 1/2 x 3001 x 300 = 300300 ÷ 2 = 150150 x 1 = 150300 + 150 = 450 450 pages were read.2.) 1 1/2 x 300(1 + 1/2) x 3001 x 300 + 1/2 x 300 = 450 pages read

Week 12Ex:Janet is running on a track that is 1/4 of a mile long. She runs down the track 5 times. How many miles did she run?1/4 x 51/4 + 1/4 + 1/4 + 1/4 + 1/4 = 5/45x 1/4 = 5/4 Can also use these other methods:number linerectangles as the wholerectangles as the whole amount repeated

Week 11Pretty simple just went over integers again and how to compare fractions.Here is how you can solve integers with subtraction using chip models:How to solve subtract integers on number line:*The numerator tells us how many pieces all together of the particular size pieces*

week 10*mainly videos because making strips and fractions is not possible*Equivalent fractions scaling upscaling downComparing factors:Same denominators/ same size pieces 5/8 < 7/8*If the denominators are the same, compare the numerators - which one has more of the same size.*Same numerator/ same number of pieces 3/5 < 3/4*If the fractions have the same numerator, compare the denominators.*bigger the denominator, the smaller the piecessmaller the denominator, the bigger the piecesFractions on number lines:Converting improper fractions to mixed fractions:

Week 9Integer with Multiplication and Division4x 3 = 12 Factors have "same" sign the -4 x -3 = 12 product is (+) positive---------------------------------------------------4 x +3 = -12 Factors have "opposite" sign the +4 x -3 = -12 product is (-) negative Multiplying integer rules: *Factors have opposite signs* -3(4) = -12 3(-2) = -6 4(-3) = -12 (-3) (2) = -6Multiply the absolute value of the factors, If the factors have opposite signs, the product is negative. Dividing Integers: 6 ÷ 2 = +3 +2 x +3 = 6 -6 ÷ -2 = +3 -2 x +3 = -6 -6 ÷ 2 = -3 2 x -3 = -6 6 ÷ 2 = -3 -2 x -3 = 6*If the dividend and divisor have the same sign, then the quotient is positive**If the dividend and divisor have the opposite signs, then the quotient is negative* 6 ÷ 2 = 3 -6 ÷ -2 = 3Fraction Parts:Numerator: How many of the whole we are talking aboutDenominator: How many pieces in the wholeProper fraction: a/b --> 2/3 The number is smaller than the denominatorImproper fraction:a/b --> 4/3 The numerator is larger than the denominatorRational number can be expressed as a fraction for a quotient.a/b a÷b

Week 8Integer: Positive and negative whole numbers, including 0Origin: Beginning or starting point Absolute value: Distance of the number from the origin | x | "the AV of x"Opposite: The number that is the same distance from the origin ex: -(4) = -4 -(-4) = 4"The opposite of 4" "The Opposite of 4"Properties of Integer Addition:Properties of addition of whole numbers also work for integers.Additive Inverse property of integers:A is the additive inverse of a a+ -a =0 = a - + a 4 + -4 = 0 -4 + 4 = 0 Integer addition: Chip model 6 + (-2) = +4 3 + (-5) = 2+ - (-3) + 5= 2 * you add the sign of whichever is the bv* + - (-6) + 2= -4++++If the addends have the opposite signs, The sign of the sum is the sign of the addend with the greater absolute value. (Which one has more? positive or negative)Subtract the smaller absolute value from the larger absolute values (how much more?