Elementary mathmatics

Converting improper fractions to mixed numbersDraw a model of 8/3 and write the equivalent mixed number Converting mixed numbers to improper fractions Draw a model of 3 1/4 and write the equivalent mixed number

Standard Mathematical Practices: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.

VocabDigit- 0,1,2,3,4,5,6,7,8,9,10Numeral- written symbol for the digits Number- an arithmetic value, expressed by a word, symbol, or figureNumeration Systems- a collection of properties and symbols agreed upon to represent numbers systematically Bar over number indicates multiple by 1000. Ex. L=50 times 1000=5000Hindu-Arabic System are all numbers are constructed from the 10 digits0,1,2,3,4,5,6,7,8,9

Convert 132 eight to base 10:power: 8^3, 8^2, 8^1, 8^0value: 512, 64, 8, 1base ^8: _, 1,3,21 times 64 +3 times 8 +2 times 164+24+2=90 tenConvert 433 five to base 10:power: 5^3, 5^2, 5^1, 5^0value: 125, 25, 5, 1base^5: _, 4,3,34 times 25+3 times 5+3 times 1100+15+3=118 ten Convert 314 six to base 10: power: 6^3, 6^2, 6^1, 6^0value: 216, 36, 6, 1base ^6: _,3,1,4

Convert 68 ten to base 6:6^3, 6^2, 6^1, 6^0216, 36, 6, 1 1 5 2 six 68-36=32-30=2-2=0Convert 49 ten to base 2:2^5, 2^4, 2^3, 2^2, 2^1, 2^032,16,8,4,2,11 1 0 0 0 1 two 49-32=17-16=1-1=0Convert 191 ten to base 5:5^3, 5^2, 5^1, 5^0125, 25, 5, 11 2 3 1 five 191-125=66-50=16-15=1-1=0

What is subtraction? Taking away something from 2 or more thingsThe difference between 2 or more numbers Vocab: Minuend- the part you start with Subtrahend- the part being taken away Difference- the result of subtraction5-3=2, 5 is minuend, 3 is subtrahend, and 2 is the difference

What is multiplication?duplicates of things same size group of things, repeated totalVocab: factor- the numbers being multiplied product- the result of multiplication 2 times 3=6, 2, and 3 are the factors and 6 is the product When teaching multiplication, what do the factors tell us?2 (first factor which is how many) times 3 (second factor which is what is in each group) equals 6 which is the product

Identity Property of Multiplication: a times 1=a=1 times aCommunicative Property of Multiplication: The order in which we multiply numbers does not change the product. a times (b)= b times (a)Associative Property of Multiplication: The product of three or more numbers remains the same regardless of how the numbers are grouped. (ab)c=a(bc)Multiplication Property of 0: a times 0=0 times aDistributive Property of Multiplication: Multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together. 4(x+3)=4x+12

Subtraction Models:Take Away Model- Show using chips/coins/cubes. ex: 6-4 you remove the chips until you have 2 leftMissing Addend Model- There are 6 red circles in the set. How can we determine how many circles are hidden?Comparison Model- Sara is 3 feet tall. Her older brother is 5 feet tall. How much taller is he? You can compare by drawing both people and using blocks to model 3 and 5 and compare how tall each person is.Number Line- Measurement ModelMultiplication Models:Groupings- 2 times 3 (2 groups of 3) 3 times 2 (3 groups of 2)Repeated Addition- 2 times 3= 3+3, 3 times 2= 2+2+2Number Line ModelArray Model-Objects (4 times 3 is 4 rows of 3)Area Model- unit squares to fill the space

210 divided by 2 105 divided by 3 35 divided by 7 5252 divided by 2 126 divided by 3 42 divided by 7 6

210 2 times 3 times 5 times 7252 2 times 3 times 2 times 3 times 7Factor Tree

When comparing fractions, if the denominators are the same, compare the numerators- which one has more of the same pieceIf the fractions have the same numerator, compare the denominators. The bigger the denominator, the smaller the piecesUse benchmark fractions- fractions that you understand/know easily

Fraction Parts- numerator: how many of the whole we are talking about, denominator: how many pieces make up the whole Proper fraction- the numerator is smaller than the denominator Improper Fraction- the numerator is larger than the denominator Equivalent Fraction- fraction that represents the same value, but use different numbers/size pieces

Integer- Positive and negative whole numbers including 0Origin- Beginning or start point (0)Absolute Value- Distance of the number from the origin Opposites- The number that is the same distance from the origin

Using absolute value if the addends have the same sign, add the absolute value of the addendsthe sign is the "same sign" Properties of integer addition also work for integers additive inverse prop of integers -a is the additive inverse of aa+-a= 0= -a+a

Integer Addition: charged-field method it is the chip model without the chip positive charge+negative charge= 0 charge Integer Addition: Number Line Model Positives walk forward and negatives walk backwards Integer Subtraction: chip model Integer Subtraction: number line model subtraction- to turn around

Factoring factorization- a method of breaking numbers into factors Factor string method: ___ times ___Ex- factor 240 2 times 10 times 128 times 3 times 104 times 6 times 103 times 4 times 20The longest factor string of 240 without using 12 times 2 times 3 times 2 times 5 times 22 times 2 times 2 times 2 times 3 times 52^4 times 3 times 5= 240Factor tree method

Greatest Common Factor (GCF)Intersection of Sets Method (Listing Factors)List all the factors of each number Circle all the common factors GCF is the largest common factor Prime Factorization Method Find the prime factorization for both numbers Circle the common prime factorsmultiply the common prime numbers to find the GCPVenn Diagram Method Put the prime factors into a venn diagram

Least Common Multiple (LCM)Intersection of Sets Methods (Listing Multiples)List some multiples of each number Circle common multiples LCM is the smallest common multiple Prime Factorization Method Find the prime factorization of both numbers Circle the most use of each prime number Multiple the "most: prime factors to find the LCM

Divisibility Rules: 2- if the units digit is even 3- if the sum of the digits is divisible by 36- if the number is divisible by 2. and 39- if the sum of the digits is divisible by 9 5- if the units digit is divisible by 510- if the units (ones) digit is divisible by 10 (ends in 0)4- if the last 2 digits are a number that is divisible by 48- if the last 3 digits is a number that is divisible by 811- if the sum of the odd power of 10 digits minus the sum of the even powers of 10 digits 7- no rule, try the division

Every odd number has all odd factorsEven numbers have more factors than odd numbers Some numbers only have factors of 1 and itself All numbers have a factor of 1 Square numbers have an odd number of factors Prime numbers have 2 factorsComposite numbers have more than 2 factors 1 is not prime or composite Even numbers all have 2 as a factor Odd numbers don't have 2 as a factor

Definition of a^n- if a, the base, and n, the exponent, are whole numbers and n doesn't equal 0, then a^n= a times a times a,,, etc For every whole number a doesn't equal 0 and natural numbers m and n a^m times a^n= a^m+nFor every whole number, a, and natural numbers m and n(a^m)^n= a^mnFor whole numbers a and b, and natural numbers n: a^n times b^n=(ab)^nDefinition of a^0 for natural number a, if a is a natural number then a^0=1If a,m,n are natural numbers with m greater than n, then a^m divided by a^n=a^m-n

Grouping Symbols Parenthesis ()ExponentsMultiplicationDivisionAdditionSubtractionMultiplication and Divison (Left to right)Addition and Subtraction (Left to right)24 divided by 3 times 4 plus 2 (3-1)24 divided by 3 times 4 plus 2 (2)8 times 4 plus 2(2)32 plus 2(2)32 plus 436

Even number- a number when divided by 2 has no remainder 2 groups- the same number in each group2 groups- all groups are the same zOdd number- a number when divided by 2 has a remainder of 1 2 groups- groups are not equal 2 in each group- one doesn't have a partner 2+4=6 even 2+3=5 odd3+5=8 even 7+8=15 odd

What is division?Break up a big group into smaller groups of the same sizeHow many times a number fits into a number Vocab: Dividend- the amount you have that is being shared/divided upDivisor- how what you "have" is being shared/broken upQuotient- the result of division6 divided by 2=3 (6 is the dividend, 2 is the divisor, and 3 is the quotient)2 types of division Partitive Model- fair sharing (ex- giving away 2 cookies at a time until we have nothing left over)Quotitive Model- Subtraction or measurement (ex- have 6, break up into 2 in each group)

Identity Property- Dividing a number by 1 equals the number itself (14 divided by 1=14, 12 divided by 1=12) Zero Property- 2 rules one is dividing a number by 0 is not possible (81 divided by 0 cannot be solved) and two is dividing 0 by a number always equals zero (0 divided by 72=0) Dividing a number by itself- Any number divided by itself equals 1 (14 divided by 14=1)