MTE 220

Numeration Systemscreated to record quantitybase-10 systemvalue changes in positionex- 348 3- hundreds place4- tens place 8- ones place These are place values in base 10348.272- one tenths 7 one hundredths Base 100,1,2,3,4,5,6,7,8,9,10,11,12...onestenshundredsExpanded Notationex- 3483 hundreds+ 4 tens+ 8 ones 300+40+8 =348(3x100)+(4x10)+(8x1)= 348(3x102 )+ (4x101)+(8x100) =348Base 50,1,2,3,4,105 ,115, 125, 135, 145, 205,...ones-50Fives- 51twenty fives-52125s- 53how do you find 2115 in base 10?(2x52)+(1x51)+(1x50)(2x25)+(1x5)+(1x1)50+25+156Base 30,1,2,103, 113,123, 203, 213how do you find 33 in base 3?27= 19= 03= 21= 0https://www.youtube.com/watch?v=HJH0gBYhFiA

Division and Multiplication Algorithms Division- repeated subtraction6➗2 division sign6/2 division or fraction bardivision bar as wellPlace Value Explicitfilling in all of the place values when solving using long division ex- John has 15 cookies. He puts 3 cookies in each bag. How many bags can he fillAlternative Algorithm-repeated subtraction 197 cookies and 16 in each box. How many boxes are needed?197-160- 10 boxes37cookies left 37-32 2 boxes5 cookies left 12 boxes in totalStandard Algoritm Multiplication Standard Algorithm- multiplying using partial products then adding together Place Value 23 x14 4x3=12 4x20=80 10x3=30+10x20=200 322Expanded Notation 23 20+3x14 x10+4. 300+ 20+2 322Lattice- Video explaining https://www.youtube.com/watch?v=W7cTvEcyyj4

Day 1The class took the 20 question test for the full class periodDay 2With our tests being grades- we review frequent questions that were missed by the class

Fractions1. part-whole boys/whole class2.3/4- quotient3.Ratio boys/girls ModelsSurface Area3 out of 4 pieces of pizza are gone 2.Length 3.Set (groups of things)1 Whole = 4/4, 6/6-fractional parts are equivalent parts-the more my whole is divided by. the smaller my pieces gethttps://www.youtube.com/watch?v=HBN568uvxi4

Test 2 Study Guidedivisibility rulesprime numbers- prime factorization treetrue-false statementsfind GCF and LCMfractions- problem solvingJim, Ken, Len and Max have a bag of bag of mini candy bars from trick or treating together. Jim took 1/4 of all bars, Ken and Len took 1/3 of all the bars. Max got the remaining 4 bars. How many bars were on the bag originally? How many bars did each get?111 1111 1111 13/12 for Jim-124/12 for Ken-164/12 for Len- 161/12 for max- 4 barsthe numbers are over 12 because the LCM of 4 and 3 are 12https://www.youtube.com/watch?v=kMPhdAXlM8k

Decimals1- Thousands9- Hundreds4- Tens3- Ones.- decimal5- Tenths1- Hundredths 3- ThousandthsSmallest-> Greatest0.3, 0378, 0.98, 0.23 0.23< 0.3< 0.378< 0.98Adding and Subtracting DecimalsThe decimals have to be lined up on the correct place values376.25 22.3 This is WRONG376.25 22.30 This is CORRECTMultiplyThese numbers do not need to line up Divisionhttps://www.youtube.com/watch?v=Val4TmjHXRY

Positive and Negative Numbers- "the chip method"additionbring more chips into the circle when you are adding a negative number, that creates a zero pair which cancels outsubtractiontake ''chips" out of the groupswhich you are subtracting a positive by a negative, you take out the negative out of one of the zero pair +5- (-1) = 6multiplying +3 x +2 = 63 groups of 2 -3 x +2 = -6 commutative property applieswhen multiplying 2 negatives, "the opposite of" cover the negative of the first integer then use the oppositedivision videohttps://www.youtube.com/watch?v=_B1fuzmonO4

Test and mindmap YAAAYUYYYYYY

Problem SolvingGorge Playa TheoryUnderstand the Problemwhat is it asking? do I know what I am looking for? Plan how to solvetrial and erroract outwork backwardsmake organized listmake tableImplement the plan-easier way?be patient and persistanttry different planstry different planlook back- Reflect does this make sense?what did you learn?was there and easier way to solve?There are 12 basketball teams in a league. If each of the teams plays each of the other teams once and only play once, how many games take place?team games 1 02 13 34 65 10 6 157 218 289 3610 4511 5512 66 1 cant play itself which is why it has 0 games. On the second row, 1 and 2 play each other for one game. Third row, 1 and 2 played, 1 and 3 played but also 2 and 3 played which is why there are 3 games played. Fourth row we are adding 3 more games because 1 also played 4, 2 played 4 and 3 played 4. this continues with all 12 teams. We can also see a pattern of adding up another number as each row goes down. 0+1=1 1+2=3 3+3=6 6+4=10 10+5=15 15+6=21continuedex- I have four 3-cent stamps and three 7-cent stamps. Using one or more of these stamps, how many different amounts of postage can I make?Stamps alone (single) 7stamps together 12 = 19 total3,3,3,3 7,7,737,377,3777337,3377,337773337,333777,333777733337,333377,3333777 = 19 total outcomeshttps://www.youtube.com/watch?v=zhL3EMFSm6o

Properties of addition, subtraction, and multiplication Addition- to put together/joinIdentity Property- a+0=aex- 4+0=4 , 3/5+0= 3/5Commutative (order) Property- the order of the number doesn't matter when adding a+b=b+a ex- 9+8=8+9Associative (grouping) Property- grouping in different ways (a+b)+c= a+(b+c)ex- (3+4)+8 = 3+(4+8) Subtraction- Take away ex- 5-3Comparison: its not adding or subracting ex- how many more coins are in group A than in group BMissing addendex- 3+ = 7Multiplication- repeated addition 3x2 = 3 groups of 2 (2+2+2) Identity Property of Multiplication- ax1 =a ex- -3x1= -3Zero Property of Multiplication- ax0=0ex- 3x0=0 , 236x0=0Commutative Property of Multiplication- axb=bxaex 3x7=7x3Associative Property of Multiplication- (axb)xc = ax(bxc)ex- (2x4)x4 = 2x(4x4)Distributive Property of Multiplication- multiplying a number by a sum is the same as multiplying each number of the sum then adding them together ex- 3x(6+1) (3x6)+ (3x1) 18+321https://www.youtube.com/watch?v=s9h-n95AXrc

Addition and Subtraction Algorithms 6 Addition algoritms1.American Standard 256 +415 671 2.Partial Sum- adding from right to leaft and carr 346+124 10 6+ 4 4703.Partial Sum w/ Place Value 346+124 10 60+4004704.Left to Right- work from the hundreds value to the ones 178+269300130+174475.Expanded Notation 576 500+70+6+ 279 +200+70+9 855 8556.Lattice 5 7 6 +2 7 9 0 1 1 7 4 5 8 5 56 Subtraction algorithms1.American Standard 645-2793662.European/Mexican- instead of taking away from the top place values, you are adding to the bottom place values3.Reverse Indian4.Left to Right- solve going from left to right in all place values5.Expanded Notation-same concept as addition just using multiplication 6.Integer Subtraction- following from right to left and allowing their to be negative numbers. Then solve https://www.youtube.com/watch?v=TClOCPBYw10

Number TheoriesTypes of numbersdivisibility rulesFactors Fractions multiplesa is divisible by b if there is a number c that meets the requirement bxc=aex- 10 is divisible by 5 because 2x5=10Divisibility Rules:Endings-by 2: 0,2,4,6,8-by 5:0,5-by 10:0Sum of digits-by 3: sum of digits is divisible by 3 ex 39- becuase 3+9=12 which is divisible by 3-by 9: sum of digits is divisible by 9Last digits-by 4: last 2 digits are divisible by 4 ex 316-by 8: last 3 digits are divisible by 86-by 6: if it is divisible by BOTH 2 and 37-by 7: double the last number and subtract the sum by the other numbers ex 826- 6 doubled is 12, then subtract 12 by 8211-by 11: "chop off"Prime factorizationthe figerprint or DNA if every composite number:ALWAYS THE SAME 24 24 6 4 8 32 3 2 2 4 2 2 2GCF; Greatest Common FactorList Method 24: 1,2,3,8,12,24,4,6 36:1,2,3,4,6,9,12,18,36GCF(24,36) : 12Prime Factorization Method24: 2x2x2x336: 2x2x3x3 2z2x3 = 12Least Common Multiple24:24,48,72,9636: 36,72The least common multiple is 72https://www.youtube.com/watch?v=Df9h5t64NlQ

Adding fractions with common denominator examples using pictures will be in video1/4 + 2/4= 3/4 when both of the fractions have the common denominator, you just need to add the number on the numerators1/4+1/6=5/12because the number in the denominators are different, you have to find the least common nuliptle of the 2 numbers 4 and 6 have a LCM of 123/12+ 2/12=5/12If there is a improper fraction, make sure to turn it into a mixed number 12/10-> 1 1/5Multiplying Fractionsmultiplying fractions decreases the outcome1/2 of 1/2= 1/4multiply the numerators together and then multiply the denominators together Division2/3 divided by 4/5 do the inverse of the second fraction and then multiply them2/3 x 5/4= 10/12 https://www.youtube.com/watch?v=ysKCXALX2sM

Day 1Took our testDay 2Reviewed tests answers

Is- =of- x (multiply)what- n (unknown)%- decimal8%- 0.08Use critical thinking when it comes to problem solving!a) 8 is what % of 22? (should be around 1/3) 8 = n x 2222 228 divided by 22 equal 0.36 with 36 repeating Therefore it is 36%A Students takes a test w/ 45 questions ad gets 37 correct. What % did they get on the test?divide 37 by 45 equals .82 with the 2 repeating so the answer is 82%7/8 as a decimal7 divided by 8 equals 0.875Practice problemsIn the US, 13 out of 20 cans are recycled. what % of cans are recycled? you can either do 13/20 and find the equivalent which is 65/100. 65% is our answerhttps://www.youtube.com/watch?v=suAikQqJD34