MTE 280 Investigating Quantity

Addition of Integers:-4+7= 3☻☻☻☻☺☺☺☺☺☺☺Subtraction of Integers:7-4=3☺☺☺☺☺☺☺☺☺☺☺Number line:7-4=37_______________++++++++++0 1 2 3 4 5 6 7----------4Multiplication of Integers: Pattern Method(-3)x(4)= -122x4=81x4=40x4=0-1x4=-4-2x4=-8-3x4=-12Division of Integers: Inverse Operations-12/-4= 3n(-4)=-12-4n=-123(-4)=-122(-4)=-81(-4)=-40(-4)=0

Fraction Concepts:4 people share 3 brownies@ ♥ /@ ♥ /♥= Whole brownie/= Half brownie@= PeopleArea/ Region Model2 people share 3 twizzlers@ ♥ /@ ♥ /Linear/ Length model5 volunteers2 people with glasses5 with long hair3 with short sleevesSet Model

Addition:1/3 + 3/4=1/3=4/12 3/4=9/124/12+9/12= 1 1/12Subtraction:4/5 - 1/3=4/5=12/15 1/3= 5/1512/15- 5/15= 7/12Multiplication:3 x 1/4 = 3/4☻☺☺ 3 rows of 1/4☻☺☺☻☺☺Division:3 / 1/4=1/ 3*4= 1/12How many 1/4 in 3?

Cube=10Flat= 1Long= 1/10Unit= 1/100Writing decimals Five Hundred, Fifty-five and three tenths= 555.3Expanded Form45.624 (10)^1 + 5(10)^0 + 6(10)^-1 + 2(10)^-2

Hindu-Arabic-1,2,3,4,5,6,7,8,9,10Tally Marks:IIIIRoman Numerals:I,II,III,IV,V,VI,VII,VIII,IX,X

Base 5:0,1,2,3,4,10,11,12,13,14,20...Base 12:0,1,2,3,4,5,6,7,8,9, dec(X), El (E)...Base 10:0,1,2,3,4,5,6,7,8,9

ModelsTake Away- Paola had 8 fishes and she gave 4 to her bestfriend Ximena. How much does Paola have now?PaolaXXXXXXXX=8-XXXX = 4________XXXXXimenaXXXX=48-4=4 fishesMissing Addend-x+6=7-6 -6x= 1Comparison Model:Jovanni has 6 bars of snicker bars and Francisco has 8 bars. How much more does Francisco have than Jovanni?♥♥♥♥♥♥♥♥= Francisco♥♥♥♥♥♥= Jovanni8-6=2Linear-6I----------II-I-I-I-I-I-I-I-I-I-I-I-I0 1 2 3 4 5 6 7 8 9 10I------I36-3=3Jovanni is 6 miles away from home, he starts to run 3 miles and takes a break. How much more miles does he need to get home?Properties:Closure Property of Subtraction: Doesn't Exist!Commutative property of Subtraction: 3-4=4-3-1 = 1Associative property of Subtraction:(a-(b-c) = (a-b)-c2-(4-3) = (2-4)-32-1 = -2-31 = -5Identity Property of Subtraction:(a-0=a=0-a)2-0=a=0-22 = -2Algorithm:Tradition:5 1161- 4219Decomposition:60-40=201- 2= -119

Factor Rainbow121,2,3,4,6,12Prime Number: A number that has 2 different factors ONLY, 1 and itselfComposite Number: A number that has more than 2 DIFFERENT factorsGreatest Common Factor:721,2,3,4,6,8,9,12,18,24,36,72901,2,3,5,6,9,10,15,18,30,45,90GCF= 18Least Common Factor12x2=248x3=24

PROPERTIESClosure property of Multiplication8x7=560x7=0If you multiply two whole number the product does come out a wholenumber.Commutative property of Multiplication8x3=243x8=24Changing the order factors will give you the same productAssociative property of Multiplication(2x1)x3=2x(1x3)2x3 = 2x36 = 6Changing groupies would get you the same productIdentity property of Multiplication1x7=77x1=7Multiplying by 1, both have to workZero property of Multiplication0x1=010x0=0When multipling by a zero the product would always equal zeroDistributive property of Multiplication over Addition(8+15)x3= (8x3) + (3x15) Distributive property of Multiplication over SubtractionFriend each have $10, they get a $2 scoop. How much did all three friend leave altogether?10+10+10= 2+2+2=30 - 624MODELSArea ModelDavid is going to 1-foot square tile to tile his patio that is 5ft across and 9ft up. How many tiles does he need?9x5=45Repeated Addition LinearHarriet ran 4 miles and took a short break. She did this a total of 3 times. How many miles did Harriet run?3x4=12Repeated Addition Set ModelRandy had 8 goldfishes in each of his 4 packages. How many goldfishes does Randy have altogether? XX XX XX XXXX XX XX XXXX XX XX XXXX XX XX XXXX XX XX XX--------------------8 8 8 84x8=32Multiplication Algorithm:Traditional;16x 4232+640672Decomposition:6x40=24010x40=4006x2= 1210 x 2= 2024040012+20672

Problem Types:Partition model: given quantity & number groups16/2=8Measurement Model: given quantity & number in group16/8=2Fact FamilyFactor- any number being multiplied2x5=10Inverse operation- an operation that undoes another operation2x5=10 10/5=2Multiplication/Division Fact Family:3x5=155x3=1515/3=515/5=3Algorithms:Traditional- 134 r14l 537 -4 13 -12 1Decomposition:537/4400/4=100120/4= 30 16/4= + 4 134 +1

Properties:Closure property of AdditionAdding 2 whole number, the sum will be a whole numberAddend + Addend= SumCommutative property of AdditionThe numbers are changing orders and equals the same sum(a+b=b+a)Associative property of Addition- Adding 3 numbers or more, the grouping of the number will not change the suma+(b+c)=(a+b)+cIdentity property of AdditionWhen adding a Zero the number stays the samea+0=a=0+aMODELSAddition: Set Modelshe combination of two sets of discrete objectsXXXXX + XXXXX=5+ 5 = 10Addition: Linear ProblemCombining two continuous quantities( Distance, Time etc...)Addition Algorithm:Traditional-+148+3381Compensation-+248 + 3350 + 33= 8383 - 2= 81