MTE 280 Concepts

G. Polya StepsDevise Plan-What problem solving strategy are you going to use? -guess and check/trial and error -draw a picture -make a tableCarrying out plan-easier than devising plan-be patient and persistent-try a different strategy if one doesn't workLook back and Check-Does answer make sense?-Did you answer all the questions?-Could you have solved it differently?

G. Polya StepsUnderstand the Problem-make sure you know how to solveDevise a Plan- decide on different strategiesCarry out Plan-implement strategy solveLook Back at Problem and Check- check if answer is reasonable

Base-3:ones 3^0threes 3^1nines 3^227s 3^31212base3=(1x3^3)+(2x3^2)+(1x3^1)+(2x3^0) =(1x27)+(2x9)+3+2 =27+18+3+2 =50Base-8:ones 8^0eights 8^164s 8^2

Addition PropertiesIdentity Property:a+0=aex: 4+0=4Commutative Property: a+b=b+a4+3=3+4Associative Property:(a+b)+c=a+(b+c)(2+3)+5=2+(3+5)Subtraction PropertiesComparison: neither subtraction or additionMissing Addend:3+_x_=7Multiplication PropertiesIdentity Property:ax1=aax0=0Commutative PropertyAxB=BxAAssociative Property:(axb)xC=ax(bxc)Distributive Propertyax(b+c)=3x7=3x(5+2)=(3x5)+(3x2)

American Standard (right to left) 576+279=8552.Partial Sums3.Partial Sums with Place Values4.Left to Right 576+279=700+140+15=8555.Lattice6.Expanded Notation

American StandardEuropean/Mexican Reverse IndianLeft to RightExpanded NotationInteger Subtraction

Base-10:ones 10^0tens 10^1hundreds 10^2thousands 10^3Base-5:ones 5^0fives 5^125s 5^2125s 5^3Ex: Base 9---> 121 group of 9s, 3 groups of 1s=13base9

Expanded NotationConvert 375 to expanded notation375= 300+70+5 = (3x100)+(7x10)+(5x1) =(3x10^2)+(7x10^1)+(5x10^0)Base-5Convert 212base 5ex 212base5=(2x5^2)+(1x5^1)+(2x5^0) =(2x25)+5+2 =50+5+2 =57Convert 31 to a base 531=111^5

American Standard Algorithm ( long division)Place Value Explicit (use pictures/diagrams)Alternating Algorithm (boxes example)

American StandardExpanded Notation 1023=20+3x14=10+4 +100 +90+2 200 +30+0 =300+20+2 =3223.Place Value