Basic Math

Problem SolvingGeorge Polya (mathematician)from Hungarywrote the book "How to Solve It"Solving Problems involves 4 steps:Understand the problem what are you being asked find out/show?can you state the problem in your own wordscan you draw a picture or diagram to help you understand the questionDevise a Planguess and check/trial and errormake the problem simplerCarry Out the Planif one strategy doesn't work try another oneusually easier than devisingbe persistentLook Back (reflect)does your answer make sense did you answer all of the questionsEx.

Numeration Systems are:a way of recording quantityare systems for representing quantity or a number in a consistent manner The numeration system used in America is Base 10 number system. It is a consistent one-to-ten relationshipThere are other number systems, such as Base 2, Base 3, Base 5, Base 8, etc.

Four Operations Addition Concepts and PropertiesAddition is combining a set of numbers togetherEx. 3+4=7Addition PropertiesIdentity Property - for every number a, a+0=a, number is not going to changeCommutative Property - order of numbers does not matter. For any numbers a & b, a+b=b+aAssociative Property - can group numbers in different ways and still get the same result. For any number a,b, & c, (a+b)+c = a+(b+c) Subtraction Concepts7-3=4take away comparison missing addendMultiplication Conceptsrepeated additioncombininga group of numbers or "groups of --- "Ex. 2+2+2 = 6 or 3 groups of 2 or 3x2=6Properties (properties are very similar to addition properties)Identity - ax1=aCommutative - axb = bxa, order doesn't matter Associative - (axb)xc = ax(bxc), group of numbers doesn't matter Zero Property - for any number a, ax0=0, any number multiplied by 0 is 0Distributive Property - ax(b+c) = (axb) + (axc)Division Conceptssharing repeated subtraction

Addition AlgorithmsThere are 6 addition algorithms:American StandardPartial SumsPartial Sums w/ place valueLeft-to-RightExpanded Notation Lattice MethodSubtraction AlgorithmsAmerican StandardEuropean/MexicanReverse IndianLeft-To-RightExpanded NotationInteger SubtractionMultiplication AlgorithmsAmerican Standard Place Value Expanded NotationLattice Method