MTE 280 Investigating Quantity

2^0 = 1 2^1 = 22^3 = 82^4 = 16....1010 base 2:1(2)^3+1(2)^18+2= 10

FACT FAMILIES...Start with a simple addition fact3+5=8Change order of addends5+3=8Inverse Operation8-3=58-5=3

AdditionSet Model (Addition)- characterized by the combining of two sets of discrete objectsLinear- characterized by the combining of two continuously quantities; no end, ongoing (i.e time, distance, etc)SubtractionTake Away- characterized by starting with some initial quantity and removing a specific amountMissing Addend- the need to determine what quantity must be added to a specific quantity to reach a goal amountComparison- determine how much larger or smaller one of the quantities is than the otherLinear- characterized on a number line using arrows to show changeMultiplicationRepeated Addition (Set)- repeatedly adding a quantity of objects a specific number of times.Repeated Addition (Linear)- repeatedly adding a quantity of continuous quantities a specific number of times.Area Model- a product of two numbers (length times width)DivisionPartition (sharing)- known: given quantity and number OF groups; unknown: number IN each groupMeasurement (Repeated Subtraction)- known: given quantity and number IN each group; unknown: number OF groups

No properties can apply to Subtraction/DivisionClosure Property of Addition- adding any two whole numbers, the sum will be a whole numberCommutative Property of Addition- switching the order of the addends will result in the SAME sumAssociative Property of Addition- adding three or more numbers; the grouping of the numbers will NOT change the sumIdentity Property of Addition- adding zero to a number will not change the number being addedClosure Property of Multiplication- multiplying two whole numbers will result in a whole number product Commutative Property of Multiplication- changing the order of the factors will result in the SAME productAssociative Property of Multiplication- multiplying 3 or more numbers; the grouping of the numbers will NOT change the product Zero Property of Multiplication- when multiplying a number by zero, the product will always be zeroDistributive Property of Multiplication over Addition/Subtraction-Identity Property of Multiplication- when multiplying a number by one, the product will result in the same number

Traditional/Standard Algorithm:48+3381 minutes61-4219 minutesExpanded Notation (Alternate Algorithm):1040 + 8+30 + 380 + 1 = 81 minutes5060 + 11-40 + 210 + 9 = 19 minutesPartial ProductOpen Area

Decomposing: 48 + 33 = 40+ 8 and 30+330+40 = 70 and 8+3= 1170+11= 81 minutesPartial Sums: 48+3370+11= 81 minutes

absolute valuea=-3 -a=3a=1 -a=-1a=0 -a= 0a=-5 -a= 5a=10 -a=-10number linechip methodred chip= negative valueyellow chip= positive value

Hindu Arabic- 1, 2, 3, 4, 5, 6, 7, 8...Roman Numeral- I, II, III, IV, V, VI, VII, VIII...Tally- l, ll, lll, llll, lllll, llllll, lllllll, llllllll...

.1 = one tenth.01 = one hundreth.001 = one thousandth.0001 = one then thousandth

Multiplication: use grid paper to solve and express the product // unit squareDivision: use base-ten blocks (partition or measurement model)

Models:area/region modellinear modelset modelfractions are pieces of a whole.equivalent fractions: 2/3 = 3/6 1/5 = 2/10

-when you multiply or divide both the top and bottom by the same number, the fraction keeps it's value Adding/Subtracting fractions: if denominators don't have the same value, use equivalent fractions to get a common denominator; then add or subtract the numerator.Multiplying: use a unit squareDividing: use a ruler to divide fractions