Alt Alg Subtraction: Expanded Form and Equal Addends
Alternate Algorithms: SUBTRACTION Expanded Form: 68-35= (60+8)-(30+5)= 30+3=33 Equal Addends: adding the same amount to the top # and bottom # to make one of the numbers with a zero and then subtract.
Alt Alg Mult and Division
Alternate Algorithmns: MULTIPLICATIONTimes Tables (In correct order): 1s, 2s, 5s, 10s, 11s then 9s, Doubles, 3s then 4s, 6s, 7s, 8s.Students need to learn their times tables automatically .Timed tests hurt students, focus more on improvement than how many answers they get right.2(3) vs 3 (3): 2 groups of 3 stars VS 3 groups of 3 starsFinger trick: Teaching or allowing students to use tricks doesn't build their fluency, and they never really learn the math facts.DIVISIONExpanded Form: 34 x 28= (30+4) x (20+8)
Build and Show Integers Add
Integers:ADDITION Building integers red is always negative and positives (yellow) are always on top and negatives are always on bottom. Start with first digit and zero (pair) bank depends on which side. Zero bank is always ZERO.Addition: Build/draw: 5+3 is 5 positives plus 3 positives & -5 +3 is (zero bank) take away 5 negatives plus 3 positives = ++
Divisibility Rules
Divisibility Rules:Any integer (not a fraction) is divisible by 1The last digit is even (0,2,4,6,8)The sum of the digits is divisible by 3 381 (3+8+1=12, and 12÷3 = 4)The last 2 digits are divisible by 41312 is (12÷4=3)
Integers-Build and Show Sub and Mult
Integers:SUBTRACTIONStart with zero bank if neededPositives on top/Negatives on bottomBuild: -3-(-1)= --- - =-2Show: 4-(-1)= ++++ + = 5
Integers-Solving Sub and Mult/Div
Integers:MULTIPLICATION-2(4) is said (zero bank) take away 2 groups of 4 positives. Build: +- +- +- +- +- +- +- +- +- Take away 2 groups of 4 positives and circle zero bank. (2 neg T.A. 4 positives)Hector's MethodK C C- - --45-(60) (add) = -105
Fractions Alg/Comparing/Solving Fractions
Fractions:Solving FractionsThe numerator tells us the number of pieces we haveThe denominator tells us the total possible things we could haveAdding whole numbers to fractions: you just combine the two for your answer.Subtracting whole number from a fraction: you will need to make the whole number into a mixed number with the same denominator as the fraction.Subtracting mixed number by mixed number: you subtract whole numbers first then multiply to get same denominator, then subtract.Mixed number multiplied by mixed number: Do the backwards "C" to multiply denominator by whole number then add to numerator. Then 1.Dividing fraction by fraction: use KEEP, CHANGE, FLIP (multiply by the reciprocal), then 1. Compare: >,<,=
Exam #2