ELEMENTARY MATH

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.

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)

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: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:SUBTRACTIONStart with zero bank if neededPositives on top/Negatives on bottomBuild: -3-(-1)= --- - =-2Show: 4-(-1)= ++++ + = 5

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: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: >,<,=

Multiply the numerators from each fraction by each other (the numbers on top). The result is the numerator of the answer.Multiply the denominators of each fraction by each other (the numbers on the bottom). The result is the denominator of the answer.Simplify or reduce the answer.Improper fractionsWhere the numerator is greater than the denominatorWith improper fractions you may need to change the answer into a mixed number.Example: you get 23/6, your teacher may want you to change this to the mixed number 3 5/6.Mixed numbers -Mixed numbers are numbers that have a whole number and a fraction, like 4 ¼When multiplying mixed numbers you need to change the mixed number into an improper fraction before you multiply.

Dividing fractions is similar to multiplying fractions except you have to find reciprocal of the second fraction.:Take the reciprocal of the divisor. : Multiply the numerators. : Multiply the denominators. : Simplify the answer.To get the reciprocal, you need to invert the fraction Example: 3/4 ÷ 5/6 →3/4 x 6/5

When building a fraction you need to know how many pieces you need for your problem. The total number of pieces would be placed on the bottom as the denominator and the rest would be on top which would be the numerator.

DecimalsWhen solving decimals make sure the decimals points are lined upPut zeros in spaces where there aren't numbers so that the numbers are the same length When multiplying decimals you ignore the decimal points and put it in after you solve the problemADDITION  1.345+1.4 1.345+1.400 1.345+1.400 2.745 SUBTRACTION 1.545-1.4  1.545-1.400 1.545-1.400 0.145 MULTIPLICATION (3.15)(5.2)≈ 15x 52 6301575 16.380 (place the decimal closest to the estimate)

Orders of OperationOrder of operations are the rules that state the order in which multiple operations in a problem should be solved. PEMDAS P- parentheses: always solve operations within the parentheses firstE- exponents: the second step after parenthesesM- multiplication: third step moving from left to rightD- division: fourth step after multiplying A- addition: fifth stepS- subtraction: sixth step

The numbers need to be between 1 and 10 If the number is bigger than 1 then the exponent will be positiveIf the number is between 0 and 1 then the exponent will be negative A negative exponent means that the number will be a decimal A positive exponent means the number will be a big numberWe use scientific notation to measure atoms or the distance to the moonAcceptable vs unacceptable 13.5 x 10^-5 ❌ (This is because the first number is not between 1 and 10)1.35 x 10^-5✅