Elementary Math 280

Build- use fraction tiles or circlesShow- Draw a box and separate it into the number of squares marked by the denominatorAdd fractions- will have 3 squares- first 2 will be perpendicularSubtraction will have 2 squaresMultiplication will have 1 square- separate with perpendicular lines

Always estimate firstNumerator times numerator= numeratorDenominator times Denominator = demoninator

Always estimate firstdo the backwards C for mixed numbers= take the denominator and times the whole number then add the product to the numeratorKeep Change Flip 15 / 18 15 X 10 22 10 22 18 k c f 3. Factor each numerator and each denominator 3*5 2*5 15 X 10 22 18 2*11 6*3 4. Use funky 1's= cross out on numerator with equal denominator 5 X 5 = 25 11 6 66

draw squares and equally divide the squares

Draw one square and divide based on place value0.1 = separate into ten0.24 = separate into 100Next color or shade the first decimalThen shade the second decimal inbigger decimals:estimate= does the answer make sincewrite it out, line up whole number

draw

estimate- make sure the answer makes sincemultiply without decimalslook at your estimate to place the decimal

estimateline up whole numbersplace decimal based on estimate

Forget- (PEMDAS)G- GroupsE- ExponentsM/D or D/M- multiplication and division left to rightA/S or S/A- Subtraction and Addition left to rightExponents:(-4)^2=(0-4)^2=16-(4)^2=0-(4)^2=-16-4^2=0-4^2=-16-(-4)^2=0-(0-4)^2=-16

Three Parts of Scientific Notation:first number always between 1 and 10always times 10has exponent (e^-1 is a decimal)( e^+ is a big number)positive exponent = number bigger than 1negative exponent = decimalExample:4.25 x 10^-4 = small number0.0004251.63 x 10^7 = big number16,300,000

weeks 11-15

Revisit previously learned content throughout a semesterUsed to reinforce materialSo students cant forget anythingReminds of old contentGives students a chance to learn the content over a matter of weeks instead of teaching all at once and the students forgetting the content

Expanded Form: expand each place value and then subtract acrossEX: 278-57200+70+8 200+60+18- 0 +50+7 - 0 +50+7 200+10+9 = 219Equal Addends: Add an equal amount to both numbers( turn theEX: 134-56134 + 4 = 138-56 + 4 = - 60 78

Finding areaTimed test: ineffective because of the stress and pressure that they put on our students (does not access long term memory) hurt self imagetimes test teach automaticityuse flash cars-(make your own) focus on the group you are working onTricks do not workteach times tables in order Red (64%), Green (24%), Yellow1's, 2's, 10's, 3's, 9's, Doubles, 4's,6's,7's,8's               

Expanded Form: separate for place values, then multiply ame place values, then add togetherLeft to Right: multiply starting with the left side using place value, then add answers togetherEX: 47*534 7X 5 72000350120+ 21 2491Lattice: draw the lattice box with diagonal cuts. Write one number on top and the other number on the right and multiply. Last add the numbers diagonally

number divided into how many groupslong division- have to be able to estimate, then multiply, next subtract and bring it down and know what to do with remainders *not a good method* Must know times tablesRepeated subtractionuse what they knowanswer ends at the bottomdon't have to know any special skillsget close to the number without going overUpwards divisionwrite it as a fraction- (the way you read it)Separate numberssolve left to rightwrite the subtraction by the nu mbersthe remainder is at the numerator and it stays, then move the denominator up below numerator

Divisibility Rules:2's- Even numbers3's- sum of the digits are divisible by 34's- the last 2 digits are divisible by 45's- last digit is a 5 or 06's- if 2 and 3 works then 6 works8's- if last 3 digits are divisible by 89's- the sum of the digits are divisible by 910's- last digit is 0no rules for 7

Integers: any numbers that are positive and negativebuild is to show with materials.use 2-color countersRed is negative and always on bottomyellow is positive and always on topadd a zero bank1 positive with 1 negative = zeroShow- use symbols + stands for positive- stands for negativeEX: show 4 using 10+ + + + + + + + +- - - - -

Hectors Method-two signs on top of the largest number; 1 sigh on top of the smaller.Circle one from from each numberThe sign not circled reminds what sign the answer will bedifferent signs =subtractionsame signs = addition

Build: use 2 color countersred is negative other color is positivesSubtraction:start with first number __ take away___example 4-7 = 4 pos take away 7 pos- add a zero bank ooooooo ooo =-3 Multiplication:first number is group. number in ( ) = how many in groupsex: -3 (-2) = take away 3 groups of 2 negoooooo= 6oo/oo/oo=0Show: draw a diagramuse + and - signsSubtraction:-2-5= 2 neg take away 5 pos +++++ =- - - - - - - =-7Multiplication:state it correctly___ groups of ___ EX: -4 (2) = Take away 4 groups of 2 pos++/++/++/++/ =0- - - - - - - - =-8

Subtraction:is the same as adding the oppositeUse KEEP-CHANGE-CHANGE then use Hector's DiagramEx: -43-20K C C-43+(-20)-- - =-63Multiplication and DivisionRulesSame signs = +Different signs = -EX:25(-60) Different signs = -

Numerator- Number of PiecesDenominator- Size of PiecesNo need to use terms like improper fraction

Compare: >,<,= > is greater than> is less thanAnchor Fractions- fractions that we know like 1/2-compare fraction to "is it more than 1/2"

what you do to the numerator you have to do to the denominatordenominators must be the sameNo cross multiplying needAlways must equal 1 EX: 10/10; 1/1(both Numerator and denominator is the same numberEx: _5_*_3__ +_8__* _2_      8 *  3   + 12 *   2 _ _15_+ 16_= 31_  24 + 24  = 24 = 1 _7  24

Additionwhole numbers: just add themmixed numbers and a mixed number: Add whole numbers first, Next Find same denominator; Last add fractions Subtractionwhole number from a fraction: Make whole number into mixed fraction using same denominator; Then subtractmixed number and mixed number: subtract whole numbers first; find same denominator; last solveWhole number + fraction = combineWhole number - fraction = take one from whole number put in form a fraction (same denominator as other fraction); Then subtract the fractions. New whole number carries over

Summarize Weeks 7- 10Give ways to solve

Weeks 7-10

Alt Algorithms- SubtractionsExpanded FormEqual addends= add same number to both sides to make friendly number on Take Away sideOrder to teach the multiplication table and why?Red (64%), Green (24%), Yellow1's, 2's, 10's, 3's, 9's, Doubles, 4's,6's,7's,8'sPreviously learned skip countingDivisionRepeat SubtractionUpwards DivisionBuilding and showing integersAdd/Subtract using TilesUse Keep Change Change and diagram to solveMultiply- Show and solveParts of a fraction and comparing fractions with reasoning'sRules of multiplicationSame signs = +Different signs = -Divisibility rules