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3 9 NUMERATOR TOP #
NUMERATOR TOP # HOW MANY PIECES OUT OF THE WHOLE 3 9 BOTTOM # DENOMINATOR HOW MANY TOTAL PARTS MAKE 1 WHOLE 1 3 2 4 6 5 8 7 9 # 9 IMPROPER MORE THAN 1 WHOLE 14 9 PROPER LESS THAN 1 WHOLE 5 9 MIXED MORE THAN 1 WHOLE WHOLE # AND A FRACTION 5 9 WHOLE # 9 1 9 WHOLE # 3 9 27 EQUIVALENT EQUAL PART OF 1 WHOLE 18 24 3 4 FRACTIONS COMMON DENOMINATOR 4 3 1 2 9 5 2 20 27 47 1 2 3 4 45 EQUIVALENT 3 4 9 12 EQUIVALENT 3 12 1 4 FRACTION N2A DECIMAL DIVIDE!! 0 .625 5 8 5.000 8 TOP DOG IN THE HOUSE IMPROPER FRACTIONS 1 2 15 7 7 15 7 TOP DOG IN THE HOUSE PROPER FRACTIONS .4 6 7 15 7.000 15 TOP DOG IN THE HOUSE PLACE VALUE THE NAME OF A DIGIT’S LOCATION AND VALUE DECIMALS / FRACTIONS LESS THAN 1 WHOLE WHOLE NUMBERS DECIMAL BACK TO A FRACTION HUNDRED MILLIONS TEN MILLIONS MILLIONS HUNDRED THOUSANDS TEN THOUSANDS THOUSANDS HUNDREDS TENS UNITS OR ONES . TENTHS HUNDREDTHS THOUSANDTHS TEN THOUSANDTHS HUNDRED THOUSANDTHS MILLIONTHS 102,102,102 102102 PLACEVALUE USE TO CHANGE A DECIMAL INTO A FRACTION .125 .08 5.6 125 THOUSANDTHS 8 HUNDREDTHS 5 AND 6 TENTHS 125 5 1 1000 40 8 8 2 100 25 6 3 5 5 10 5 .05 is NOT .5 DECIMAL OUT OF SIGHT 7060 TO THE RIGHT 7060.0 OR DECIMALS LINE THEM UP!! 67 4.8 67.0 - 4.8 DECIMALS 1.5 6.0 MOVE DECIMAL TO MAKE THE DIVISOR A WHOLE NUMBER DECIMALS .15 6.00 MOVE DECIMAL TO MAKE THE DIVISOR A WHOLE NUMBER DECIMALS 1.5 .06 MOVE DECIMAL TO MAKE THE DIVISOR A WHOLE NUMBER DECIMALS DON’T LINE THEM UP!! COUNT …. TOTAL DECIMAL PLACES!! 6.04 X2.5 15.100 3020 +1208 15100 A NUMBER BY 10, 100, 1000, 10000 COUNT ZEROS MOVE DECIMAL TO THE A NUMBER BY 10, 100, 1000, 10000 COUNT ZEROS MOVE DECIMAL TO THE CONVERSION BIG TO SMALL X BY 16 X BY 100 X BY 36 CONVERSION BIG SMALL TO ÷BY 16 ÷BY 100 ÷BY 60 PERCENT PER HUNDRED PERCENT OF A NUMBER 25 25 USE FOR TIPS, TAX, AND SALES! DECIMAL TO DECIMAL 2 TO THE RIGHT 1.85 TO DECIMAL DECIMAL 2 TO THE LEFT. .285 FRACTIONTO 1.TOP DOG IN THE HOUSE 17 .85 20 2.DECIMAL TO 0.85 85% TO 1. 2. FRACTION TO DECIMAL 28.5% .285 PLACE VALUE AS FRACTION & SIMPLIFY 285 57 1000 200 TAX MULTIPLY ADD • BYABOUT 8 CENTS OR $0.08 FOR DENTON TEXAS. • BACKONTO THE TOTAL COST. TOTAL WITH X .08 = TAX TOTAL COST= $3.6296 OR 45.37 + 3.63 = $3.63 $45.37 $49.00 HALF X BY .5 1 X BY 2 BY 2 61 NUMBERS .5 122 THAT EQUAL HALF 1 17 00.5000 .50 0.500 2 0.5 0.50 .500 34 HALF OF HALF HALF HALF OF HALF 1 1 1 2 2 4 1 4 OR .25 DIVISIBILITY SIMPLIFY FRACTIONS 27 57 SIMPLIFY 27 X PROPORTIONS 57 38 27 3 9 57 3 19 9 X 19 38 SIMPLIFY RATIOS SIMPLIFY RATES 4 OUT OF 28 FREE THROWS 1 OUT OF 7 FREE THROWS 2 FOR $1.50 1 FOR $0.75 FACTORS WHAT YOU CAN DIVIDE A NUMBER BY (DIVISIBILITY) WITHOUT A REMAINDER FACTORS OF 72: 1, 72, 2, 36, 3, 24, 4, 18, 6, 12, 8, 9 GCF GREATEST COMMON FACTOR GCF OF 36 AND 90 1 36 2 18 3 12 4 9 6 6 1 90 2 45 3 30 5 18 6 15 10 9 GCF =18 DIVISIBILITY BY “ ” 27 27 9 3 45 45 9 5 SUM OF THE DIGITS is DIVISIBILITY BY “ ” 3942 SUM OF THE DIGITS is DIVISIBILITY BY “ ” 9 27 27 3 57 57 3 19 SUM OF THE DIGITS is , , DIVISIBILITY BY “ ” 7341 SUM OF THE DIGITS is , , DIVISIBILITY BY “ ” 28 28 4 7 108 108 4 27 EVEN AND ARE 04, 08, 12, 16, 20, 24, 28, 32, ….. DIVISIBILITY BY “ ” 136 EVEN AND ARE 04, 08, 12, 16, 20, 24, 28, 32, ….. DIVISIBILITY BY “ ” 18 18 6 3 48 6 8 48 EVEN AND SUM OF DIGITS IS DIVISIBILITY BY “ ” 978 EVEN AND SUM OF DIGITS is DIVISIBILITY BY “ ” 3.5 3.5 5 .7 10 10 5 2 LAST DIGIT IS A “ ” OR “ ” DIVISIBILITY BY “ ” 3.75 LAST DIGIT IS A “ ” OR “ ” DIVISIBILITY BY “ 50 330 50 10 330 10 ” 5 33 LAST DIGIT IS A “ ” Move decimal once to the left DIVISIBILITY BY “ ” 3170 LAST DIGIT IS A “ ” Move decimal once to the left DIVISIBILITY BY “ ” 3.178 LAST DIGIT IS A “ ” CHECKIE THINGY 7 39 4 8 8 OR FRACTIONS FRACTIONS AINT NO PROBLEM TOP TOP AND BOTTOM BOTTOM 2 3 27 3 5 5 4 5 4 81 1 4 20 20 FRACTION A # ⅔ OF 84 2 84 168 3 1 3 FRACTIONS DON’T CRY!! FLIP THE Right & MULTIPLY 3 1 28 1 5 5 3 5 3 28 3 84 5 1 5 4 16 5 RECIPROCAL FLIP THE 2 5 2 1 3 1 3 5 MULTIPLES A NUMBER’S MULTIPLICATION FACTS MULTIPLES OF 72: 72, 144, 216, 288, 360, 432, 504, 576, 648, 720, 792, 864… LCM LEAST COMMON MULTIPLE LCM OF 36 AND 90 36 2=72 90 2=180 X X 36X3=108 36X4=144 36X5=180 90X3=270 90X4=360 LCM =180 PERIMETER TOTAL DISTANCE AROUND THE OUTER EDGES JUST ADD! FENCE, BORDER, TAPE, CUT AROUND, FRINGE, LACE, CUFF, OUTLINE, FRAME, EDGE, TRACE, AREA TOTAL INSIDE FLAT SPACE MEASURED IN SQUARE UNITS USES MULTIPLICATION!! FLAT SPACE, INSIDE, PAINT, CARPET, COVER, SPREAD, ROOM, TILE, MOW LAWN, VACUUM, …. MEASURES OF CENTRAL TENDENCY MEAN MODE MEDIAN CONCLUSION OF THE DATA Average +, ÷ MEDIAN Middle # MODE MOST RANGE Highest – lowest WHOLE NUMBERS ARE ARE NOT •RATIONAL •IRRATIONAL •IMPROPER •PROPER •LESS THAN •EQUAL TO OR ONE MORE THAN 1 DECIMAL OUT OF SIGHT TO THE RIGHT!! RATIONAL ARE NOT π CAN BE MADE INTO A FRACTION 1 4 67, … -8 -38 -101….. ⅔ ⅓ ½ .833333333…… 6 1.625 2.4494897.... 16 4 IRRATIONAL CAN NOT BE MADE INTO A FRACTION π 6 2.4494897.... DECIMAL GOES ON FOREVER WITH NO REPEATING PATTERN INEQUALITIES READ LEFT TO RIGHT = EQUAL TO INEQUALITIES READ LEFT TO RIGHT 5 2.83 = 2 6 IS EQUAL TO INEQUALITIES READ LEFT TO RIGHT -4 2 INEQUALITIES READ LEFT TO RIGHT 2 -4 CONSECUTIVE ONE AFTER THE OTHER CONSECUTIVE PRIME NUMBERS 1, 3, 5, 7, 11, 13, 17, 19, 23.. PRIME NUMBERS ONLY TWO FACTORS ONE AND ITSELF 3 = 1X3 5 = 1X5 7 = 1X7 19 = 1 X 19 11 = 1 X 11 13 = 1 X 13 17 = 1 X 17 23 = 1 X 23 COMPOSITE NUMBERS THAT HAVE MORE THAN 2 FACTORS UNPOPULAR COMPOSITE NUMBERS: THEYLOOKPRIME,BUTAREACTUALLYCOMPOSITE! 39, 51, 57, 87, 91, 117, 119, 133, 203 AND 5.007 FIVE AND SEVEN THOUSDANDTHS 1¾ ONE AND THREE FOURTHS INTERVALS SKIP COUNTING EXAMPLE: AN INTERVAL OF 1 8 .125 .25 .375 .5 .625… FREQUENCY TABLE SHOWS THE NUMBER OF TIMES AN EVENT OCCURS BAR GRAPH DISPLAY, REPRESENT, COMPARE DATA 90 80 70 60 50 40 30 20 10 0 GIRLS BOYS PERIODPERIOD 1 PERIOD 2 PERIOD 3 4 LINE PLOT A NUMBER LINE THAT USES “X” MARKS TO SHOW THE FREQUENCY OF AN EVENT X X X X XX X X X X X X X X X X X X X X X X X X M L XL XXL XS # OF TEAM UNIFORMS S LINE GRAPH SHOW A CHANGE OF DATA OVER VERTICAL AXIS 100 90 80 70 60 50 40 30 20 10 0 TIME East West North 2005 2006 2007 2008 HORIZONTAL AXIS CIRCLE GRAPH PARTS OF THE WHOLE 100% REPRESENTS DATA parts AS A FRACTION, DECIMAL, OR PERCENT .25 ¼ OR 25% ELECTRIC GAS .2, 1/5, OR 20% PHONE WATER CAR HOUSE VENN DIAGRAM USES OVERLAPPING SHAPES TO SHOW HOW DATA IS RELATED WHOLE NUMBERS FROM 1 TO 10 PRIME EVEN NUMBERS NUMBERS 1,3,5 7 9 2 4, 6, 8, 10 STEM AND LEAF PLOT 11, 13, 14, 15, 21, 24, 27, 27, 34, 35, 34, 36 STEMS 1 1,3,4,5 2 1,4,7,7 3 4,4,5,6 LEAF(S) HISTOGRAM A GRAPH THAT DISPLAYS DATA FROM A STEM AND LEAF PLOT. Groups information together!! PATTERN SHAPES, SYMBOLS OR NUMBERS THAT OCCUR IN A PREDICTABLE ORDER. 3, 9, 27, 81, 243….. POSITION THE NUMBER THAT TELLS WHERE SOMETHING OCCURS IN A PATTERN POSITION 1 2 3 4 5 3, 9, 27, 81, 243….. TERM THE ACTUAL NUMBERS IN A PATTERN OR ANSWERS IN A SEQUENCE POSITION 1 2 3 TERMS 3 9 27 4 5 81 243 SEQUENCE A PATTERN WHERE A RULE SHOWS THE RELATIONSHIP BETWEEN THE POSITION AND THE TERM POSITION 1 2 3 4 TERMS 3 9 27 81 10 N 3 3 10 N 3 3 TO THE POWER OF THE POSITION RULE : n RULE An expression that describes the relationship between the POSITION and TERM .5n ORDER OF OPERATIONS 2 3 P 6(7) 6y 6 7 6 7 5y 42 7 7 42 42 7 DIVISION DIVISION INTEGERS POSITIVE AND NEGATIVE WHOLE NUMBERS + 1 -72 -1001 29 INTEGER EXPRESSION NUMBER LINE 1+3+3-8 ABSOLUTE VALUE 8=8 -13=13 DISTANCE FROM 0 OR INTEGERS MOVE ON A NUMBER LINE 1+3+3-8 INTEGERS MOVE ON A NUMBER LINE MOVE RIGHT 7 MOVE RIGHT 6 +(6) +7 -(-3) MOVE RIGHT 3 DOUBLE NEGATIVE! INTEGERS MOVE ON A NUMBER LINE MOVE LEFT 9 MOVE LEFT 9 -(9) -1 +(-3) MOVE LEFT 3 SUBTRACTING INTEGERS IT’S ADDING A NEGATIVE!! -7-8 -15 IS THE ANSWER -7+(-8) MOVE LEFT 8 SUBTRACTING INTEGERS IT’S ADDING A NEGATIVE!! 7-8 -1 IS THE ANSWER 7+(-8) MOVE LEFT 8 T CHART EVALUATING INTEGER EXPRESSIONS 14-24+2+(-12) 20 More negatives, so a negative answer DOUBLE NEGATIVES Become PUNCH EM OUT! or INTEGERS 24 3 72 72 3 24 or INTEGERS 24 3 72 72 3 24 $120 FOR 15 HOURS $120 15h UNIT RATE DENOMINATOR OF 1 $8 1h RATIO 45 STUDENTS 18 GIRLS GIRLS TO STUDENTS 18 2 OR 45 5 BOYS TO GIRLS 27 3 OR 18 2 PROPORTION $8 $150 1h ?h CROSS PRODUCTS ARE EQUAL $8 $150 1h ?h 8h 150 CONGRUENT SAME SIZE SIMILAR DIFFERENT SIZE SAME SHAPE CORRESPONDING SAME LOCATION ~ SIMILAR SAME SHAPE DIFFERENT SIZE A B ~ a b SCALE 1: 3 ON A MAP, 1 CM REPRESENTS 3 KM 1CM 3KM ACUTE ANGLES LESS THAN 90˚ 50 ˚ 89.5 ˚ 22 ˚ OBTUSE ANGLES MORE THAN 90˚ 91 ˚ RIGHT ANGLES 90˚ 90 ˚ 90 ˚ STRAIGHT ANGLES 180 ˚ COMPLEMENTARY ANGLES ADD TO 90 ˚ 31˚ 59˚ 31 + 59 = 90 SUPPLEMENTARY ANGLES ADD TO 180 ˚ 133˚ 47˚ 47 + 133 = 180 ADJACENT ANGLES SHARE A VERTEX AND SIDE VERTICAL ANGLES SHARE A VERTEX OPPOSITES ARE EQUAL! 115˚ 65˚ 65˚ 115˚ CORRESPONDING ANGLES SAME LOCATION ARE EQUAL! 75˚ 75˚ CONGRUENT ANGLES ARE EQUAL! 47˚ 47˚ PLANE INTERSECTING LINES PARALLELL LINES NEVER INTERSECT PERPINDICULAR LINES INTERSECT TO FORM 90˚ RIGHT ANLGES A CLOSED FIGURE WITH STRAIGHT SIDES 4 SIDES QUADRILATERAL QUADRILATERAL TOP AND BOTTOM II AND RIGHT AND LEFT II AND OPPOSITE ANGLES SQUARE RHOMBUS RECTANGLE PARALLELOGRAM QUADRILATERAL RIGHT & LEFT TOP CORNERS SUPPLEMENTARY ∠ RIGHT & LEFT BOTTOM CORNERS SUPPLEMENTARY ∠ =180° SQUARE RHOMBUS =180° RECTANGLE PARALLELOGRAM QUADRILATERAL TRAPEZOID KITE TRAPEZIUM QUADRILATERAL ANGLES ADD TO 360˚ 40 ˚ 100 ˚ 40 ˚ 90˚ 80 ˚ 90˚ 90 ˚ + 90 ˚ + 100 ˚+80 ˚ = 360 ˚ 3 SIDES TRIANGLE ACUTE OBTUSE RIGHT ISOSCELES ISOSCELES EQUILATERAL ACUTE OBTUSE ACUTE RIGHT SCALENE SCALENE SCALENE ISOSCELES TRIANGLE ANGLES ADD TO 180˚ 110 ˚ 40 ˚ 30 ˚ 110 ˚+ 40 + 30 = 180 30˚ 75˚ 75˚ 45˚ 45˚ 90˚ ISOSCELES 2 = SIDES 2 = ANGLES REGULAR POLYGON ALL SIDES EQUAL REGULAR OCTAGON 5 CM 5 CM 5 CM 5 CM IRREGULAR OCTAGON 3.141592…. PI THE CIRCUMFERENCE THE DIAMETER OF A CIRCLE A LITTLE MORE THAN 3! DIAMETER CIRCUMFERENCE THE PERIMETER OF A CIRCLE MULTIPLY PI x d C πd DIAMETER MULTIPLY PI x 2r C 2 r RADIUS CIRCUMFERENCE PERIMETER , DISTANCE AROUND, EDGE, RIM, FENCE, BORDER… AREA INSIDE SPACE, INSIDE FLAT SQUARES, COVER, OVERLAY, CARPET, FLOOR, …. RADIUS RADIUS HALFWAY ACROSS A CIRCLE FROM THE CENTER 2r=d DIAMETER DIAMETER ALL THE WAY ACROSS A CIRCLE THROUGH THE CENTER d d r 2 EQUALS EVALUATE SIMPLIFY OR SOLVE GET AN ANSWER! EXPRESSION A MATH SENTENCE NO EQUAL SIGN NUMERICAL EXPRESSION HAS ONLY NUMBERS 3 (3 3 ) 3 3 3 3 2 EVALUATE THEM! VARIABLE EXPRESSION HASNUMBERS ANDVARIABLES 3X 2Y+4 SUBSTiTUTION VARIABLE OUT NUMBER IN VARIABLE A LETTER REPRSENTS AN AMOUNT OR QUANTITY EQUATION MATH SENTENCE WITH = SIGN (b1 b 2 )h A 2 SOLVE FOR THE VARIABLE 3X - 4 = 5 X = ???? THE TO THE OF POWERS EXPONENTS POWER OR EXPONENT BASE = CUBED RD 3 POWER VOLUME of CUBE V=SxSxS S S S S³ SQUARED ND 2 POWER AREA of SQUARE A=SxS S S S² SQUARE ROOT SQUARE ROOT SQUARE ROOT DIVISION 3 ways BABY ADULT TEEN BABY ÷ REMAINDER r1 5 3 16 15 ADULT ÷ REMAINDER AS FRACTION 1 5 3 3 16 15 1 TEEN ÷ DECIMAL KEEP DIVIDING! 5. 3 16. 15 1 1 TESSELATIONS RELFECTIONS TRANSLATIONS ROTATIONS TESSELATIONS RELFECTIONS REFLECT ACROSS Y AXIS Y STAYS THE SAME REFLECT ACROSS X AXIS X STAYS THE SAME TRANSLATION SLIDE` ROTATION TURN COORDINATE PLANE QUADRANT QUADRANT (+X,+Y) (-X,+Y) POINTOFORIGIN START QUADRANT QUADRANT (-X,-Y) (+X,-Y) ORDERED PAIR -LEFT OR +RIGHT FIRST -DOWN OR +UP NEXT LOCATION OF A COORDINATE POINT COORDINATE POINT (-4, 3) +3 (-X, Y) -4 AXIS X AXIS HORIZONTAL Y AXIS VERTICAL EVEN LAST DIGIT 0, 2, 4, 6, 8 ODD LAST DIGIT 1, 3, 5, 7, 9 SYMMETRY