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From 06-07 DPI 5th grade indicators CCS 2007 CCS 2007 A real number that can be written as a positive or negative whole number, fraction, or decimal, Rational Number CCS 2007 Expanded notation form Picture Form 300+20+6 Forms of Numbers Three hundred twenty-six Word Form 326 Standard form http://www.aaamath.com/plc31d-placevalue-add.html CCS 2007 The position of a single digit in a whole number or decimal number containing one or more digits. tenthousands hundreds ones hundredths 145,305.791 Hundredthousands thousands tens tenths thousandths Place Value http://mrsbogucki.com/aemes/resource/apps/placeval/placeval.htm CCS 2007 Arranged from smallest to largest Ascending Order http://www.studyzone.org/testprep/math4/e/decorderl.cfm CCS 2007 Arranged from largest to smallest Descending Order CCS 2007 An answer close to the exact answer. Usually found by rounding to the nearest 10 or 100. 366 370 400 Approximately/About http://www.myschoolhouse.com/courses/O/1/16.asp CCS 2007 Numbers that divide exactly into another number. 12 – 1,2,3,4,6,12 36 – 1,2,3,4,6,9,12,18,36 48 – 1,2,3,4,6,8,12,16,24,48 Factors http://illuminations.nctm.org/tools/tool_detail.aspx?id=12 CCS 2007 Number that results from multiplying a given number by a set of whole numbers. 4 – 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 6 – 6, 12, 18, 24, 36, 42, 48, 54 8 – 8,16, 24, 32, 40, 48, 56 Multiples http://www.tki.org.nz/r/wick_ed/maths/interactives_matrix.php http://www.bbc.co.uk/education/mathsfile/shockwave/games/gridgame.html CCS 2007 Having the same amount or value; the state of being equal. Equivalence http://nlvm.usu.edu/en/nav/frames_asid_105_g_2_t_1.html CCS 2007 Symbol used to compare relationships of inequalities. Symbol used to compare numbers Symbol used to compare numbers Less Than/Greater Than http://www.studyzone.org/testprep/math4/k/greaterlessthanl.cfm CCS 2007 Symbols used to determine relationships of equalities. .5 = .50 ? < .5 .30 = .300 equal to .5 =.05 .3 = .003 ? =.1,.2,.3,.4,or .5 less than or equal to not equal to Equal to/not equal to http://www.studyzone.org/testprep/math4/k/greaterlessthanl.cfm CCS 2007 Equal parts of a whole or group written with a numerator and a denominator. 3 -Numerator 7 -Denominator Fraction http://www.kidsolr.com/math/fractions.html http://math.rice.edu/~lanius/fractions/ CCS 2007 Denominator: number of parts 3 4 Numerator: number of each part Fractions 7 3 Improper fraction Whole number 1 2 2 fraction mixed number http://www.visualfractions.com/MixtoFrCircle.html CCS 2007 Fractions that are the same or equal 1/2 = 3/6 Equivalent Fractions http://www.learningplanet.com/sam/ff/index.asp http://euclid.barry.edu/~marinas/mat476/journal/sim319df.html http://www.shodor.org/interactivate/activities/fracsorter/index.ht CCS 2007 Numbers written in standard form to show a value less than 1. .1 one-tenth .01 one-hundredth .001 one-thousandth Decimal http://www.321know.com/cmp42bx2.htm CCS 2007 Problem Solving Strategies http://www.mathstories.com/strategies.htm CCS 2007 Problem Solving Method Look Back Justify, prove, evaluate or explain the reasonableness of your answer. CCS 2007 Using a table/chart X X X http://www.studyzone.org/testprep/math4/k/chartprobl.cfm http://www.mathstories.com/strategies_makeatable.htm CCS 2007 Guess and Check Prince Carl divided 15 stone games into two piles: games he owns and games his brother owns. He owns 3 more games than his brother. How many games does his brother own? Answer: Prince Carl – 9 Brother - 6 http://www.mathstories.com/strategies_guesscheck.htm CCS 2007 Make a diagram/ picture Question: Laura has 3 green chips, 4 blue chips and 1 red chip in her bag. What fractional part of the bag of chips is green? http://www.mathstories.com/strategies_drawpicture.htm CCS 2007 Make an organized list Question: Jill, Makayla and Tanya don’t want to ride the Farris-wheel alone. How many ways can they ride if the ride will only fit two at a time? Organized list Answer Jill/Makayla Jill/Tanya Makayla/Tanya 3 ways http://www.mathstories.com/strategies_makealist.htm CCS 2007 Work Backwards The castle kitchen servants brought in 4 pies left over from the feast. 12 pies were eaten at the feast. Queen Mab took 2 home with her. How many pies did the servants bring into the feast at the beginning? 2 12 4= 2 + 12 + 4 = 18 http://www.mathstories.com/strategies_working_backward.htm CCS 2007 Using a calculator http://edschool.csuhayward.edu/departments/ted/instruction/howe/ 5350/1-calculatorRiddles.html CCS 2007 Using Objects, models, representations http://nlvm.usu.edu/en/nav/frames_asid_273_g_2_t_4.html CCS 2007 Information in a problem that does NOT help you solve the problem. The peasants had to dig a trench 3 feet side to side and 10 times as long. It took them 4 days to dig it. There were 7 of them digging. How long was the trench? Extra Information CCS 2007 Putting numbers together to make them easier to work with 1 + 4 + 3 +7 + 6 + 8 + 9 + 2 = ? 10 + 10 + 10 + 10 = 40 Compose http://www.studyzone.org/testprep/math4/d/commutativep.cfm CCS 2007 Breaking a number apart to make it easier to work with. 30 X 14 (30 X 10) + (30 X 4) 300 + 120 = 420 Decompose http://www.studyzone.org/testprep/math4/d/commutativep.cfm CCS 2007 Mathematical sentence where the left side of the equals sign has the same value as the right side. Equation http://www.aplusmath.com/Games/PlanetBlast/index.html CCS 2007 CCS 2007 Units of capacity in the metric system. 1000 ml = 1 L milliliter, liter http://www.metricamerica.com/litre.htm http://www.metricamerica.com/millilitre.htm CCS 2007 Units of capacity in the customary system. QQ PP PP QQ PP PP cc cc cc cc cc cc 2c=1p 2p=1q 4 q = 1 gal cc cc cup, pint, quart, gallon http://www.edhelper.com/math/capacity_fg1943.htm CCS 2007 Benchmark/landmark Benchmark Comparisons for Metric ad Customary Measurements Greater Than/ Less Than Metric Units Customary Units 2.54 cm (about 2.5) 1 in cm < in 0.9 m (about 1) 1 yd m > yd 1.6 km (about 1.5) 1 mi km <mi .45 kg (about .5) 1 lb kg > lb .95 L (about 1) 1 qt L > qt http://www.mathcats.com/explore/convert.html CCS 2007 Units of length, width and distance in the metric system. 100cm = 1m 1000 m = 1 km centimeter, meter, kilometer http://www.metricamerica.com/centimetre.htm CCS 2007 Units of length, width and distance in the customary system. 12in = 1 ft 3 ft = 1 yd 5280 ft = 1 mi Inches, Feet, Yards, Miles http://www.funbrain.com/measure/ CCS 2007 Benchmark/landmark Benchmark Comparisons for Metric ad Customary Measurements Metric Units Customary Units 2.54 cm (about 2.5) 1 in 0.9 m (about 1) 1 yd 1.6 km (about 1.5) 1 mi .45 kg (about .5) 1 lb .95 L (about 1) 1 qt Greater Than/ Less Than cm < in m > yd km <mi kg > lb L >qt http://www.aaamath.com/B/mea69_x2.htm CCS 2007 Units of weight (or mass) in the metric system. 1000g = 1kg gram and kilogram http://www.studyzone.org/testprep/math4/d/metgraml.cfm CCS 2007 Units of weight (or mass) in the customary system. 16 oz = 1lb 2000 lbs = 1 ton ounce, pound, and ton http://www.edhelper.com/math/length_weight_fg2255.htm CCS 2007 Benchmark/landmark Benchmark Comparisons for Metric ad Customary Measurements Greater Than/ Less Than Metric Units Customary Units 2.54 cm (about 2.5) 1 in cm < in 0.9 m (about 1) 1 yd m > yd 1.6 km (about 1.5) 1 mi km <mi .45 kg (about .5) 1 lb kg > lb .95 L (about 1) 1 qt L >qt CCS 2007 Tool used to measure angles Protractor http://www.amblesideprimary.com/ambleweb/mentalmaths/protractor.html http://www.enchantedlearning.com/math/label/protractor/ CCS 2007 Two perpendicular lines which form a 90 degree angle. Right Angle http://www.icteachers.co.uk/children/sats/triangles.htm http://www.mathsnet.net/shape/category1.html CCS 2007 An angle with a measure of more than 90 degrees, but less than 180 degrees. 110 35 35 Obtuse Angle http://www.manatee.k12.fl.us/sites/elementary/palmasola/mathlabtutan1b.htm http://www.toonuniversity.com/6m_angle_d.html CCS 2007 An angle less than 90 degrees 60 60 60 Acute Angle http://www.mathsnet.net/shape/category2.html CCS 2007 Two angles that share a common side 130 50 Adjacent Angles http://www.mathwords.com/a/adjacent_angles.htm CCS 2007 Symbol used to identify an angle A = ABC C B Angle Notation CCS 2007 Two adjacent angles that total 180 degrees 130 50 Supplementary Angles http://www.mathsisfun.com/geometry/supplementary-angles.html http://www.mathopenref.com/anglesupplementary.html CCS 2007 Two adjacent angles that total 90 degrees 45 45 Complementary Angles http://www.mathwarehouse.com/geometry/angle/complementary-angles.php http://www.mathopenref.com/anglecomplementary.html CCS 2007 Angles that have the same measure. 45 45 Congruent Angles http://www.kidport.com/Grade5/Math/MeasureGeo/MeasuringAngles.htm CCS 2007 CCS 2007 When sides of a shape are equal in length These markings indicate congruent sides Congruent Sides CCS 2007 All three sides of this triangle are congruent. 4 in 4 in 4 in Equilateral Triangle http://www.factmonster.com/ipka/A0876325.html http://www.amblesideprimary.com/ambleweb/sketchpad/equilateral.htm http://library.thinkquest.org/20991/textonly/quizzes/geo/q4/p1.html CCS 2007 This triangle has two congruent sides. 4 in 4 in 3 in Isosceles Triangle http://www.homeschoolmath.net/gy/equilateral_isosceles.php http://www.amblesideprimary.com/ambleweb/sketchpad/isosco.htm CCS 2007 This triangle has no congruent sides 4 in 3 in 5 in Scalene Triangle http://www.amblesideprimary.com/ambleweb/sketchpad/scalene.htm http://www.mathsisfun.com/triangle.html CCS 2007 A polygon for which all sides are congruent and all angles are congruent. Regular Polygon http://mathworld.wolfram.com/RegularPolygon.html http://www.ul.ie/~cahird/polyhedronmode/regular.htm CCS 2007 A polygon for which all sides and all angles are not congruent. Irregular Polygon http://www.ul.ie/~cahird/polyhedronmode/irregula.htm CCS 2007 Any four sided figure. Quadrilateral http://regentsprep.org/Regents/math/quad/LQuad.htm CCS 2007 A line with two endpoints Midpoint A B Line Segment http://www.pinkmonkey.com/studyguides/subjects/geometry/chap1/g0101201.asp CCS 2007 A line with one endpoint Ray http://www.mathleague.com/help/geometry/basicterms.htm#rays CCS 2007 The Point at which two rays meet. Vertex http://mathworld.wolfram.com/VertexAngle.html CCS 2007 Two rays that meet at a vertex Angle http://www.kidport.com/Grade5/Math/MeasureGeo/MeasuringAngles.htm CCS 2007 Sides or angles immediately next to each other. Adjacent http://www.kidport.com/Grade5/Math/MeasureGeo/MeasuringAngles.htm CCS 2007 To divide into two equal sections; to cut in half. Bisect CCS 2007 Two lines that will never touch or intersect because they are the same distance apart. Parallel Lines http://www.homeschoolmath.net/teaching/g/parallel_and_perpendicular.php CCS 2007 Lines that intersect at right angles to each other. Perpendicular Lines http://www.homeschoolmath.net/teaching/g/parallel_and_perpendicular.php CCS 2007 Making an estimate or best guess by appearance or with little evidence. Is this a right triangle? How do you know? What is your evidence? Can you tell without measuring? Conjecture CCS 2007 A line joining two non-adjacent vertices of a polygon. Diagonal http://www.math.fau.edu/Richman/Liberal/polydiag.htm CCS 2007 Four sided figure, all sides equal, opposite sides parallel, all right angles Sum of interior angles- 360º 2 intersecting, bisecting, perpendicular diagonals Square http://www.mathleague.com/help/geometry/polygons.htm#righttriangle CCS 2007 Four sided figure. opposite sides equal lengths and parallel, all right angles Rectangle CCS 2007 Four sided figure. opposite sides equal lengths and parallel, all right angles Sum of interior angles- 360º 2 intersecting diagonals. Rectangle http://encyclopedia.laborlawtalk.com/Rectangle http://www.standards.dfes.gov.uk/primary/publications/mathematics/12874/nns_useict026000carroll.swf CCS 2007 A four-sided figure in which the two pairs of adjacent sides have the same length. Sum of interior angles- 360º 2 intersecting, perpendicular diagonals Kite CCS 2007 Four sided figure. Opposite sides equal lengths and parallel An six sided figure Four sided figure. Top and bottom sides parallel Parallelogram Four sided figure. opposite sides equal lengths and parallel, opposite angles equal Hexagon Trapezoid An eight sided figure An five sided figure Octagon Rhombus Pentagon http://ejad.best.vwh.net/java/patterns/patterns_j.shtml http://www.aplusmath.com/cgi-bin/games/geopicture CCS 2007 2 intersecting diagonals/ sum of interior angles 360º 2 intersecting diagonals/ sum of interior angles 360º Parallelogram 2 intersecting perpendicular diagonals/ sum of interior angles 360º Rhombus Trapezoid 5 diagonals/ Sum of interior angles - 540º Pentagon 9 diagonals/ sum of interior angles- 720º Hexagon 20 diagonals/ sum of interior angles- 1080º Octagon CCS 2007 Number of diagonals in a polygon: #of sides 4 5 6 7 8 # of diagonals 2 5 9 14 20 +3 +4 +5 +6 Sum of interior angles in a polygon: #of sides 3 4 5 Sum of int. angles 180º 360º 540º 720º +180 +180 +180 6 +180 7 8 900º 1080º +180 CCS 2007 two types of trapezoids Two right angles No right angles Two congruent sides Right Trapezoid Isosceles Trapezoid CCS 2007 A ten sided polygon Decagon http://www.ul.ie/~cahird/polyhedronmode/decagon.htm CCS 2007 When a straight line is drawn through a shape so that the two halves are congruent. Line of symmetry Symmetry http://library.thinkquest.org/J002441F/symmetry.htm CCS 2007 When an outline of a turning figure matches its original shape . Rotational Symmetry http://www.adrianbruce.com/Symmetry/10.htm http://www.learner.org/channel/courses/learningmath/geometry/session7/part_b/index.html CCS 2007 To turn an object, usually 90 degrees or 180 degrees, 0r 270 degrees. Point of rotation Half turn- 180 degrees Quarter turn- 90 degrees 3 Quarter turn-270 degrees Rotations http://regentsprep.org/Regents/Math/rotate/PracRot.htm http://www.studyzone.org/mtestprep/math8/f/symturns5p.cfm CCS 2007 The same direction as the way hands on the clock go. Clockwise Counter Clockwise The opposite direction of the way the hands on the clock go. CCS 2007 CCS 2007 Collection of information often organized on graphs or charts for analysis. Data http://www.studyzone.org/testprep/math4/d/graphdatal.cfm CCS 2007 The middle number in a set of data; must put numbers in order from least to greatest first. 93, 84, 97, 98, 100, 78, 86, 100, 85, 92 78, 84, 85, 86, 92, 93, 97, 98, 100, 100 78, 84, 85, 86, 92, 93, 97, 98, 100, 100 92 + 93 = 185 185 / 2 = 92.5 92.5 Median http://regentsprep.org/Regents/math/mean/Pmeasure.htm CCS 2007 The number that occurs most in a set of data. 56, 66, 68, 73, 44, 62, 73, 44, 89, 55, 41, 73 41, 44, 44, 55, 56, 62, 66, 68, 73, 73, 73, 89 41, 44, 44, 55, 56, 62, 66, 68, 73, 73, 73, 89 73 Mode http://www.oswego.org/ocsd-web/match/matchgeneric.asp?filename=ccarrollmode http://www.bbc.co.uk/education/mathsfile/shockwave/games/train.html CCS 2007 Subtract the smallest number from the largest number in a set of data. 89, 73, 84, 91, 87, 77, 94 73, 77, 84, 87, 89, 91, 94 94 – 73 = 21 21 Range http://www.mathgoodies.com/lessons/vol8/range.html http://www.quizville.com/range.php CCS 2007 A way to arrange data with the tens on the left and the ones listed on the right. 1 3, 3, 7 2 2, 9, 9, 9 3 1 4 3, 9 5 1, 4, 6 6 2 7 5, 7, 7, 8 Stem and Leaf Plot http://regentsprep.org/Regents/math/data/stemleaf.htm http://www.shodor.org/interactivate/activities/stemleaf/index.html CCS 2007 Used to find coordinates for ordered pairs for the X and Y axis. Coordinate Grid/ X-Y Chart http://www.shodor.org/interactivate/activities/pcoords/index.html http://www.shodor.org/interactivate/activities/coords2/index.html CCS 2007 A horizontal number line on which each value of a set is denoted by an “x” over a value. The number of x’s indicates how many times each score occurred Line Plot http://www.studyzone.org/testprep/math4/d/rangel.cfm CCS 2007 A graph that uses pictures to represent data. Key Pictograph http://www.studyzone.org/testprep/math4/d/graphdatal.cfm http://www.oswego.org/ocsd-web/quiz/mquiz.asp?filename=ccarrollgraph CCS 2007 Shows change over time; will have months, days or other time words in the problem. label scale interval title Line Graph http://www.mcwdn.org/Graphs/LineGraph.html CCS 2007 Is used to compare facts about groups and numbers that can be counted title labels scale Bar Graph http://www.mcwdn.org/Graphs/BarGraph.html CCS 2007 Compares parts to the whole; decimals and fractions may be used on this graph title key labels Circle Graph http://www.mcwdn.org/Graphs/CirclePieQuiz.html CCS 2007 The number of times an event occurs; may use tally marks to record tallies IIII IIII IIII Frequency http://www.studyzone.org/testprep/math4/d/tablestallyl.cfm CCS 2007 CCS 2007 A letter or symbol that represents a number in an algebraic expression. Each side of the = symbol must balance Variable http://www.aplusmath.com/Games/PlanetBlast/index.html http://www.vectorkids.com/vkvariable.htm CCS 2007 Contains at least one variable as well as other numbers and/or operations. 16 10 20 5 20 100 Algebraic Expression http://mathsnet.net/algebra/l2_equation.html CCS 2007 A mathematical sentence where the left side equals the right side. Equation http://www.studyzone.org/testprep/math4/d/numericalp.cfm CCS 2007 A chart that shows a consistent rate of change. Function Machine T-chart Input/Output chart http://www.studyzone.org/testprep/math4/k/addpatternsl.cfm http://www.shodor.org/interactivate/activities/NumberCruncher/ CCS 2007 The variable represents the number you are solving to find, termed as the… Unknown http://nlvm.usu.edu/en/nav/frames_asid_201_g_4_t_2.html CCS 2007 An ordered set of numbers, shapes, or other mathematical objects, arranged according to a rule. Pattern http://www.studyzone.org/testprep/math4/i/dpatternsl.cfm http://www.studyzone.org/testprep/math4/k/patternsl.cfm http://www.studyzone.org/testprep/math4/k/patternsp.cfm CCS 2007 Pattern Changes Constant Change 2,4,6,8,10…. Varying Change 3,7,4,8,5,9,6,10,7… Proportional Change 3 4 5 6 7 8 9… 20 5 6 7 8 9 10 11…. 22 CCS 2007 Pattern Types Geometric Pattern Patterns using shapes Numeric Pattern 4, 8,16,32,…. Patterns using numbers CCS 2007 Any number in the pattern can be found by finding the relation ship or rule of the pattern. 3,6,9,12,15,18…… Nth term = 3n 10th term = 3(10) = 30 Nth Term CCS 2007 Symbols used to determine relationships of equalities. .5 = .50 ? < .5 .30 = .300 equal to .5 =.05 .3 = .003 ? =.1,.2,.3,.4,or .5 less than or equal to not equal to Equal to/not equal to http://www.studyzone.org/testprep/math4/k/greaterlessthanl.cfm CCS 2007 The quotient of two numbers used to compare two qualities. 3 5 Red chips Blue chips Ratio http://www.studyzone.org/mtestprep/math8/c/ratiol.cfm CCS 2007 Resources • Web Resources are listed at the bottom of each slide. • Additional resources: – http://www.teachers.ash.org.au/jeather/maths/ dictionary.html CCS 2007