The document provides definitions and examples for various math terms related to numbers, operations, measurement, geometry, and problem solving strategies. It includes 3 or fewer sentence summaries of rational numbers, place value, ordering numbers, estimating, factors and multiples, equivalence, symbols for relationships, fractions, decimals, angles, shapes, and units of measurement. Visual examples and links are provided with several terms.

1. From 06-07 DPI 5 th grade indicators Math Vocabulary

2. Goal 1

3. A real number that can be written as a positive or negative whole number, fraction, or decimal, Rational Number

4. Forms of Numbers Expanded notation form 300+20+6 Three hundred twenty-six Word Form 326 Standard form Picture Form http://www.aaamath.com/plc31d-placevalue-add.html

5. The position of a single digit in a whole number or decimal number containing one or more digits. Place Value http://mrsbogucki.com/aemes/resource/apps/placeval/placeval.htm 145,305.791 Hundred- thousands ten- thousands ones thousands hundreds tens tenths hundredths thousandths

6. Arranged from smallest to largest Ascending Order http://www.studyzone.org/testprep/math4/e/decorderl.cfm

7. Arranged from largest to smallest Descending Order

8. An answer close to the exact answer. Usually found by rounding to the nearest 10 or 100. Approximately/About 366 370 400 http://www.myschoolhouse.com/courses/O/1/16.asp

9. Numbers that divide exactly into another number. Factors 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 http://illuminations.nctm.org/tools/tool_detail.aspx?id=12

10. Number that results from multiplying a given number by a set of whole numbers. Multiples 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 http://www.tki.org.nz/r/wick_ed/maths/interactives_matrix.php http://www.bbc.co.uk/education/mathsfile/shockwave/games/gridgame.html

11. 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

12. Less Than/Greater Than Symbol used to compare relationships of inequalities. Symbol used to compare numbers Symbol used to compare numbers http://www.studyzone.org/testprep/math4/k/greaterlessthanl.cfm

13. Equal to/not equal to Symbols used to determine relationships of equalities. http://www.studyzone.org/testprep/math4/k/greaterlessthanl.cfm equal to .5 = .50 .30 = .300 .5 =.05 .3 = .003 ? < .5 ? =.1,.2,.3,.4,or .5 not equal to less than or equal to

14. Equal parts of a whole or group written with a numerator and a denominator. Fraction http://www.kidsolr.com/math/fractions.html http://math.rice.edu/~lanius/fractions/ 3 -Numerator 7 -Denominator

15. 7 3 http://www.visualfractions.com/MixtoFrCircle.html Fractions Improper fraction mixed number 1 2 2 Whole number fraction 3 4 Numerator: number of each part Denominator: number of parts

16. Fractions that are the same or equal 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.html 1/2 = 3/6

17. Numbers written in standard form to show a value less than 1. Decimal http://www.321know.com/cmp42bx2.htm one-tenth one-hundredth one-thousandth .1 .01 .001

18. Problem Solving Strategies http://www.mathstories.com/strategies.htm

19. Problem Solving Method Look Back Justify, prove, evaluate or explain the reasonableness of your answer.

20. Using a table/chart http://www.studyzone.org/testprep/math4/k/chartprobl.cfm http://www.mathstories.com/strategies_makeatable.htm X X X

21. Guess and Check http://www.mathstories.com/strategies_guesscheck.htm 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

22. Make a diagram/ picture http://www.mathstories.com/strategies_drawpicture.htm 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?

23. 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? Jill/Makayla Jill/Tanya Makayla/Tanya 3 ways http://www.mathstories.com/strategies_makealist.htm \ Organized list Answer

24. 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? http://www.mathstories.com/strategies_working_backward.htm 2 12 4 = 2 + 12 + 4 = 18

25. Using a calculator http://edschool.csuhayward.edu/departments/ted/instruction/howe/5350/1-calculatorRiddles.html

26. Using Objects, models, representations http://nlvm.usu.edu/en/nav/frames_asid_273_g_2_t_4.html

27. Information in a problem that does NOT help you solve the problem. Extra Information 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?

28. 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

29. Breaking a number apart to make it easier to work with. 30 X 14 Decompose http://www.studyzone.org/testprep/math4/d/commutativep.cfm (30 X 10) + (30 X 4) 300 + 120 = 420

30. 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

31. Goal 2

32. Units of capacity in the metric system. milliliter, liter http://www.metricamerica.com/litre.htm http://www.metricamerica.com/millilitre.htm 1000 ml = 1 L 1 L 1 ml

33. http://www.edhelper.com/math/capacity_fg1943.htm Units of capacity in the customary system. cup, pint, quart, gallon G Q Q Q Q PP PP PP PP cc 2 c = 1 p 2 p = 1 q 4 q = 1 gal cc cc cc cc cc cc cc

34. Benchmark/landmark http://www.mathcats.com/explore/convert.html 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

35. Units of length, width and distance in the metric system. centimeter, meter, kilometer http://www.metricamerica.com/centimetre.htm 100cm = 1m 1000 m = 1 km

36. Units of length, width and distance in the customary system. Inches, Feet, Yards, Miles http://www.funbrain.com/measure/ 12in = 1 ft 3 ft = 1 yd 5280 ft = 1 mi

37. Benchmark/landmark http://www.aaamath.com/B/mea69_x2.htm 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

38. Units of weight (or mass) in the metric system. gram and kilogram http://www.studyzone.org/testprep/math4/d/metgraml.cfm 1000g = 1kg

39. Units of weight (or mass) in the customary system. ounce, pound, and ton http://www.edhelper.com/math/length_weight_fg2255.htm 16 oz = 1lb 2000 lbs = 1 ton

40. 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

41. Tool used to measure angles Protractor http://www.amblesideprimary.com/ambleweb/mentalmaths/protractor.html http://www.enchantedlearning.com/math/label/protractor/

42. 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

43. An angle with a measure of more than 90 degrees, but less than 180 degrees. Obtuse Angle http://www.manatee.k12.fl.us/sites/elementary/palmasola/mathlabtutan1b.htm http://www.toonuniversity.com/6m_angle_d.html 110 35 35

44. An angle less than 90 degrees Acute Angle http://www.mathsnet.net/shape/category2.html 60 60 60

45. Two angles that share a common side Adjacent Angles http://www.mathwords.com/a/adjacent_angles.htm 130 50

46. Angle Notation ABC = A B C Symbol used to identify an angle

47. Two adjacent angles that total 180 degrees Supplementary Angles http://www.mathsisfun.com/geometry/supplementary-angles.html http://www.mathopenref.com/anglesupplementary.html 130 50

48. Two adjacent angles that total 90 degrees Complementary Angles http://www.mathwarehouse.com/geometry/angle/complementary-angles.php http://www.mathopenref.com/anglecomplementary.html 45 45

49. Angles that have the same measure. Congruent Angles http://www.kidport.com/Grade5/Math/MeasureGeo/MeasuringAngles.htm 45 45

50. Goal 3

51. When sides of a shape are equal in length Congruent Sides These markings indicate congruent sides

52. All three sides of this triangle are congruent. 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 4 in 4 in 4 in

53. This triangle has two congruent sides. Isosceles Triangle http://www.homeschoolmath.net/gy/equilateral_isosceles.php http://www.amblesideprimary.com/ambleweb/sketchpad/isosco.htm 4 in 3 in 4 in

54. This triangle has no congruent sides Scalene Triangle http://www.amblesideprimary.com/ambleweb/sketchpad/scalene.htm http://www.mathsisfun.com/triangle.html 5 in 4 in 3 in

55. 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

56. A polygon for which all sides and all angles are not congruent. Irregular Polygon http://www.ul.ie/~cahird/polyhedronmode/irregula.htm

57. Any four sided figure. Quadrilateral http://regentsprep.org/Regents/math/quad/LQuad.htm

58. A line with two endpoints Line Segment http://www.pinkmonkey.com/studyguides/subjects/geometry/chap1/g0101201.asp Midpoint A B

59. A line with one endpoint Ray http://www.mathleague.com/help/geometry/basicterms.htm#rays

60. The Point at which two rays meet. Vertex http://mathworld.wolfram.com/VertexAngle.html

61. Two rays that meet at a vertex Angle http://www.kidport.com/Grade5/Math/MeasureGeo/MeasuringAngles.htm

62. Sides or angles immediately next to each other. Adjacent http://www.kidport.com/Grade5/Math/MeasureGeo/MeasuringAngles.htm

63. To divide into two equal sections; to cut in half. Bisect

64. 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

65. Lines that intersect at right angles to each other. Perpendicular Lines http://www.homeschoolmath.net/teaching/g/parallel_and_perpendicular.php

66. Making an estimate or best guess by appearance or with little evidence. Conjecture Is this a right triangle? How do you know? What is your evidence? Can you tell without measuring?

67. A line joining two non-adjacent vertices of a polygon. Diagonal http://www.math.fau.edu/Richman/Liberal/polydiag.htm

68. Four sided figure, all sides equal, opposite sides parallel, all right angles Square http://www.mathleague.com/help/geometry/polygons.htm#righttriangle Sum of interior angles- 360 º 2 intersecting, bisecting, perpendicular diagonals

69. Four sided figure. opposite sides equal lengths and parallel, all right angles Rectangle

70. Four sided figure. opposite sides equal lengths and parallel, all right angles Rectangle http://encyclopedia.laborlawtalk.com/Rectangle http://www.standards.dfes.gov.uk/primary/publications/mathematics/12874/nns_useict026000carroll.swf Sum of interior angles- 360 º 2 intersecting diagonals.

71. A four-sided figure in which the two pairs of adjacent sides have the same length. Kite Sum of interior angles- 360 º 2 intersecting, perpendicular diagonals

72. Four sided figure. Opposite sides equal lengths and parallel Parallelogram http://ejad.best.vwh.net/java/patterns/patterns_j.shtml http://www.aplusmath.com/cgi-bin/games/geopicture Four sided figure. opposite sides equal lengths and parallel, opposite angles equal Rhombus An six sided figure Hexagon An eight sided figure Octagon Four sided figure. Top and bottom sides parallel Trapezoid An five sided figure Pentagon

73. Parallelogram Rhombus 9 diagonals/ sum of interior angles- 720 º Hexagon 20 diagonals/ sum of interior angles- 1080 º Octagon 2 intersecting diagonals/ sum of interior angles 360 º Trapezoid 5 diagonals/ Sum of interior angles - 540 º Pentagon 2 intersecting diagonals/ sum of interior angles 360 º 2 intersecting perpendicular diagonals/ sum of interior angles 360 º

74. Number of diagonals in a polygon: +3 +4 +5 +6 Sum of interior angles in a polygon: +180 +180 +180 +180 +180 #of sides 4 5 6 7 8 # of diagonals 2 5 9 14 20 #of sides 3 4 5 6 7 8 Sum of int. angles 180 º 360 º 540 º 720 º 900 º 1080 º

75. two types of trapezoids Right Trapezoid Two right angles Isosceles Trapezoid No right angles Two congruent sides

76. A ten sided polygon Decagon http://www.ul.ie/~cahird/polyhedronmode/decagon.htm

77. When a straight line is drawn through a shape so that the two halves are congruent. Symmetry http://library.thinkquest.org/J002441F/symmetry.htm Line of symmetry

78. 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

79. To turn an object, usually 90 degrees or 180 degrees, 0r 270 degrees. Point of rotation Half turn- 180 degrees Quarter turn- 90 degrees http://regentsprep.org/Regents/Math/rotate/PracRot.htm http://www.studyzone.org/mtestprep/math8/f/symturns5p.cfm Rotations 3 Quarter turn-270 degrees

80. Counter Clockwise The same direction as the way hands on the clock go. Clockwise The opposite direction of the way the hands on the clock go.

81. Goal 4

82. Collection of information often organized on graphs or charts for analysis. Data http://www.studyzone.org/testprep/math4/d/graphdatal.cfm

83. The middle number in a set of data; must put numbers in order from least to greatest first. Median http://regentsprep.org/Regents/math/mean/Pmeasure.htm 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

84. The number that occurs most in a set of data. Mode http://www.oswego.org/ocsd-web/match/matchgeneric.asp?filename=ccarrollmode http://www.bbc.co.uk/education/mathsfile/shockwave/games/train.html 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

85. Subtract the smallest number from the largest number in a set of data. Range http://www.mathgoodies.com/lessons/vol8/range.html http://www.quizville.com/range.php 89, 73, 84, 91, 87, 77, 94 73, 77, 84, 87, 89, 91, 94 94 – 73 = 21 21

86. A way to arrange data with the tens on the left and the ones listed on the right. Stem and Leaf Plot http://regentsprep.org/Regents/math/data/stemleaf.htm http://www.shodor.org/interactivate/activities/stemleaf/index.html 1 2 3 4 5 6 7 3, 3, 7 2, 9, 9, 9 1 3, 9 1, 4, 6 2 5, 7, 7, 8

87. Coordinate Grid/ X-Y Chart Used to find coordinates for ordered pairs for the X and Y axis. http://www.shodor.org/interactivate/activities/pcoords/index.html http://www.shodor.org/interactivate/activities/coords2/index.html

88. A horizontal number line on which each value of a set is denoted by an “x” over a value. Line Plot The number of x’s indicates how many times each score occurred http://www.studyzone.org/testprep/math4/d/rangel.cfm l

89. A graph that uses pictures to represent data. Pictograph Key http://www.oswego.org/ocsd-web/quiz/mquiz.asp?filename=ccarrollgraph http://www.studyzone.org/testprep/math4/d/graphdatal.cfm

90. Shows change over time; will have months, days or other time words in the problem. Line Graph http://www.mcwdn.org/Graphs/LineGraph.html interval label title scale

91. Is used to compare facts about groups and numbers that can be counted Bar Graph http://www.mcwdn.org/Graphs/BarGraph.html labels title scale

92. Compares parts to the whole; decimals and fractions may be used on this graph Circle Graph http://www.mcwdn.org/Graphs/CirclePieQuiz.html key title labels

93. The number of times an event occurs; may use tally marks to record Frequency tallies http://www.studyzone.org/testprep/math4/d/tablestallyl.cfm IIII IIII IIII

94. Goal 5

95. A letter or symbol that represents a number in an algebraic expression. Variable http://www.aplusmath.com/Games/PlanetBlast/index.html http://www.vectorkids.com/vkvariable.htm Each side of the = symbol must balance

96. Contains at least one variable as well as other numbers and/or operations. Algebraic Expression 16 5 10 20 20 100 http://mathsnet.net/algebra/l2_equation.html l

97. A mathematical sentence where the left side equals the right side. Equation http://www.studyzone.org/testprep/math4/d/numericalp.cfm

98. Input/Output chart http://www.studyzone.org/testprep/math4/k/addpatternsl.cfm http://www.shodor.org/interactivate/activities/NumberCruncher/ A chart that shows a consistent rate of change. T-chart Function Machine

99. Unknown The variable represents the number you are solving to find, termed as the… http://nlvm.usu.edu/en/nav/frames_asid_201_g_4_t_2.html X + 3 = 7

100. 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 An ordered set of numbers, shapes, or other mathematical objects, arranged according to a rule. Pattern

101. Constant Change Pattern Changes Varying Change Proportional Change 5 6 7 8 9 10 11…. 22 3,7,4,8,5,9,6,10,7… 2,4,6,8,10…. 3 4 5 6 7 8 9… 20

102. Geometric Pattern Pattern Types Numeric Pattern Patterns using shapes 4, 8,16,32,…. Patterns using numbers

103. Nth Term 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 10 th term = 3(10) = 30

104. Equal to/not equal to Symbols used to determine relationships of equalities. http://www.studyzone.org/testprep/math4/k/greaterlessthanl.cfm equal to .5 = .50 .30 = .300 .5 =.05 .3 = .003 ? < .5 ? =.1,.2,.3,.4,or .5 not equal to less than or equal to

105. The quotient of two numbers used to compare two qualities. Ratio http://www.studyzone.org/mtestprep/math8/c/ratiol.cfm 3 5 Red chips Blue chips

106. Resources Web Resources are listed at the bottom of each slide. Additional resources: http://www.teachers.ash.org.au/jeather/maths/dictionary.html