# CCS 2007 From 06-07 DPI 4th grade indicators CCS 2007.

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CCS 2007 From 06-07 DPI 4th grade indicators

CCS 2007

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

CCS 2007 Forms of Numbers Expanded notation form 300+20+6 Three hundred twenty-six Written Form 326 Standard form Picture 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. Place Value http://mrsbogucki.com/aemes/resource/apps/placeval/placeval.htm 45,305.79 ten- thousands ones thousands hundreds tenstenths hundredths

CCS 2007 Blocks which show base 10 number values. Base Ten Blocks http://www.arcytech.org/java/b10blocks/b10blocks.html

CCS 2007 Blocks which show base 10 number values. Hundred Board http://www.amblesideprimary.com/ambleweb/mentalmaths/interactivenumbergrids.html

CCS 2007 Compose http://www.studyzone.org/testprep/math4/d/commutativep.cfm Putting numbers together to make them easier to work with 1 + 4 + 3 +7 + 6 + 8 + 9 + 2 = ? 10 + 10 + 10 + 10 = 40

CCS 2007 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

CCS 2007 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

CCS 2007 A mathematical operation where a number is added to itself a number of times Multiply http://www.arcytech.org/java/b10blocks/b10blocks.html factors product Repeated Addition http://www.harcourtschool.com/activity/mult/mult.html

CCS 2007 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

CCS 2007 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

CCS 2007 array A set of objects or numbers arranged in rows and columns. http://www.beaconlearningcenter.com/WebLessons/GroupsOfD ogs/default.htm

CCS 2007 Sharing or Grouping a number into equal parts. Divide http://www.amblesideprimary.com/ambleweb/mentalmaths/dividermachine.html quotient

CCS 2007 Division Vocabulary The Number being divided A number that will divide the dividend The result of a division Dividend Divisor Quotient

CCS 2007 Divisibility Rules

CCS 2007 Amount left over after dividing a number Remainder Fair shares ** Dividing is Sharing Equally!** http://nlvm.usu.edu/en/nav/frames_asid_193_g_2_t_1.html

CCS 2007 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

CCS 2007 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

CCS 2007 1212 2 Whole number fraction 7373 3434 http://www.visualfractions.com/MixtoFrCircle.html Fractions Numerator: number of each part Denominator: number of parts Improper fraction mixed number

CCS 2007 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.ht ml 1/2 = 3/6 Equal Portions

CCS 2007 A fraction written as a decimal Decimal Fraction http://www.amblesideprimary.com/ambleweb/mentalmaths/frac to.html

CCS 2007 Numbers written in standard form to show a value less than 1. Decimal http://www.321know.com/cmp42bx2.htm.1.01.001 one-tenth one-hundredth one-thousandth

CCS 2007 A line on which numbers, decimals and fractions can be compared and ordered. Number Line http://www.mathsonline.co.uk/freesite_tour/resource/whiteboard/decimals/dec_notes.htm l http://www.shodor.org/interactivate/activities/fracsorter/index.html.8.08 2.25.08 <.8.08 is less than.8 2.25 >.8 2.25 is greater than.8

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 http://www.studyzone.org/testprep/math4/k/chartprobl.cfm http://www.mathstories.com/strategies_makeatable.htm X X X

CCS 2007 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

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 Ferris-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

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

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. 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?

CCS 2007

A peg-board on which elastic bands are used to make shapes and patterns. Geo Board http://nlvm.usu.edu/en/nav/frames_asid_172_g_2_t_3.html

CCS 2007 A three sided polygon. Triangle http://www.factmonster.com/ipka/A0876325.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 Four sided figure, all sides equal, opposite sides parallel, and all right angles. 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 http://www.standards.dfes.gov.uk/primary/publications/mathem atics/12874/nns_useict026000carroll.swf

CCS 2007 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

CCS 2007 A ten sided polygon Decagon http://www.ul.ie/~cahird/polyhedronmode/decagon.htm

CCS 2007 A line with two endpoints Line Segment http://www.pinkmonkey.com/studyguides/subjects/geometry/chap1/g0101201.asp AB

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 This triangle contains 3 vertices

CCS 2007 Two rays that meet at a vertex Angle http://www.kidport.com/Grade5/Math/MeasureGeo/MeasuringAngles.htm

CCS 2007 The measurement of the longest side of a figure.

CCS 2007 The measurement of the shortest side of a figure.

CCS 2007 The measurement of all sides of a plane figure Perimeter http://www.funbrain.com/poly/ 3 in 4 in The DIMENSIONS of this rectangle ar 4 inches long, and 3 inches wide. To find the perimeter: length + length+ width + width 4in + 4in + 3in + 3in= 12in Hint:P lus all sides! http://www.shodor.org/interactivate/activities/permarea/index.html

CCS 2007 The measurement of square units needed to cover a figure. Area 3 in 4 in Length X Width 3in X 4in = 12 square inches http://www.shodor.org/interactivate/activities/perm/index.html http://www.studyzone.org/testprep/math4/d/metricunitl.cfm http://www.studyzone.org/testprep/math4/d/customaryunitl.cfm

CCS 2007 units used to measure area Square Units http://www.shodor.org/interactivate/activities/perm/index.html http://www.studyzone.org/testprep/math4/d/metricunitl.cfm http://www.studyzone.org/testprep/math4/d/customaryunitl.cfm 3 in 4 in Length X Width 3in X 4in = 12 square inches Each of these is a square unit.

CCS 2007

A pair of numbers that gives the coordinates of a point on a grid Ordered Pair http://www.mathcats.com/crafts/grids.html http://www.studyzone.org/testprep/math4/d/orderpairp.cfm 0 1 2 3 4 3 2 13 2 1 (1,2)

CCS 2007 Coordinate Grid/ X-Y Chart http://www.shodor.org/interactivate/activities/coords2/index.html Used to find coordinates for ordered pairs for the X and y axis.

CCS 2007 Quadrant Any quarter of a plane divided by an X and Y axis.

CCS 2007 A line joining two non-adjacent vertices of a polygon. Diagonal http://www.homeschoolmath.net/teaching/g/parallel_and_perpendicular.php

CCS 2007 When lines cross over one another Intersect http://www.homeschoolmath.net/teaching/g/parallel_and_perpendicular.php

CCS 2007 Two perpendicular lines which form a 90 degree angle. Right Angle http://www.mathsnet.net/shape/category1.html

CCS 2007 Two lines, equal distance apart that will never touch or intersect; non- intersecting lines 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 Any 2-dimensional (flat) area Plane

CCS 2007 A change in position or size Transformations http://www.harcourtschool.com/activity/icy_slides_flips_turns/

CCS 2007 A mirror view Reflection http://regentsprep.org/Regents/Math/reflect/PracRefl.htm l Pre-image (before) -image (after)

CCS 2007 Move or shift an item in any direction without rotating it. Translation Also called a slide http://regentsprep.org/Regents/Math/trans/PracTran.htm

CCS 2007 To turn an object, usually 90 degrees or 180 degrees. Rotation origin Half turn- 180 degrees Quarter turn- 90 degrees http://www.utc.edu/Faculty/Christopher-Mawata/transformations/rotations/lesson1c.html http://regentsprep.org/Regents/Math/rotate/PracRot.htm

CCS 2007 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.

CCS 2007

Used to collect and organize data http://www.studyzone.org/testprep/math4/d/collectdata4l.cfm Table rows columns

CCS 2007 The number of times an event occurs; may use tally marks to record Frequency IIII IIII IIII tallies http://www.studyzone.org/testprep/math4/d/tablestallyl.cfm

CCS 2007 A diagram using circles or other shapes to show the relationship between sets Venn Diagram http://www.shodor.org/interactivate/activities/venndia/index.html Guess the rule for this Venn Diagram

CCS 2007 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

CCS 2007 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 title

CCS 2007 Graph used to compare facts about groups and numbers that can be counted Bar Graph http://www.mcwdn.org/Graphs/BarGraph.html labels title scale

CCS 2007 This graph is similar to a regular bar graph, but it gives 2 pieces of information for each item, rather than just 1. Double Bar Graph Fruit Sold at the Market Scale title labels http://www.mathleague.com/help/data/data.htm

CCS 2007 http://www.mcwdn.org/Graphs/LineGraph.html interval label title scale A graph that shows change over time. Line Graph

CCS 2007 A graph that 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

CCS 2007 93, 84, 97, 98, 100, 78, 86, 100, 85, 92 78, 84, 85, 86, 92, 93, 97, 98, 100, 100 92 + 93 = 185 185 / 2 = 92.5 92.5 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

CCS 2007 The number that occurs most in a set of data. Mode 56, 66, 68, 73, 44, 62, 73, 44, 89, 55, 41, 73 41, 44, 44, 55, 56, 62, 66, 68, 73, 73, 73, 89 73 http://www.bbc.co.uk/education/mathsfile/shockwave/games/train.html http://www.oswego.org/ocsd-web/match/matchgeneric.asp?filename=ccarrollmode

CCS 2007 Subtract the smallest number from the largest number in a set of data. Range http://www.quizville.com/range.php 89, 73, 84, 91, 87, 77, 94 73, 77, 84, 87, 89, 91, 94 94 – 73 = 21 21

CCS 2007 The likelihood that an event will happen Probability What color did the spinner land on? Was this one of the favorable choices? Were there equal chances for both colors? http://www.mathgoodies.com/lessons/vol6/intro_probability.html

CCS 2007 An event that occurs or happens. Outcome What color did the spinner land on? Was this one of the favorable choices? Were there equal chances for both colors? http://www.studyzone.org/testprep/math4/d/outcomel.cfm

CCS 2007 An outcome that will probably occur or happen. Likely http://www.studyzone.org/testprep/math4/d/likelyl.cfm What are the chances of the arrow landing on white? When spinning the spinner 10 times, where is the arrow likely to land most often? Less often? Is your answer certain or uncertain?

CCS 2007 Each outcome has the same chance of occurring Equally Likely http://www.studyzone.org/testprep/math4/d/likelyl.cfm

CCS 2007 An event that you think will occur or happen. Prediction What color do you think the arrow will land on? Which color is less likely? http://www.shodor.org/interactivate/activities/spinner/index.html Which color is more likely?

CCS 2007 An outcome that will never occur or happen. Impossible http://www.bbc.co.uk/education/mathsfile/shockwave/games/fish.html What are the chances of the arrow landing on blue?

CCS 2007 http://www.mathagonyaunt.co.uk/STATISTICS/ESP/Perms_combs.html Steps: 1. Determine whether or not order matters. 2.Make an organized list of all possible outcomes. 3. Use this sample set of possible outcomes to determine your answer. Using the digits 3,4 and 5. What are all the possible three digit numbers you could create? 345, 354 435, 453 534, 543 Answer- 6 Order matters in this problem. Different orders make different numbers. Strategy for solving problems for determining outcomes: (Combinations and Permutations)

CCS 2007

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

CCS 2007 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. Function Machine T-chart

CCS 2007 A mathematical sentence where the left side equals the right side. Equation/Expression http://www.studyzone.org/testprep/math4/d/numericalp.cfm

CCS 2007 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

CCS 2007 Unknown The variable represents the number you are solving to find, termed as the… “X” or some other symbol is used to represent the unknown http://nlvm.usu.edu/en/nav/frames_asid_201_g_4_t_2.html

CCS 2007 Order of Operations The order in which operations should be done. http://www.mathgoodies.com/lessons/vol7/order_operations.html http://www.scweb4free.com/oper.html

CCS 2007 Resources Web Resources are listed at the bottom of each slide. Additional resources: –http://www.teachers.ash.org.au/jeather/maths/ dictionary.htmlhttp://www.teachers.ash.org.au/jeather/maths/ dictionary.html