2003 MATHEMATICS NCSCOS Grade 3 Indicators
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Transcript of 2003 MATHEMATICS NCSCOS Grade 3 Indicators
2003 MATHEMATICS NCSCOSGrade 3 Indicators
The learner will model, identify, and compute with whole numbers through 9,999.
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
1,111
The position of a single digit in a whole number or decimal number containing
one or more digits.
Place Valuehttp://mrsbogucki.com/aemes/resource/apps/placeval/placeval.htm
5,305
ones
thousands
hundreds
tens
Blocks which show base 10 number values.
Base Ten Blockshttp://www.arcytech.org/java/b10blocks/b10blocks.html
A diagram using circles or other shapes ( i. e. rectangles) to show the
relationship between sets
Venn Diagramhttp://www.shodor.org/interactivate/activities/venndia/index.html
Guess the rule for this
Venn Diagram
Putting numbers together.
Addhttp://www.studyzone.org/testprep/math4/d/commutativep.cfm
17 + 34 = 51
SumAddends
Putting numbers together to make them easier to use
1 + 4 + 3 +7 + 6 + 8 + 9 + 2 = ?
10 + 10 + 10 + 10 = 40
Composehttp://www.studyzone.org/testprep/math4/d/commutativep.cfm
Breaking a number apart to make it easier to use.
30 X 14
Decomposehttp://www.studyzone.org/testprep/math4/d/commutativep.cfm
(30 X 10) + (30 X 4)300 + 120 = 420
Subtracthttp://www.aplusmath.com/Games/PlanetBlasterBasics/index.html
To take numbers apart
95 – 36 = 59
Difference
A mathematical operation where a number is added to itself a number of times
Multiply
http://www.arcytech.org/java/b10blocks/b10blocks.html
factorsproduct
Repeated Addition
http://www.harcourtschool.com/activity/mult/mult.html
Sharing or Grouping a number into equal parts
Divide
Repeated Subtraction: 20-2-2-2-2-2-2-2-2-2-2=0
http://www.amblesideprimary.com/ambleweb/mentalmaths/dividermachine.html
quotient
Guess how many gumballs are in
the jar!
The use of rounding and/or other strategies to make an educated guess or reasonably accurate approximation.
Estimatehttp://www.shodor.org/interactivate/activities/estim3/index.html
http://www.janbrett.com/piggybacks/rounding.htm
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
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
Equal to/not equal to
Symbols used to determine relationships of equalities.
http://www.studyzone.org/testprep/math4/k/greaterlessthanl.cfm
equal to
5 = 5
30 = 13 + 174 = 5
17 = 3 +12
? < 5
? = 1,2,3,4,5
not equal to
less than or equal to
Combining numbers of multiple groups
Multiply
Groups or sets
** Multiplying is repeated addition**
http://nlvm.usu.edu/en/nav/frames_asid_193_g_2_t_1.html
4 X 2 = 8
2 + 2 + 2 + 2
arrayhttp://www.beaconlearningcenter.com/WebLessons/GroupsOfDogs/default.htm
A set of objects or numbers arranged in rows and columns
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
Numbers that result 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.bbc.co.uk/education/mathsfile/shockwave/games/gridgame.html
An ordered set of numbers, shapes, or other mathematical objects, arranged according to
a rule.
Patternhttp://www.studyzone.org/testprep/math4/k/patternsl.cfmhttp://www.studyzone.org/testprep/math4/k/patternsp.cfm
Division Vocabulary
The number being
divided
A number that will
divide the dividend
The result of a
division
Dividend Divisor Quotient
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
Left over
Equal parts of a whole or group written with a numerator and a
denominator.
Fractionhttp://math.rice.edu/~lanius/fractions/
3 -Numerator
7 -Denominator
Shaded region/area
Un-shaded region/area
12
2Whole number
fraction
73
34
http://www.visualfractions.com/MixtoFrCircle.html
Fractions
Numerator: number of each part
Denominator: number of
parts
Improper fraction mixed number
Proper fraction
Having the same amount or value; the state of being equal.
Equivalenthttp://nlvm.usu.edu/en/nav/frames_asid_105_g_2_t_1.html
Fractions that are the same or equal
Equivalent Fractionshttp://www.learningplanet.com/sam/ff/index.asp
1/2 = 3/6
Equal Portions
A line on which numbers, and fractions can be compared and ordered.
Number Linehttp://www.shodor.org/interactivate/activities/fracsorter/index.html
½ 1¾ 3¼
½ < 1¾ ½ is less than 1¾
3¾ > 1¾ 3¾ is greater than 1¾
Order of Operations
The order in which operations should be done.
http://www.mathgoodies.com/lessons/vol7/order_operations.htmlhttp://www.scweb4free.com/oper.html
No exponents in Grade 3!!
Problem Solving Method
Look Back Justify, prove, evaluate or explain the
reasonableness of your answer.
Using a table/chart
http://www.studyzone.org/testprep/math4/k/chartprobl.cfmhttp://www.mathstories.com/strategies_makeatable.htm
XX
X
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
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
Make an organized listQuestion: 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/MakaylaJill/Tanya
Makayla/Tanya
3 ways
http://www.mathstories.com/strategies_makealist.htm\
Organized list
Answer
Work BackwardsThe castle kitchen waiters
brought in 4 pies left over from the feast. Twelve pies were
eaten at the feast. Queen Mab took 2 home with her. How many pies did the waiters bring into the feast at the
beginning?
http://www.mathstories.com/strategies_working_backward.htm
2 12 4 = 2 + 12 + 4 = 18
Using a calculator
Using objects, models, representations
http://nlvm.usu.edu/en/nav/frames_asid_273_g_2_t_4.html
The learner will recognize and use
standard units of metric and customary
measurement.
Use of standard units to find out size or quantity in regard to length,
weight, capacity, temperature and time.
Measure
The system of measurement used in the United States
Customary Systemhttp://www.harcourtschool.com/activity/con_math/g04c24.htmlhttp://www.studyzone.org/testprep/math4/d/customaryl.cfm
The system of measurement used in most countries of the world
Metric System
Beans Candy Steps
Counters
Non-Standard
UnitsInches Grams Gallons
Degrees
Standard Units
Units of length, width and distance in the customary system.
Inches, Feet, Yards, Mileshttp://www.funbrain.com/measure/
12in = 1 ft
3 ft = 1 yd
5280 ft = 1 mi
Customary Units of Linear Measurement:
Units of length, width and distance in the metric system.
centimeter, meter, kilometerhttp://www.metricamerica.com/centimetre.htm
100cm = 1m
1000 m = 1 km
Metric Units of Linear
Measurement:
Ruler- tool of linear
measurement
Tools for Linear Measurement
Yard Stick-
length of one yard Trundle
Wheel- measure
long distances
Ruler- length of one foot
Meter Stick-
Length of one meter
Tape Measure- measure
length and width
http://www.studyzone.org/testprep/math4/d/measuretooll.cfm
The measurement of the longest side of a figure.
4 ft
12 ft
How long is this figure?
The measurement of the shortest side of a figure.
4 ft
12 ftHow wide is this figure?
The measurement of the tallest side of a figure.
Tools for Mass Measurement
Scale
Weights
Balance
http://www.studyzone.org/testprep/math4/d/measuretoolp.cfm
The amount of matter an object contains.
Mass
Units of weight (or mass) in the customary system.
ounce and pound
16 oz = 1lbCustomary
Units of Mass Measurement:
http://www.321know.com/mea-add_lboz.htm
Units of weight (or mass) in the metric system.
gram and kilogram
1000g = 1kgMetric Units of
Mass Measurement:
http://www.studyzone.org/testprep/math4/d/metgraml.cfm
The amount of liquid or poured solid a container will hold.
Capacity
1 liter
http://www.studyzone.org/testprep/math4/d/capacityl.cfm
http://www.edhelper.com/math/capacity_fg1943.htm
Units of capacity in the customary system.
cup, pint, quart, gallon
GQQQQ
PP PP
PP PP
cc 2 c = 1 pt
2 p = 1 qt
4 qt = 1 gal
cc cc cc
cc cc cc ccCustomary
Units of Capacity
Measurement:
Unit of capacity in the metric system.
literhttp://www.metricamerica.com/litre.htm
1000 ml = 1 L1 L
1 ml1
ml
Metric Units of Capacity
Measurement:
The measure of warmth or coldness.
Temperature
Customary- measured in
degrees Fahrenheit
Metric- measured in degrees Celsius
Tool used for measuring Temperature:
Thermometer-
Unit of temperature measurement:
Degrees
Increase or decrease in temperature
Rising/Falling
Rising Temperature- increase in temperature
Falling Temperature- decrease in temperature
Intervals/increments: distance between numbers on the scale of the thermometer
http://www.studyzone.org/mtestprep/math8/f/thermometerl.cfm
Commonly known temperatures to refer to.
Benchmark Temperatures
Body Temperature-98.6 degrees
Room Temperature:70° Fahrenheit
http://oncampus.richmond.edu/academics/education/projects/webunits/measurement/temp2.html
Units of Time
Seconds:
Smallest unit of time
Days:
24 hours
Hours:
60 minutes
Minute:
60 seconds
Years:
365 days
Months:
28-31 days
Divide to convert to larger units
Multiply to convert to smaller units
http://www.amblesideprimary.com/ambleweb/mentalmaths/clock.htmlhttp://www.oswego.org/ocsd-web/games/BangOnTime/clockwordres.html
Analog Clock
http://www.studyzone.org/testprep/math4/j/timep.cfm
Digital Clock
Telling Time
Quarter hour
Quarter past
15 Minutes after
Half past
Half hour
Quarter till
15 minutes until
15 minutes before
http://www.studyzone.org/testprep/math4/j/time.swf
1.2. 3.
Elapsed Timehttp://www.shodor.org/interactivate/activities/clock3/index.html
Measuring the amount of time that has passed
Starting Time Ending TimeWhat is the estimated elapsed time between the starting time and the ending time on the clocks?
What is the exact elapsed time between the starting time and the ending time on the clocks?
Duration of Time
Intervals of Time-
Morning Afternoon
http://www.studyzone.org/testprep/math4/j/timeminute.swf
? ?
The learner will recognize and use basic
geometric properties of two- and three-
dimensional figures.
Any 2-dimensional (flat) shape
Plane Figures
A closed plane figure with three or more sides.
Polygon
A plane shape with many sides. A CIRCLE IS NOT ONE OF THESE
http://www.aaamath.com/B/geo318x4.htm
These are FLAT shapes:
A polygon for which all sides are congruent and all angles are congruent.
Regular Polygon
A polygon for which all sides and all angles are not congruent.
Irregular Polygon
Shapes that are the same shape and the same size
Congruent Shapeshttp://www.beaconlearningcenter.com/WebLessons/CongruentConcentration/default.htm
When a straight line is drawn through a shape so that the two halves are
congruent.
Symmetryhttp://library.thinkquest.org/J002441F/symmetry.htm
Line of symmetry
Two perpendicular lines which form a 90 degree angle.
Right Anglehttp://www.mathsnet.net/shape/category1.html
An angle with a measure of more than 90 degrees, but less than 180 degrees.
Obtuse Angle
110o
35o35o
A three sided polygon.
Trianglehttp://www.factmonster.com/ipka/A0876325.html
http://www.mathsnet.net/shape/category2.html
This shape has 3 sides.
Any four sided figure.
Quadrilateralhttp://regentsprep.org/Regents/math/quad/LQuad.htm
Four sided figure, all sides equal, opposite sides parallel, and all right
angles.
Squarehttp://www.mathleague.com/help/geometry/polygons.htm#righttriangle
Four sided figure, opposite sides equal lengths and parallel, all right
angles
Rectangle
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
A six sided figure
Hexagon
An eight sided figure
Octagon
Four sided figure; top and bottom sides parallel
Trapezoid
A five sided figure
Pentagon
A line with two endpoints
Line Segment
A B
end points
A line with one endpoint
Rayhttp://www.mathleague.com/help/geometry/basicterms.htm#rays
The point at which two rays meet.
Vertex
This shape has 3 vertices.
Two lines that will never touch or intersect because they are the same
distance apart.
Parallel Lineshttp://www.homeschoolmath.net/teaching/g/parallel_and_perpendicular.php
Any 3-dimensional shapes that take up space
Solid Figures
These are 3-D shapes!
http://www.factmonster.com/math/knowledgebox/player.html?movie=sfw50631
These are also called
polyhedrons.
One of the plane polygon shapes on a solid shape.
Facehttp://illuminations.nctm.org/tools/tool_detail.aspx?id=70
http://illuminations.nctm.org/Lessons/imath/GeoSolids/GeoSolids-AS1.pdf
Where two faces meet on a solid shape.
Edgehttp://illuminations.nctm.org/tools/tool_detail.aspx?id=70
http://illuminations.nctm.org/Lessons/imath/GeoSolids/GeoSolids-AS1.pdf
Where two edges meet on a solid shape.
Cornerhttp://illuminations.nctm.org/tools/tool_detail.aspx?id=70
http://illuminations.nctm.org/Lessons/imath/GeoSolids/GeoSolids-AS1.pdf
The flat circle shaped bottom of cylinders and cones
Basehttp://illuminations.nctm.org/tools/tool_detail.aspx?id=70
http://illuminations.nctm.org/Lessons/imath/GeoSolids/GeoSolids-AS1.pdf
Solid
Figures
Prism
Sphere
Cylinder
Cone
Pyramid
Cube
Have faces, edges, and corners Have 2, 1, or zero circle bases
http://www.harcourtschool.com/activity/solid_figures/
Solid
Figures
Pentagonal
Hexagonal
Decagonal
Octagonal
Have faces, edges, and corners
A pair of numbers that gives the coordinates of a point on a grid
Ordered Pairhttp://www.oswego.org/ocsd-web/games/BillyBug/bugcoord.html
0 1 2 3 4
3
2
1
(1, 2)
Ordered pairs are found on a coordinate grid
point
“ x “ and “ y ”
http://www.studyzone.org/testprep/math4/d/orderpairp.cfm
x axis
y axis
A description of a line that forms between two points on a line.
Pathhttp://www.shodor.org/interactivate/activities/pcoords/index.html
0 1 2 3 4
3
2
1
Describe a path (along grid lines) between (1, 1) and (2, 2)
Diagonal up
Describe a path (along grid lines) between (1, 1) and (4, 1)
Horizontal Right
Horizontal East
The learner will understand and use data
and simple probability concepts.
A graph that compares parts to the whole; decimals and fractions may be used on this graph
Circle Graphhttp://www.mcwdn.org/Graphs/CirclePieQuiz.html
key
title
labels
Used for collecting data
Tablehttp://www.studyzone.org/testprep/math4/d/collectdata4l.cfm
A graph that uses pictures to represent data.
Pictograph
Key
http://www.studyzone.org/testprep/math4/d/graphdatal.cfm
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
The number of times an event occurs; may use tally marks to record
Frequency
IIII IIII IIIItallies
http://www.studyzone.org/testprep/math4/d/tablestallyl.cfm
A method of collecting a sample of data by asking people questions.
Surveyhttp://www.studyzone.org/testprep/math4/d/randomsamp.cfm
A diagram using circles or other shapes (i.e. rectangles) to show the
relationship(s) between sets
Venn Diagramhttp://www.shodor.org/interactivate/activities/venndia/index.html
Guess the rule for this
Venn Diagram
Strategy for solving problems for determining outcomes:
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.
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
An outcome that will probably occur or happen.
Likelyhttp://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?
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?
An outcome that will never occur or happen.
Impossiblehttp://www.mathgoodies.com/lessons/vol6/intro_probability.html
What are the chances of the arrow landing on
blue?
An outcome that will always occur or happen.
Certainhttp://www.bbc.co.uk/education/mathsfile/shockwave/games/fish.html
What are the chances of the arrow landing on orange?
The learner will recognize, determine,
and represent patterns and simple
mathematical relationships.
http://www.studyzone.org/testprep/math4/i/dpatternsl.cfm
The first three numbers of a pattern which show the pattern’s rule
Pattern Core/Unit
50,75,45,70 Rule: +25, -30, 18th number: 35
18th
Mathematical sentence written in numerals and mathematical symbols.
Number Sentencehttp://www.studyzone.org/testprep/math4/d/numericalp.cfm
A letter or symbol that represents an unknown in an algebraic expression.
Variablehttp://www.aplusmath.com/Games/PlanetBlast/index.html
Each side of the = symbol must
balance
A mathematical sentence where the left side equals the right side.
Equationhttp://www.shodor.org/interactivate/activities/NumberCruncher/
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
Resources
• Web resources are listed at the bottom of each slide.
• Additional resources:– NCDPI Math Glossary
• http://community.learnnc.org/dpi/math/archives/GlossarySP.pdf
– Houghton Mifflin Math http://www.eduplace.com/kids/hmm/g_3.html