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 ten sided polygon

Decagon

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