2003 MATHEMATICS NCSCOSGrade 5 Indicators

The learner will understand and compute

with nonnegative rational numbers.

A real number that can be written as the ratio of two integers (positive or negative whole number, fraction, or

decimal)

Rational Number

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

145,305.791Hundred- thousands

ten- thousands

ones

thousands

hundreds

tens tenths

hundredths

thousandths

Arranged from smallest to largest

Ascending Orderhttp://www.studyzone.org/testprep/math4/e/decorderl.cfm

Arranged from largest to smallest

Descending Order

An answer close to the exact answer. Usually found by rounding.

Approximately/About

366

370

400

http://www.myschoolhouse.com/courses/O/1/16.asp

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

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.bbc.co.uk/education/mathsfile/shockwave/games/gridgame.html

Having the same amount or value; the state of being equal.

Equivalencehttp://nlvm.usu.edu/en/nav/frames_asid_105_g_2_t_1.html

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 = .50

.30 = .300.5 =.05

.3 = .003

? < .5

? =.1,.2,.3,.4,or .5

not equal to

less than or equal to

Equal parts of a whole or group written with a numerator and a

denominator.

Fractionhttp://math.rice.edu/~lanius/fractions/

3 -Numerator

7 -Denominator

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

Fractions that are the same or equal

Equivalent Fractionshttp://www.learningplanet.com/sam/ff/index.asp

http://www.shodor.org/interactivate/activities/fracsorter/index.html

1/2 = 3/6

Numbers written in standard form to show a value less than 1.

Decimalhttp://www.321know.com/cmp42bx2.htm

.1

.01

.001

one-tenth

one-hundredth

one-thousandth

Problem Solving Strategies

http://www.mathstories.com/strategies.htm

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

http://community.learnnc.org/dpi/math/archives/2005/06/problem_solving.php

Calculator Riddles

From DPI

Using objects, models, representations

http://nlvm.usu.edu/en/nav/frames_asid_273_g_2_t_4.html

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?

Putting numbers together to make them easier to work with

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 work with.

30 X 14

Decomposehttp://www.studyzone.org/testprep/math4/d/commutativep.cfm

(30 X 10) + (30 X 4)300 + 120 = 420

Mathematical sentence where the left side of the equals sign has the

same value as the right side.

Equationhttp://www.aplusmath.com/Games/PlanetBlast/index.html

The learner will recognize and use

standard units of metric and customary

measurement.

Units of capacity in the metric system.

literhttp://www.metricamerica.com/litre.htm

1000 ml = 1 L1 L

1 ml1

ml

GQQQQ

PP PP

PP PP

cc 2 c = 1 pt

2 pt = 1 qt

4 qt = 1 gal

cc cc cc

cc cc cc cc

http://www.edhelper.com/math/capacity_fg1943.htm

Units of capacity in the customary system.

cup, pint, quart, gallon

Benchmark/landmarkBenchmark Comparisons for

Metric and 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.mathcats.com/explore/convert.html

Units of length, width and distance in the metric system.

centimeter, meter, kilometerhttp://www.metricamerica.com/centimetre.htm

100cm = 1m

1000 m = 1 km

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

Benchmark/landmark

Benchmark Comparisons for Metric and 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 >qthttp://www.aaamath.com/B/mea69_x2.htm

Units of weight (or mass) in the metric system.

gram and kilogram

1000g = 1kg

http://www.studyzone.org/testprep/math4/d/metgraml.cfm

Units of weight (or mass) in the customary system.

ounce, pound, and tonhttp://www.edhelper.com/math/length_weight_fg2255.htm

16 oz = 1lb

2000 lbs = 1 ton

Benchmark/landmark

Benchmark Comparisons for Metric and 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

Tool used to measure angles

Protractorhttp://www.amblesideprimary.com/ambleweb/mentalmaths/protractor.html

http://www.enchantedlearning.com/math/label/protractor/

Two segments that meet to form a 90 degree angle.

Right Anglehttp://www.icteachers.co.uk/children/sats/triangles.htm

http://www.mathsnet.net/shape/category1.html

An angle with a measure of more than 90 degrees, but less than 180 degrees.

Obtuse Anglehttp://www.manatee.k12.fl.us/sites/elementary/palmasola/mathlabtutan1b.htmhttp://www.toonuniversity.com/6m_angle_d.html

1100

350350

An angle less than 90 degrees

Acute Angle

600

600

600

http://www.mathsnet.net/shape/category2.html

Two angles that share a common side

Adjacent Angles

130 50

http://www.mathwords.com/a/adjacent_angles.htm

Angle Notation

ABC=

A

B C

Symbol used to identify an angle

Two adjacent angles whose sum is 180 degrees

Supplementary Angles

130 50

http://www.mathsisfun.com/geometry/supplementary-angles.htmlhttp://www.mathopenref.com/anglesupplementary.html

Two adjacent angles whose sum is 90 degrees

Complementary Angleshttp://www.mathwarehouse.com/geometry/angle/complementary-angles.php

http://www.mathopenref.com/anglecomplementary.html

45

45

Angles that have the same measure.

Congruent Angleshttp://www.kidport.com/Grade5/Math/MeasureGeo/MeasuringAngles.htm

45

45

The learner will understand and use

properties and relationships of plane

figures.

When sides of a shape are equal in length

Congruent Sides

These markings indicate congruent sides.

All three sides of this triangle are congruent.

Equilateral Trianglehttp://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

This triangle has two congruent sides.

Isosceles Trianglehttp://www.homeschoolmath.net/gy/equilateral_isosceles.php

http://www.amblesideprimary.com/ambleweb/sketchpad/isosco.htm

4 in

3 in

4 in

This triangle has no congruent sides

Scalene Trianglehttp://www.amblesideprimary.com/ambleweb/sketchpad/scalene.htm

http://www.mathsisfun.com/triangle.html

5 in

4 in3 in

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

Any four sided figure

Quadrilateralhttp://regentsprep.org/Regents/math/quad/LQuad.htm

A line with two endpoints

Line Segmenthttp://www.pinkmonkey.com/studyguides/subjects/geometry/chap1/g0101201.asp

A B

Midpoint

A line with one endpoint

Rayhttp://www.mathleague.com/help/geometry/basicterms.htm#rays

The point at which two rays meet.

Vertex

Two rays that meet at a vertex

Anglehttp://www.kidport.com/Grade5/Math/MeasureGeo/MeasuringAngles.htm

Sides or angles immediately next to each other.

Adjacenthttp://www.kidport.com/Grade5/Math/MeasureGeo/MeasuringAngles.htm

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

Bisect

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

Lines that intersect at right angles to each other.

Perpendicular Lineshttp://www.homeschoolmath.net/teaching/g/parallel_and_perpendicular.php

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?

A line joining two non-adjacent vertices of a polygon.

Diagonalhttp://www.math.fau.edu/Richman/Liberal/polydiag.htm

Four sided figure; all sides equal; opposite sides parallel; all right

angles

Squarehttp://www.mathleague.com/help/geometry/polygons.htm#righttriangle

Sum of interior angles - 360º

2 intersecting, bisecting,

perpendicular diagonals

Four sided figure; opposite sides equal lengths and parallel; all right

angles

Rectangle

Four sided figure; opposite sides equal lengths and parallel; all right

angles

Rectanglehttp://encyclopedia.laborlawtalk.com/Rectangle

http://www.standards.dfes.gov.uk/primary/publications/mathematics/12874/nns_useict026000carroll.swf

Sum of interior angles - 360º

2 intersecting diagonals.

A four-sided figure in which the two pairs of adjacent sides have

the same length.

Kite

Sum of interior angles - 360º

2 intersecting, perpendicular

diagonals

Four sided figure. Opposite sides equal lengths and parallel

Parallelogram

http://ejad.best.vwh.net/java/patterns/patterns_j.shtmlhttp://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

Parallelogram

Rhombus

9 diagonals/ sum of interior angles - 720º

Hexagon

20 diagonals/ sum of interior angles - 1080º

Octagon

2 intersecting diagonals/ sum of interior angles 360º

Trapezoid

5 diagonals/ Sum of interior angles - 540º

Pentagon

2 intersecting diagonals/ sum of interior angles 360º

2 intersecting perpendicular diagonals/ sum of interior

angles 360º

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 6 7 8Sum of int. angles

180º 360º 540º 720º 900º 1080º

+180 +180 +180 +180 +180

two types of trapezoids

Right Trapezoid

Two right angles

Isosceles Trapezoid

No right angles

Two congruent sides

A ten sided polygon

Decagon

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

When an outline of a turning figure

matches its original shape.

Rotational Symmetryhttp://www.adrianbruce.com/Symmetry/10.htm

http://www.learner.org/channel/courses/learningmath/geometry/session7/part_b/index.html

To turn an object, usually 90 degrees, 180 degrees, or 270 degrees.

Point of rotation

Half turn - 180 degrees

Quarter turn - 90 degrees

http://regentsprep.org/Regents/Math/rotate/PracRot.htmhttp://www.studyzone.org/mtestprep/math8/f/symturns5p.cfm

Rotations

3 Quarter turn -270 degrees

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.

The learner will understand and use

graphs and data analysis.

Collection of information often organized on graphs or charts for analysis.

Datahttp://www.studyzone.org/testprep/math4/d/graphdatal.cfm

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

The middle number in a set of data; must put numbers in order from least to greatest first.

Medianhttp://regentsprep.org/Regents/math/mean/Pmeasure.htm

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

41, 44, 44, 55, 56, 62, 66, 68, 73, 73, 73, 89

73

Subtract the smallest number from the largest number in a set of data.

Rangehttp://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

A way to arrange data with the tens on the left and the ones listed on the right.

Stem and Leaf Plothttp://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

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.htmlhttp://www.shodor.org/interactivate/activities/coords2/index.html

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

A graph that uses pictures to represent data.

Pictograph

Key

http://www.studyzone.org/testprep/math4/d/graphdatal.cfm

http://www.mcwdn.org/Graphs/LineGraph.html

interval

label

title

scale

Shows change over time; will have months, days or other time words in the problem.

Line Graph

Is used to compare facts about groups and numbers that can be counted

Bar Graphhttp://www.mcwdn.org/Graphs/BarGraph.html

labelstitle

scale

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

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

The learner will demonstrate an

understanding of patterns, relationships,

and elementary algebraic representation.

A letter or symbol that represents a number in an algebraic expression.

Variablehttp://www.aplusmath.com/Games/PlanetBlast/index.htmlhttp://www.vectorkids.com/vkvariable.htm

Each side of the = symbol must

balance

Contains at least one variable as well as other numbers and/or operations.

Algebraic Expression

16

5

10

2020

100

http://mathsnet.net/algebra/l2_equation.html

l

A mathematical sentence where the left side equals the right side.

Equationhttp://www.studyzone.org/testprep/math4/d/numericalp.cfm

Input/Output charthttp://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

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

http://www.studyzone.org/testprep/math4/i/dpatternsl.cfmhttp://www.studyzone.org/testprep/math4/k/patternsl.cfmhttp://www.studyzone.org/testprep/math4/k/patternsp.cfm

An ordered set of numbers, shapes, or other mathematical objects, arranged according to

a rule.

Pattern

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

Geometric Pattern

Pattern Types

Numeric PatternPatterns using shapes

4, 8,16,32,….

Patterns using numbers

Nth Term

Any number in the pattern can be found by finding the relationship or rule

of the pattern.

3,6,9,12,15,18…… Nth term = 3n

10th term = 3(10) = 30

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

The quotient of two numbers used to compare two quantities.

Ratio

3

5

Red chips

Blue chips

http://www.studyzone.org/mtestprep/math8/c/ratiol.cfm

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_5.html