2003 mathematics ncscos grade 5 indicators
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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
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
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