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From 06-07 DPI 5th grade
indicators
CCS 2007
CCS 2007
A real number that can be written as
a positive or negative whole number,
fraction, or decimal,
Rational Number
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Expanded
notation form
Picture Form
300+20+6
Forms of
Numbers
Three hundred twenty-six
Word Form
326
Standard 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.
tenthousands
hundreds
ones
hundredths
145,305.791
Hundredthousands
thousands
tens
tenths
thousandths
Place Value
http://mrsbogucki.com/aemes/resource/apps/placeval/placeval.htm
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Arranged from smallest to largest
Ascending Order
http://www.studyzone.org/testprep/math4/e/decorderl.cfm
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Arranged from largest to smallest
Descending Order
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An answer close to the exact
answer. Usually found by rounding
to the nearest 10 or 100.
366
370
400
Approximately/About
http://www.myschoolhouse.com/courses/O/1/16.asp
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Numbers that divide exactly into
another number.
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
Factors
http://illuminations.nctm.org/tools/tool_detail.aspx?id=12
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Number that results from multiplying
a given number by a set of whole
numbers.
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
Multiples
http://www.tki.org.nz/r/wick_ed/maths/interactives_matrix.php
http://www.bbc.co.uk/education/mathsfile/shockwave/games/gridgame.html
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Having the same amount or value;
the state of being equal.
Equivalence
http://nlvm.usu.edu/en/nav/frames_asid_105_g_2_t_1.html
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Symbol used to compare relationships
of inequalities.
Symbol used to compare numbers
Symbol used to compare numbers
Less Than/Greater Than
http://www.studyzone.org/testprep/math4/k/greaterlessthanl.cfm
CCS 2007
Symbols used to determine
relationships of equalities.
.5 = .50
? < .5
.30 = .300
equal to
.5 =.05
.3 = .003
? =.1,.2,.3,.4,or .5
less than or
equal to
not equal to
Equal to/not equal to
http://www.studyzone.org/testprep/math4/k/greaterlessthanl.cfm
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Equal parts of a whole or group
written with a numerator and a
denominator.
3
-Numerator
7
-Denominator
Fraction
http://www.kidsolr.com/math/fractions.html
http://math.rice.edu/~lanius/fractions/
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Denominator:
number of
parts
3
4
Numerator:
number of
each part
Fractions
7
3
Improper fraction
Whole
number
1
2
2
fraction
mixed number
http://www.visualfractions.com/MixtoFrCircle.html
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Fractions that are the same or equal
1/2
=
3/6
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
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Numbers written in standard form to
show a value less than 1.
.1
one-tenth
.01
one-hundredth
.001
one-thousandth
Decimal
http://www.321know.com/cmp42bx2.htm
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Problem Solving
Strategies
http://www.mathstories.com/strategies.htm
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Problem Solving Method
Look Back
Justify, prove, evaluate or explain the
reasonableness of your answer.
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Using a table/chart
X
X
X
http://www.studyzone.org/testprep/math4/k/chartprobl.cfm
http://www.mathstories.com/strategies_makeatable.htm
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Guess and Check
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
http://www.mathstories.com/strategies_guesscheck.htm
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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
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Make an organized list
Question: Jill, Makayla and Tanya
don’t want to ride the Farris-wheel
alone. How many ways can they ride
if the ride will only fit two at a time?
Organized
list
Answer
Jill/Makayla
Jill/Tanya
Makayla/Tanya
3 ways
http://www.mathstories.com/strategies_makealist.htm
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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?
2
12
4=
2 + 12 + 4 =
18
http://www.mathstories.com/strategies_working_backward.htm
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Using a calculator
http://edschool.csuhayward.edu/departments/ted/instruction/howe/
5350/1-calculatorRiddles.html
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Using Objects, models,
representations
http://nlvm.usu.edu/en/nav/frames_asid_273_g_2_t_4.html
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Information in a problem that does NOT help
you solve the problem.
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?
Extra Information
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Putting numbers together to make
them easier to work with
1 + 4 + 3 +7 + 6 + 8 + 9 + 2 = ?
10 + 10 + 10 + 10 = 40
Compose
http://www.studyzone.org/testprep/math4/d/commutativep.cfm
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Breaking a number apart to make it
easier to work with.
30 X 14
(30 X 10) + (30 X 4)
300 + 120 = 420
Decompose
http://www.studyzone.org/testprep/math4/d/commutativep.cfm
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Mathematical sentence where the
left side of the equals sign has the
same value as the right side.
Equation
http://www.aplusmath.com/Games/PlanetBlast/index.html
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Units of capacity in the metric
system.
1000 ml = 1 L
milliliter, liter
http://www.metricamerica.com/litre.htm
http://www.metricamerica.com/millilitre.htm
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Units of capacity in the customary system.
QQ
PP
PP
QQ
PP PP
cc cc
cc cc
cc cc
2c=1p
2p=1q
4 q = 1 gal
cc cc
cup, pint, quart, gallon
http://www.edhelper.com/math/capacity_fg1943.htm
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Benchmark/landmark
Benchmark Comparisons for
Metric ad Customary Measurements
Greater Than/
Less Than
Metric Units
Customary Units
2.54 cm (about 2.5)
1 in
cm < in
0.9 m (about 1)
1 yd
m > yd
1.6 km (about 1.5)
1 mi
km <mi
.45 kg (about .5)
1 lb
kg > lb
.95 L (about 1)
1 qt
L > qt
http://www.mathcats.com/explore/convert.html
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Units of length, width and distance
in the metric system.
100cm = 1m
1000 m = 1 km
centimeter, meter, kilometer
http://www.metricamerica.com/centimetre.htm
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Units of length, width and distance
in the customary system.
12in = 1 ft
3 ft = 1 yd
5280 ft = 1 mi
Inches, Feet, Yards, Miles
http://www.funbrain.com/measure/
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Benchmark/landmark
Benchmark Comparisons for
Metric ad 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.aaamath.com/B/mea69_x2.htm
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Units of weight (or mass) in the
metric system.
1000g = 1kg
gram and kilogram
http://www.studyzone.org/testprep/math4/d/metgraml.cfm
CCS 2007
Units of weight (or mass) in the
customary system.
16 oz = 1lb
2000 lbs = 1 ton
ounce, pound, and ton
http://www.edhelper.com/math/length_weight_fg2255.htm
CCS 2007
Benchmark/landmark
Benchmark Comparisons for
Metric ad Customary Measurements
Greater Than/
Less Than
Metric Units
Customary Units
2.54 cm (about 2.5)
1 in
cm < in
0.9 m (about 1)
1 yd
m > yd
1.6 km (about 1.5)
1 mi
km <mi
.45 kg (about .5)
1 lb
kg > lb
.95 L (about 1)
1 qt
L >qt
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Tool used to measure angles
Protractor
http://www.amblesideprimary.com/ambleweb/mentalmaths/protractor.html
http://www.enchantedlearning.com/math/label/protractor/
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Two perpendicular lines which form
a 90 degree angle.
Right Angle
http://www.icteachers.co.uk/children/sats/triangles.htm
http://www.mathsnet.net/shape/category1.html
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An angle with a measure of more than
90 degrees, but less than 180 degrees.
110
35
35
Obtuse Angle
http://www.manatee.k12.fl.us/sites/elementary/palmasola/mathlabtutan1b.htm
http://www.toonuniversity.com/6m_angle_d.html
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An angle less than 90 degrees
60
60
60
Acute Angle
http://www.mathsnet.net/shape/category2.html
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Two angles that share a common
side
130
50
Adjacent Angles
http://www.mathwords.com/a/adjacent_angles.htm
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Symbol used to identify an
angle
A
=
ABC
C
B
Angle Notation
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Two adjacent angles that total 180
degrees
130
50
Supplementary Angles
http://www.mathsisfun.com/geometry/supplementary-angles.html
http://www.mathopenref.com/anglesupplementary.html
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Two adjacent angles that
total 90 degrees
45
45
Complementary Angles
http://www.mathwarehouse.com/geometry/angle/complementary-angles.php
http://www.mathopenref.com/anglecomplementary.html
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Angles that have the same measure.
45
45
Congruent Angles
http://www.kidport.com/Grade5/Math/MeasureGeo/MeasuringAngles.htm
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When sides of a shape are equal in
length
These markings indicate
congruent sides
Congruent Sides
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All three sides of this triangle are
congruent.
4 in
4 in
4 in
Equilateral Triangle
http://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
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This triangle has two congruent
sides.
4 in
4 in
3 in
Isosceles Triangle
http://www.homeschoolmath.net/gy/equilateral_isosceles.php
http://www.amblesideprimary.com/ambleweb/sketchpad/isosco.htm
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This triangle has no congruent sides
4 in
3 in
5 in
Scalene Triangle
http://www.amblesideprimary.com/ambleweb/sketchpad/scalene.htm
http://www.mathsisfun.com/triangle.html
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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
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A polygon for which all sides and all
angles are not congruent.
Irregular Polygon
http://www.ul.ie/~cahird/polyhedronmode/irregula.htm
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Any four sided figure.
Quadrilateral
http://regentsprep.org/Regents/math/quad/LQuad.htm
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A line with two endpoints
Midpoint
A
B
Line Segment
http://www.pinkmonkey.com/studyguides/subjects/geometry/chap1/g0101201.asp
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A line with one endpoint
Ray
http://www.mathleague.com/help/geometry/basicterms.htm#rays
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The Point at which two rays meet.
Vertex
http://mathworld.wolfram.com/VertexAngle.html
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Two rays that meet at a vertex
Angle
http://www.kidport.com/Grade5/Math/MeasureGeo/MeasuringAngles.htm
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Sides or angles immediately next to
each other.
Adjacent
http://www.kidport.com/Grade5/Math/MeasureGeo/MeasuringAngles.htm
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To divide into two equal sections;
to cut in half.
Bisect
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Two lines that will never touch or
intersect because they are the same
distance apart.
Parallel Lines
http://www.homeschoolmath.net/teaching/g/parallel_and_perpendicular.php
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Lines that intersect at right angles to
each other.
Perpendicular Lines
http://www.homeschoolmath.net/teaching/g/parallel_and_perpendicular.php
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Making an estimate or best guess
by appearance or with little
evidence.
Is this a right triangle?
How do you know?
What is your evidence? Can
you tell without measuring?
Conjecture
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A line joining two non-adjacent
vertices of a polygon.
Diagonal
http://www.math.fau.edu/Richman/Liberal/polydiag.htm
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Four sided figure, all sides equal,
opposite sides parallel, all right
angles
Sum of interior
angles- 360º
2 intersecting,
bisecting,
perpendicular
diagonals
Square
http://www.mathleague.com/help/geometry/polygons.htm#righttriangle
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Four sided figure. opposite sides
equal lengths and parallel, all right
angles
Rectangle
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Four sided figure. opposite sides
equal lengths and parallel, all right
angles
Sum of interior
angles- 360º
2 intersecting
diagonals.
Rectangle
http://encyclopedia.laborlawtalk.com/Rectangle
http://www.standards.dfes.gov.uk/primary/publications/mathematics/12874/nns_useict026000carroll.swf
CCS 2007
A four-sided figure in which the
two pairs of adjacent sides have
the same length.
Sum of interior
angles- 360º
2 intersecting,
perpendicular
diagonals
Kite
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Four sided figure. Opposite sides
equal lengths and parallel
An six sided figure
Four sided figure. Top and
bottom sides parallel
Parallelogram
Four sided figure. opposite sides equal
lengths and parallel, opposite angles
equal
Hexagon
Trapezoid
An eight sided figure
An five sided figure
Octagon
Rhombus
Pentagon
http://ejad.best.vwh.net/java/patterns/patterns_j.shtml
http://www.aplusmath.com/cgi-bin/games/geopicture
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2 intersecting diagonals/ sum of
interior angles 360º
2 intersecting diagonals/ sum of
interior angles 360º
Parallelogram
2 intersecting perpendicular
diagonals/ sum of interior
angles 360º
Rhombus
Trapezoid
5 diagonals/
Sum of interior
angles - 540º
Pentagon
9 diagonals/ sum of
interior angles- 720º
Hexagon
20 diagonals/ sum of
interior angles- 1080º
Octagon
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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
Sum of
int.
angles
180º
360º
540º 720º
+180
+180
+180
6
+180
7
8
900º
1080º
+180
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two types of trapezoids
Two right angles
No right angles
Two congruent sides
Right Trapezoid
Isosceles Trapezoid
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A ten sided polygon
Decagon
http://www.ul.ie/~cahird/polyhedronmode/decagon.htm
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When a straight line is drawn through a
shape so that the two halves are
congruent.
Line of symmetry
Symmetry
http://library.thinkquest.org/J002441F/symmetry.htm
CCS 2007
When an outline of a turning figure
matches its original shape
.
Rotational Symmetry
http://www.adrianbruce.com/Symmetry/10.htm
http://www.learner.org/channel/courses/learningmath/geometry/session7/part_b/index.html
CCS 2007
To turn an object, usually 90 degrees or
180 degrees, 0r 270 degrees.
Point of
rotation
Half turn- 180
degrees
Quarter
turn- 90
degrees
3 Quarter
turn-270
degrees
Rotations
http://regentsprep.org/Regents/Math/rotate/PracRot.htm
http://www.studyzone.org/mtestprep/math8/f/symturns5p.cfm
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The same direction as the way
hands on the clock go.
Clockwise
Counter Clockwise
The opposite direction of the way
the hands on the clock go.
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Collection of information often organized
on graphs or charts for analysis.
Data
http://www.studyzone.org/testprep/math4/d/graphdatal.cfm
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The middle number in a set of data; must put
numbers in order from least to greatest first.
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
Median
http://regentsprep.org/Regents/math/mean/Pmeasure.htm
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The number that occurs most in a set of data.
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
Mode
http://www.oswego.org/ocsd-web/match/matchgeneric.asp?filename=ccarrollmode
http://www.bbc.co.uk/education/mathsfile/shockwave/games/train.html
CCS 2007
Subtract the smallest number from the largest
number in a set of data.
89, 73, 84, 91, 87, 77, 94
73, 77, 84, 87, 89, 91, 94
94 – 73 = 21
21
Range
http://www.mathgoodies.com/lessons/vol8/range.html
http://www.quizville.com/range.php
CCS 2007
A way to arrange data with the tens on the left and
the ones listed on the right.
1
3, 3, 7
2
2, 9, 9, 9
3
1
4
3, 9
5
1, 4, 6
6
2
7
5, 7, 7, 8
Stem and Leaf Plot
http://regentsprep.org/Regents/math/data/stemleaf.htm
http://www.shodor.org/interactivate/activities/stemleaf/index.html
CCS 2007
Used to find coordinates for ordered
pairs for the X and Y axis.
Coordinate Grid/ X-Y Chart
http://www.shodor.org/interactivate/activities/pcoords/index.html
http://www.shodor.org/interactivate/activities/coords2/index.html
CCS 2007
A horizontal number line on which each
value of a set is denoted by an “x” over
a value.
The number of x’s
indicates how many
times each score
occurred
Line Plot
http://www.studyzone.org/testprep/math4/d/rangel.cfm
CCS 2007
A graph that uses pictures to represent
data.
Key
Pictograph
http://www.studyzone.org/testprep/math4/d/graphdatal.cfm
http://www.oswego.org/ocsd-web/quiz/mquiz.asp?filename=ccarrollgraph
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Shows change over time; will have months, days or
other time words in the problem.
label
scale
interval
title
Line Graph
http://www.mcwdn.org/Graphs/LineGraph.html
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Is used to compare facts about groups and numbers
that can be counted
title
labels
scale
Bar Graph
http://www.mcwdn.org/Graphs/BarGraph.html
CCS 2007
Compares parts to the whole; decimals and
fractions may be used on this graph
title
key
labels
Circle Graph
http://www.mcwdn.org/Graphs/CirclePieQuiz.html
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The number of times an event occurs;
may use tally marks to record
tallies
IIII IIII IIII
Frequency
http://www.studyzone.org/testprep/math4/d/tablestallyl.cfm
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A letter or symbol that represents a
number in an algebraic expression.
Each side of
the =
symbol
must
balance
Variable
http://www.aplusmath.com/Games/PlanetBlast/index.html
http://www.vectorkids.com/vkvariable.htm
CCS 2007
Contains at least one variable as well
as other numbers and/or operations.
16
10
20
5
20
100
Algebraic Expression
http://mathsnet.net/algebra/l2_equation.html
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A mathematical sentence where the
left side equals the right side.
Equation
http://www.studyzone.org/testprep/math4/d/numericalp.cfm
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A chart that shows a consistent rate of
change.
Function
Machine
T-chart
Input/Output chart
http://www.studyzone.org/testprep/math4/k/addpatternsl.cfm
http://www.shodor.org/interactivate/activities/NumberCruncher/
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The variable represents the number
you are solving to find, termed as the…
Unknown
http://nlvm.usu.edu/en/nav/frames_asid_201_g_4_t_2.html
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An ordered set of numbers, shapes, or other
mathematical objects, arranged according to
a rule.
Pattern
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
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Pattern Changes
Constant Change
2,4,6,8,10….
Varying Change
3,7,4,8,5,9,6,10,7…
Proportional Change
3 4 5 6 7 8 9…
20
5 6 7 8 9 10 11….
22
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Pattern Types
Geometric Pattern
Patterns using shapes
Numeric Pattern
4, 8,16,32,….
Patterns using numbers
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Any number in the pattern can be
found by finding the relation ship or
rule of the pattern.
3,6,9,12,15,18…… Nth term = 3n
10th term = 3(10) = 30
Nth Term
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Symbols used to determine
relationships of equalities.
.5 = .50
? < .5
.30 = .300
equal to
.5 =.05
.3 = .003
? =.1,.2,.3,.4,or .5
less than or
equal to
not equal to
Equal to/not equal to
http://www.studyzone.org/testprep/math4/k/greaterlessthanl.cfm
CCS 2007
The quotient of two numbers used to compare
two qualities.
3
5
Red chips
Blue chips
Ratio
http://www.studyzone.org/mtestprep/math8/c/ratiol.cfm
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Resources
• Web Resources are listed at the bottom of
each slide.
• Additional resources:
– http://www.teachers.ash.org.au/jeather/maths/
dictionary.html
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