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Middle School Mathematics Vocabulary Word Wall Cards
Table of Contents (Grades 6-8)
Number and Number SenseRatioAbsolute ValueFraction MultiplicationFraction DivisionFraction DivisionPercentEquivalent RelationshipsExponential FormPerfect SquaresPowers of TenScientific NotationNatural NumbersWhole NumbersIntegersRational NumbersIrrational NumbersReal NumbersComparing Integers
Computation and EstimationOrder of OperationsInteger OperationsInteger OperationsInteger OperationsProportionScale FactorUnit RatePercent of Increase
Percent of DecreaseSquare RootSquare Root
MeasurementBallpark Comparisons – LengthBallpark Comparisons – Weight/MassBallpark Comparisons – VolumeBallpark Comparisons – TemperaturePerimeterAreaPiCircumferenceArea of a CircleVolume of a PrismSurface AreaVertexFace and BasePyramidPrismConeCylinderVolume – Changing One AttributeComplementary AnglesSupplementary AnglesVertical AnglesAdjacent AnglesSimilar FiguresSimilar Figures and Proportions
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GeometryCongruent FiguresTrianglesQuadrilateralsQuadrilateral RelationshipsParallelogramRhombusRectangleSquareTrapezoidKiteComposite FiguresRight TrianglePythagorean TheoremThree Dimensional ModelsCoordinate PlaneRotationReflectionTranslationDilation
Probability and StatisticsProbabilityProbability of Independent EventsProbability of Dependent EventsFundamental Counting PrincipleTree DiagramMeanMedianModeRangeBar GraphLine GraphStem-and-Leaf PlotCircle GraphHistogramScatterplot
Positive CorrelationNegative CorrelationConstant CorrelationNo Correlation
Patterns, Functions and AlgebraArithmetic SequenceGeometric SequenceAdditive Identity PropertyAdditive Inverse PropertyAssociative PropertyCommutative PropertyMultiplicative Identity PropertyMultiplicative Inverse PropertyMultiplicative Property of ZeroDistributive PropertyEquationExpressionVariableCoefficientTermConstantInequalityLike TermsRelationsFunctionsTable of ValuesDomainRangeDependent/independent VariableIndependent VariableDependent VariableConnecting RepresentationsMultistep EquationsMultistep EquationsUnit Rate as Slope
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Ratioa comparison of any two quantities
SET A SET B
to 4 to 3
to all of set A
to 3:5
set B to set A 9 to 7 or 9:7
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Absolute Value
|5| = 5 |-5| = 5
5 units 5 units
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
distance a number is from zero
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FractionMultiplication
How much is of ?
38
x 2 = 63 24
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Fraction Division
How many halves are in three-fourths?one “whole” half
half
There are 1 halves in three-fourths.
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Fraction Division
How many halves are in three-fourths?
three-fourths one-half 1 “whole” one-half one-half
There are 1 halves in three-fourths.
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Percent
Per hundred
56% = = = 0.56
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EquivalentRelationships
Fraction:
Decimal: 0.4
Percent: 40%
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Exponential Form
exponent
23 = 2 2 2base
n4 = n n n nfactors
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Perfect Squares02 = 0 0= 012 = 1 1= 122 = 2 2= 432 = 3 3= 942 = 4 4= 16
52 = 5 5= 2516 = 4 ⋅ 4 = 4
perfect square
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Powers of TenMeaning Value
104 10 10 10 10 10,000
103 10 10 10 1000
102 10 10 100
101 10 10
100 1 1
10-1 0.1
10-2 = 0.01
10-3 = 0.001
10-4 = 0.0001
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Scientific Notation
a x 10n
a = number greater than or
equal to 1 and less than 10
n = integer
17,500,000 = 1.75 x 107
0.0000026 = 2.6 x 10-6
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Natural Numbers
The set of numbers 1, 2, 3, 4…
Rational Numbers rati alIrrational
Numbers
IntegersNumbers
Whole Numbers
NaturalNumbers
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Whole Numbers
The set of numbers 0, 1, 2, 3, 4…
RationalNumbers Irrationalrat alrs
Integers Numbers
Whole Numbers
NaturalNumbers
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Integers
The set of numbers …-3, -2, -1, 0, 1, 2, 3…
Rational Numbers Irrational
IntegersNumbers
Whole Numbers
NaturalNumbers
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Rational Numbers
Rational Numbers Irrational
IntegersNumbers
Whole Numbers
NaturalNumbers
A number that can be written as the quotient of two integers
2 -5
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Irrational Numbers
Rational Numbers Irrational
IntegersNumbers
Whole NumbersNatural Numbers
NaturalNumbers
A number that cannot be expressed as the quotient
of two integers
-0.23223222322223…
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Real Numbers
Rational Numbers IrrationalNumbers
Integers
Whole Numbers
Natural Numbers
The set of all rational and irrational numbers
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ComparingIntegers
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-5 < 1 or 1> -5
-4 > -5 or -5 < -4
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Order ofOperations
Grouping Symbols
Exponents
( ){ } [ ] |abs| Fraction bar
MultiplicationDivision
AdditionSubtraction
Leftto
right
Leftto
right
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Integer OperationsAddition-5 + 6 = 1
-6 -5 -4 -3 -2 -1 0 1 2
Subtraction1 – 6 = -5
-6 -5 -4 -3 -2 -1 0 1 2
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Integer OperationsAddition-5 + 6 = 1
Subtraction1 – 6 = -5
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Integer OperationsMultiplication 3 (-4) = -12
Division-12 -4 = 3
How many tilesare in 3 groupsof -4 tiles?
How manygroups of -4 tilesare in -12 tiles?
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Proportion
ab = d
c
a:b = c:d
a is to b as c is to d
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Scale FactorFigures A and B are similar.
2 4A
B
1
2
What is the scale factor from A to B? Scale factor = 2
What is the scale factor from B to
A? Scale factor =
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Unit Rate
$4 per gallon =
70 miles per hour =
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Percent of Increase
Percent of change = new – original original
Was $3.25per gallon
Now $3.85per gallon
What is the percent ofincrease?
3.85 – 3.253.25
increase of 18%
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Percent of Decrease
Percent of change = new – original original
Was $1200Now only $900
What is the percent ofdecrease?
900 – 12001200
decrease of 25%
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Square Rootradical symbol
= 6
= = = 6Squaring a number and taking a square
root are inverse operations.
- = -6(-6)2 = -6 ∙ -6 = 36
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Square Root
0 3 4
between and
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BallparkComparisons
Length
1 inch or2.5 centimeter
1 yard < 1 meter
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BallparkComparisons
Weight/Mass
≈
≈
≈
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BallparkComparisons
Volume
≈
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BallparkComparisons
TemperatureFahrenheit Celsius
Water32°F 0°Cfreezes
Water boils 212°F 100°CBody
98°F 37°CTemperatureRoom
70°F 20°CTemperature
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Perimeter
the measure of the distance around a figure
b
a c
d
P = a + b + c + d
r
u se f
t g
P = r + s + t + u P = e + f + g
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Areathe number of square units needed to cover a surface
or figure
Area = 12 Square Units
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Pi
π≈ 3.14159…
diameter
π =
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Circumference
radius
C = 2πrC = perimeter of a circle
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Area of a Circle
A = πr 2
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Volume of a Prism
height
width
length
Volume = length x width x height
V = lwh
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Surface Areah
wl
back
left side top right side
front
bottom
Surface Area (S.A.) = sum of areas of faces
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Vertex
vertex
vertices
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Face and Base
Face
FaceBase Face
Base
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Pyramid
h l
h l
B = area of basep = perimeter of base
V = Bh
S.A. = lp + B
B = area of basep = perimeter of base
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Prism
h
B = area of basep = perimeter of base h
V = Bh B = area of basep = perimeter of base
S.A. = hp + 2B
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Cone
lh
r
V = π r 2h
S.A. = π r 2 + π r lPage 45
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Cylinder
h
r
V = π r 2h
S.A. = 2π r 2 + 2π r h
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VolumeChanging one attribute
3
28
Height increases to 6
3
6
32
8
What happens to the volume?
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Complementary Angles
1
2 1
2Fig 1
Fig 2
m∠1 + m∠2 = 90°in each figure
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Supplementary Angles
1
2
Fig 1
1 2
Fig 2
m∠1 + m∠2 = 180°in each figure
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Vertical Angles
1
42
3
∠1 and ∠3 are vertical angles.∠2 and ∠4 are vertical angles.
∠1 ≅ ∠3 and ∠2 ≅ ∠4
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Adjacent Angles∠1 is adjacent to ∠2
in each figure
1
2
1
2 Fig 2
Fig 1 1 2Fig 3
Share a common side and a common vertex
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Similar FiguresB C
4
A 12 D G F2
H 6 E
ABCD ∼ HGFE
Angles Sides∠A corresponds to ∠H corresponds to∠B corresponds to ∠G corresponds to∠C corresponds to ∠F corresponds to∠D corresponds to ∠E corresponds to
Corresponding angles are congruent.Corresponding sides are proportional.
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Similar Figures and Proportions
BC
4
A 12 D G F2
H x E
ABCD ∼ HGFE
=
=
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Congruent Figureshave exactly the
same shape and sizeB
P
A ≅ Q B
A C
H G P
B C F R
A DE Q
∠BAC ≅ ∠PQR
ABCD ≅ HGFE
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Triangles
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Quadrilaterals
parallelogramrhombus
rectangle
kite
trapezoidsquare
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Quadrilaterals Relationships
Quadrilateral
Kite Parallelogram Trapezoid
Rhombus Rectangle
Square
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Parallelogram
• opposite angles are congruent
• 2 pairs of parallel sides• 2 pairs of opposite
sides congruent
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Rhombus
• opposite angles are congruent
• 2 pairs of parallel sides• 4 congruent sides
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Rectangle
• 4 right angles• 2 pairs of parallel sides• 2 pairs of opposite
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Square
• 4 right angles• 2 pairs of parallel sides• 4 congruent sides
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Trapezoid
• may have zero or two right angles
• exactly one pair of parallel sides
• may have one pair of congruent sides
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Kite
• one pair of opposite congruent angles
• 2 pairs of adjacent congruent sides
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Composite Figures20 cm
14 cm
Subdivide into other figures thendetermine the perimeter.
5′ 5′22.5′ 5′
10′
25′
Subdivide into other figures thendetermine the area.
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Right TriangleC
leg lega b
B c Ahypotenuse
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PythagoreanTheorem
b c
a
a2 + b2 = c2
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Three Dimensional Models
front side top
front side top
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Coordinate Planey axis
Quadrant II4
Quadrant I
(4, 3)3
2
1
x axis- 4 -3 -2 -1 1 2 3 4
(- 2,-1)-1
-2
-3( 0,- 3)-4
Quadrant III Quadrant IV
ordered pair (x,y)
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Rotationy
B C A′ B′
D′ C′ xA D
center of rotation
Preimage ImageA(-3,0) A′(0,3)B(-3,3) B′(3,3)
C(-1,3) C′(3,1)D(-1,0) D′(0,1)
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Reflectiony
F′ F
x
E′ D′ D E
Preimage ImageD(1,-2) D′(-1,-2)E(3,-2) E′(-3,-2)
F(3,2) F′(-3,2)
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Translationy
E D
C
A B
x
E′ D′
C′
A′ B′
Preimage ImageA(1,2) ′
A (-2,-3)
B(3,2) ′B (0,-3)
C(4,3) ′C (1,-2)
D(3,4) ′D (0,-1)
E(1,4) ′E (-2,-1)
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Dilationy
Acenter of dilation = (0,0)
1
A′
C ′B
′ B xC
Preimage ImageA(0,4) A′(0,2)B(4,0) B′(2,0)C(0,0) C′(0,0)
y
center of dilation = (0,0) scale factor = 2
Preimage ImageG(0,-2) G′(0,-4)H(0,0) H′(0,0)J(1,0) J′(2,0)
K(2, -1) K′(4,-2)L(1, -2) L′(2,-4)
H J J′xH′
K
G L K′
G′ L′
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Dilationy
E′ F′
E F x
H′ G′
H G
O
center of dilation = (-4,-3)scale factor = 2
Preimage ImageE(-2,0) E′(0,3)F(-1,0) F (2,3)′G(0, -2) G (4,-1)′H(-1,-2) H (2,-1)′
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Dilation
6
6
center of dilation = Cscale factor = 1/3
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Probability
A B A BA C C
P(A) = unlikely likely
0 1impossible certain
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Probability of Independent Events
P(green) =
P(yellow) = =
P(green and yellow) =
P(green) P(yellow) = =
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Probability of Dependent Events
What is the probability of getting a red jelly bean on first
pick and then without replacing it, getting a green
jelly bean on the second pick?
P(red) ∙ P(green after red) =
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Fundamental Counting PrincipleIf there are m ways for one
event to occur and n ways for a second event to occur, thenthere are m n ways for both
events to occur.
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Tree DiagramJoe has two pairs of pants (blue and tan). He
also has three shirts (red, green and white). List the possible outfits that Joe can make.
PANTS SHIRTS POSSIBLE OUTCOMESred blue pants with red shirt
blue green blue pants with green shirtwhite blue pants with white shirtred tan pants with red shirt
tan green tan pants with green shirtwhite tan pants with white shirt
2 3 or 6 possible outcomes
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Meana measure of central tendency
2, 3, 4, 7
Balance Point2 3
1
-1 0 1 2 3 4 5 6 7
Numerical Average
2 + 3 + 4 + 7 = 16 = 44 4
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Mediana measure of central tendency
6, 7, 8, 9, 9
8 = median
5, 6, 8, 9, 11, 12
8.5 = median
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Modea measure of central tendency
Data Sets Mode2, 3, 3, 3, 5, 5, 9, 10 3
5.2, 5.4, 5.5, 5.6,none5.8, 5.9, 6.0
1, 1, 2, 5, 6, 7, 7, 9,1, 711, 12
bimodal
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RangeData set
2 , 3, 3 , 3 , 5, 5 , 9 , 10 , 15 , 20
20 – 2 = 17
Range = 17
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Bar Graph
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Line Graph
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Stem-and-Leaf PlotMath Test Scores
56, 65, 98, 82, 64, 71, 78, 86, 95, 91,59, 70, 80, 92, 76, 82, 85, 91, 92, 73
STEM LEAF5 6 96 4 57 0 1 3 6 88 0 2 2 5 69 1 1 2 2 5 8
Key: 5|6 means 56
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Circle GraphFavorite Ice Cream
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Histogram
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Scatterplotillustrates the relationship between two sets of data.
y
x
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Positive Correlationy-coordinates increase as
x-coordinates increasey
x
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NegativeCorrelation
y-coordinates decrease as x-coordinates increase
y
x
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ConstantCorrelation
y-coordinates remain about the same as x-coordinates increase
y
x
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No Correlation
no pattern exists between the x- and y- coordinates
y
x
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ArithmeticSequences
What is the next term?
+6 +6 +6
4, 10, 16, 22 ...common difference
+ + + +
3, , 4, , 5 …
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GeometricSequences
What is the next term?x3 x3 x3
9, 27, 81, 243 …
common ratio
x x x x
7, 0.7, 0.07, 0.007, 0.0007 …
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Additive Identity Property
0.3 + 0 = 0.3
0 + (-7) = -7
= 0 +
w + 0 = w
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Additive Inverse Property
1.4 + (-1.4) = 0
(-9) + 9 = 0
0 = + (- )
x + (-x) = 0
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AssociativeProperty
Addition:(4 + 2) + 8 = 4 + (2 + 8)
x + (3x + ) = (x + 3x) +
Multiplication:
(3 ∙ 1.5) ∙ 6 = 3 ∙ (1.5 ∙ 6) 2(3x) = (2 ∙ 3)x
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CommutativeProperty
Addition:2.76 + 3 = 3 + 2.76
(a + 5) + 7 = (5 + a) + 7
Multiplication:
-8 = (-8)
y ∙ 9 = 9y
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Multiplicative Identity Property
9 1 = 9
1 (-10) = -10
= 1
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Multiplicative Inverse Property
2 ∙ = 1
1 = ∙ -9
x = 1 (x ≠ 0)
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Multiplicative Property of Zero
0 = 8
0(-13) = 0
x 0 = 0
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DistributiveProperty
-4(2 + 3) = -4(2) + -4(3)
5 ∙ (y – 7) = (5 ∙ y) – (5 ∙ 7)
(2 ∙ ) + (2 ∙ 5) = 2( + 5)
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Equation
6 + 2x = 10
A mathematical sentence stating that two expressions are equal.
2.76 + 3 = 3 + 2.76
3x = 6.9
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Expression
x
-
2x + 34
3(y + 3.9) –
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Variable
2(y + 3)
3 + x = 2.08
A = π r 2
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Coefficient
(-4) + 2x
-7y 2
ab –
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Term3x + 2y – 8
3 terms
-5x2 + (-2x)2 terms
ab1 term
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Constant
4x – 12
7 – 2y + x – 6x 2
3(x + 3.9) –
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Inequalityy < 4
0 1 2 3 4 5
3r ≥ -7.5
-4 -3 -2 -1 0 1
-3(n – 4) < 0
0 1 2 3 4 5
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Like Terms
4x – 3y + 6x – 7
2y 2 – 3y + 7y 2
-5r 2 – 6 + 2r + 2
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Relations{(2,3), (4,1), (2,5)}
x y2 2-3 45 -10 41 -6
{(0,4), (0,3), (0,2), (0,1)}
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Functions{(2,4), (3,2), (0,2), (-1,2)}
x y3 22 40 2-1 2
y
x
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Table of Values
x y0 1
1 2
2 5
3 10
4 17
a 1 2 3 4b 22,500 22,000 21,500 21,000
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Domain
{(-2,0), (-1,1), (0,2), (1,3)}
x y{-2,-1, 0, 1}-2 0
-1 10 21 3
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Range
{(-2,0), (-1,1), (0,2), (1,3)}
x y-2 0
{0, 1, 2, 3}-1 10 21 3
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Dependent/ Independent Variable
Determine the distance a car will travel going 55 mph.
d = 55h
independent h d dependent0 01 552 1103 165
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IndependentVariable
y = 2x + 7
x represents the independent variable
(input values or domain)
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DependentVariable
y = 2x + 7
y represents the dependent variable
(output values or range)
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Connecting Representations
The total distance Sam walks depends on how long he walks. If he walks at 2.1 mph, show multiple representations of the relationship.
t dd
0 01 2.12 4.24 8.4
t
d = 2.1t
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Multistep Equations
2x – 5.7 = -3.4x + 11.04
(n + 9) = - n
25 =
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Multistep Equation
3x + 5 = -3 – x
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Unit Rate as SlopeA student walks 2 miles per hour
2 miles 1 hour
miles
1 2
21
hours
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