Middle School Math Vocabulary Word Wall Cards
Grade 8 MathematicsVocabulary Word Wall CardsMathematics vocabulary word wall cards provide a display of mathematics content words and associated visual cues to assist in vocabulary development.?The cards should be used as an instructional tool for teachers and then as a reference for all students. The cards are designed for print use only.Table of ContentsNumber and Number SenseComparing Real Numbers HYPERLINK \l "natural" Natural NumbersWhole NumbersIntegersRational Numbers HYPERLINK \l "irrational" Irrational NumbersReal NumbersComputation and Estimation HYPERLINK \l "sq_root" Square Root - Definition HYPERLINK \l "sq_root2" Square Root - Example HYPERLINK \l "proportion" ProportionPercent of IncreasePercent of DecreaseReconcile an AccountMeasurement and GeometryComplementary AnglesSupplementary AnglesVertical AnglesAdjacent AnglesPyramidConeVolume – Changing One AttributeSurface Area – Changing One AttributeReflectionTranslationDilationReflection and Translation Three Dimensional ModelsComposite figuresRight TrianglePythagorean TheoremProbability and StatisticsProbability of Independent EventsProbability of Dependent EventsBoxplotsComparing Boxplots HYPERLINK \l "scatterplot" ScatterplotPositive Linear RelationshipNegative Linear RelationshipNo RelationshipPatterns, Functions and AlgebraTermConstantLike TermsOrder of OperationsRelationsFunctionsDomainRangeSlope – DefinitionSlopeLinear FunctionIdentifying Slope and y-InterceptHYPERLINK \l "depent_independ"Dependent/independent VariableIndependent VariableDependent VariableConnecting RepresentationsMultistep Equations HYPERLINK \l "multi_equ2" Multistep Equations (model)Verbal and Algebraic Expressions and EquationsInequalityComparing Real Numbers5702935269698 00 826770158501-5200-5236093401904181200125398467238511212 00212 1245343176183-200-22967491746250058972452724155570468270869right343116Values for numbers get larger as move further to the right on the number line0Values for numbers get larger as move further to the right on the number line-522761370013Values for numbers get smaller as move further to the left on the number line0Values for numbers get smaller as move further to the left on the number line29718061069 -3 -2 -1 0 1 2 3 00 -3 -2 -1 0 1 2 3 -52 < 12 or 12 > -52-2 > -212 or -212 < -2212<8 or 8>212Natural NumbersThe set of numbers 1, 2, 3, 4…2537460356235Real Numbers020000Real Numbers472313072390000137985572453500464248597790Irrational Numbers020000Irrational Numbers192341588265Rational Numbers020000Rational Numbers2143760629920Integers020000Integers1692275578485005085715100330Irrational Numbers00Irrational Numbers225679062230Rational Numbers00Rational Numbers2199640662305Integers00Integers2153285577850Whole Numbers020000Whole Numbers1973580286385002190115422910Whole Numbers00Whole Numbers2277110361950Natural Numbers020000Natural Numbers234315021463000Examples15 , 81, 101 , 1, 5.0, 16 , 102 Whole NumbersThe set of numbers 0, 1, 2, 3, 4…2013585585470Real Numbers020000Real Numbers4118610327660Irrational Numbers020000Irrational Numbers1400810318135Rational Numbers020000Rational Numbers420052521209000857250212725004563110332740Irrational Numbers00Irrational Numbers1734185294640Rational Numbers00Rational Numbers1621155116840Integers020000Integers145097551879500116967066675001677035150495Integers00Integers1667510655320Whole Numbers00Whole Numbers163068066040Whole Numbers020000Whole Numbers1754505597535Natural Numbers020000Natural Numbers182054544704000Examples19 , 991, 953 , 1, 7.0, 0, 81 , 183 IntegersThe set of numbers…-3, -2, -1, 0, 1, 2, 3…1042670380365Whole NumbersIntegersRational NumbersIrrational NumbersNatural NumbersWhole NumbersIntegersRational NumbersIrrational NumbersReal Numbers00Whole NumbersIntegersRational NumbersIrrational NumbersNatural NumbersWhole NumbersIntegersRational NumbersIrrational NumbersReal NumbersExamples-13 , 61, 27 , (-3)2, 5.0, -25 , 0, 2211 Rational Numbers868045288925Whole NumbersIntegersRational NumbersIrrational NumbersNatural NumbersWhole NumbersIntegersRational NumbersIrrational NumbersReal Numbers00Whole NumbersIntegersRational NumbersIrrational NumbersNatural NumbersWhole NumbersIntegersRational NumbersIrrational NumbersReal NumbersExamples235 , -5 , 0, 0.3, 16 , , 137 The set of all numbers that can be written as the ratio of two integers with a non-zero denominatorIrrational Numbers979170208915Whole NumbersIntegersRational NumbersIrrational NumbersNatural NumbersWhole NumbersIntegersRational NumbersIrrational NumbersReal Numbers00Whole NumbersIntegersRational NumbersIrrational NumbersNatural NumbersWhole NumbersIntegersRational NumbersIrrational NumbersReal NumbersThe set of all numbers that cannot be expressed as the ratio of integerscenter308610Examples7 , π , -0.23223222322223…0Examples7 , π , -0.23223222322223…Real Numbers939800615950Whole NumbersIntegersRational NumbersIrrational NumbersNatural NumbersWhole NumbersIntegersRational NumbersIrrational Numbers00Whole NumbersIntegersRational NumbersIrrational NumbersNatural NumbersWhole NumbersIntegersRational NumbersIrrational NumbersThe set of all rational and irrational numbersSquare Rootany number which, when multiplied by itself, equals the number3561331151501radical symbol00radical symbol41527551296490052067673570025 = 525 = 5?5 = 52 = 5Squaring a number and taking a square root are inverse operations.-36 = -6(-6)2 = -6 ? -6 = 36Square Root10 ≈ 3.163611880825500502475574168000398272011036304020000434709101114425302000034556760741680009207507632700021107401114425002000005471160742315004121150730885003631565741680003206750741680002738755763270002281555763270001803400763270001367155752475006280151206500010 is between9 and 16 Proportiona statement of equality between two ratios3069590237490 a:b = c:da is to b as c is to dExample469864038102 is to 5 as4 is to 10002 is to 5 as4 is to 1023442972021002:5 = 4:10002:5 = 4:10 Percent of Increase Percent of change = · 100 80010454660002302510370840What is the percent of increase? increase of 13%00What is the percent of increase? increase of 13%146050179070Was $2.25 per gallonNow $2.55 per gallon00Was $2.25 per gallonNow $2.55 per gallonPercent of DecreasePercent of change = · 100 2365157843526What is the percent of decrease? decrease of 25%00What is the percent of decrease? decrease of 25%103505784860001504952656205Was $1200Now only $90000Was $1200Now only $900Reconcile an AccountJoe owed a balance of $147.60 on his credit card account on June 1. Below is a list of transactions that occurred during June.TransactionsDateDescriptionAmount6/3Giddy-up Gas$ 31.006/7Payment $ 150.006/12Food-o-rama$ 134.126/22Big Top Pizza$ 34.326/28Bart’s Sport Shop$ 16.04Determine how much he owes on his credit card account after the purchase at Bart’s Sport Shop.476523212790460right50644Purchases: Balance - Purchases: ? $147.60 ? $215.48 = ? $363.08Amount Owed: ? $363.08 + $150.00 = ? $213.0800Purchases: Balance - Purchases: ? $147.60 ? $215.48 = ? $363.08Amount Owed: ? $363.08 + $150.00 = ? $213.08Complementary Angles67283532855121002132575506445251200121613535579754Fig 100Fig 14775835515619Fig 200Fig 2m1 + m2 = 90in each figureSupplementary Angles2025652222521002127051002571752100211925955246380Fig 1020000Fig 14311015583565Fig 2020000Fig 2m1 + m2 = 180in each figureVertical Angles1869440169545143200143231089602089150028803602279650030130751828801 and 3 are vertical angles.2 and 4 are vertical angles.1 3 and 2 4Adjacent Angles is adjacent to in each figure1804035299720Fig 21200Fig 212649605680085210021509524028892500339725032702521002164960532702500880110102235Fig 100Fig 14831080235585Fig 3020000Fig 3Share a common side and a common vertexSquare-Based Pyramid15722603924304227830669290l020000l 3417602142875h020000h6153150250825020000338251860652718800061218260B = area of square basep = perimeter of baseh = heightl = slant height00B = area of square basep = perimeter of baseh = heightl = slant height14606532646071V = 13BhS.A. = 12lp + B00V = 13BhS.A. = 12lp + B3383016446405003176905454025005242560743585020000Cone1571625115679rh00rh19598132854935r = radius of baseh = heightl = slant height00r = radius of baseh = heightl = slant height7978654165219V = 13 r 2hS.A. = r 2 + r l020000V = 13 r 2hS.A. = r 2 + r l4288155253365l020000lVolume of Rectangular Prism(Changing one attribute)3577046574675V = lwh8 · 2 · 3 = 48 cm30V = lwh8 · 2 · 3 = 48 cm3-4535423308353 cm2 cm 8 cm82336Height is multiplied by 2Volume is multiplied by 2003 cm2 cm 8 cm82336Height is multiplied by 2Volume is multiplied by 2-2438403486693New Volume V = 8 · 2 · 6 = 96 cm30New Volume V = 8 · 2 · 6 = 96 cm3Surface Area of a Rectangular right1195251S.A. = 2lw + 2lh + 2whS.A. = 2(8·2) + 2(8·3) + 2(2·3)S.A. = 32 + 48 +12 = 92 units200S.A. = 2lw + 2lh + 2whS.A. = 2(8·2) + 2(8·3) + 2(2·3)S.A. = 32 + 48 +12 = 92 units2Prism (Changing one attribute) 50643744237280085130805956300200001642374280035bottombacktopfrontleft sideright side66660bottombacktopfrontleft sideright side6666-1390656009005New S.A. = 2(8·2) + 2(8·6) + 2(2·6)New S.A. = 32 + 96 + 24 = 152 units200New S.A. = 2(8·2) + 2(8·6) + 2(2·6)New S.A. = 32 + 96 + 24 = 152 units213716058247600left321174023368233688817431371273Height is multiplied by 200Height is multiplied by 222056146324112223111320535733Reflection13576301217295yxDFEDEF00yxDFEDEFa transformation in which an image is formed by reflecting the preimage over a line called the line of reflection (all corresponding points in the image and preimage are equidistant from the line of reflection)2145157317037445799531315800PreimageImageD(1,-2)D(-1,-2)E(3,-2)E(-3,-2)F(3,2)F(-3,2)44564302667021483073777529179912549636975872260810204451246505The preimage of triangle DEF is reflected across the y-axis to create the image D’E’F’0The preimage of triangle DEF is reflected across the y-axis to create the image D’E’F’Translationa transformation in which an image is formed by moving every point on the preimage the same distance in the same direction. 3055620144476yycenter3778095The preimage of rectangle ABCD is translated 5 units to the left and 3 units down to create the image A’B’C’D’00The preimage of rectangle ABCD is translated 5 units to the left and 3 units down to create the image A’B’C’D’15645281373910BADC00BADC1842135144837900184355121631520029188372165133291840414554203657370109192147323131081007364617037227847264233638623402330238760ACBD00ACBD52254151684655xxPreimageImageA(1,2)A(-4,-1)B(4,2)B(-1,-1)C(4,4)C(1, 1)D(1,4)D(-4, 1)DilationPreimageImageA(0,4)A(0,2)B(4,0)B(2,0)C(0,0)C(0,0)1082165675005003373755338455center of dilation is (0,0)scale factor = 020000center of dilation is (0,0)scale factor = 37020543815xyCABABC00xyCABABC10871206342400017829556197600024911056069350081887683365center of dilation is (0,0)scale factor = 2020000center of dilation is (0,0)scale factor = 24544695323215y00y304228556959500PreimageImageG(0,-2)G(0,-4)H(0,0)H(0,0)J(1,0)J(2,0)L(1, -2)L(2,-4)49612551884045L00L52514501062355J′00J′49244251057910J00J49447661299761V00V46328461938374V00V52624742567368V00V52623701301115V00V46291502557270V00V49524901945005V00V46297851297180V00V43700701299372H′00H′44145201080932H00H43848671891414G00G4661313132788800747331569151500466131313278880062103001257300x00x52203352584450L′00L′43192702586355G′00G′Reflection and TranslationPreimageImageD(1,-2)D(-1,0)E(3,-2)E(-3,0)F(3,2)F(-3,4)110564415240yxDFEDEF00yxDFEDEF11658604825365Figure DEF is reflected over the y-axis and translated up 2 units to create the image D’E’F’.0Figure DEF is reflected over the y-axis and translated up 2 units to create the image D’E’F’.46303923239587V00V46403821455368V00V37559213239504V00V28859812362356V00V20016032353341V00V2008682580942V00VThree Dimensional Models-63505499100052616103357top020000top411289569723000223393068008500526097568262500414401077470side020000side248412082550front020000front5071110578485bottom020000bottom3883660556895side020000side2252345571500front020000front-119380444500047986953816350037585653492500185102519304000Right Triangle-224790683260c hypotenuseleg alegbCBA00c hypotenuseleg alegbCBA69913534925In a right triangle, the hypotenuse is the side opposite the right angle. The hypotenuse is the longest side of the right triangle.0In a right triangle, the hypotenuse is the side opposite the right angle. The hypotenuse is the longest side of the right triangle.Pythagorean Theorem32061155715002727960198755bca00bca85661516192500275018553340000a2 + b2 = c2Composite Figures2644433-4953020 cm02000020 cm182261111493501613535267970003312160110490017945102286000011880855969014 cm02000014 cm160401036385500674370010372725002857500754380000285750075438000028575007543800002857500754380000285750075438000028575007543800002857500754380000285750075438000051435007543800002857500754380000Example 1: Subdivide the composite figure into other figures, then determine the perimeter.1806371390369001576070156210004417695137795A – 40 ftB – 21 ftC – 38 ft00A – 40 ftB – 21 ftC – 38 ft182362412533500Example 2: Subdivide the composite figure into other figures to determine the area of the side of the house. Area = = 798 + 361 = 1159 ft2Probability of Independent EventsThe outcome of one event does not affect the outcome of the other event.2975610198755What is the probability of landing on green on the first spin and then landing on yellow on the second spin?00What is the probability of landing on green on the first spin and then landing on yellow on the second spin?1484630125857000P(green and yellow) = P(green) ? P(yellow) = Probability of Dependent Events45948601172210Candy JarRRGYPBRRGYPB00Candy JarRRGYPBRRGYPBThe outcome of one event has an impact on the outcome of the other event.left108070What is the probability of choosing a red jelly bean on the first pick and then without replacing it, choosing a green jelly bean on the second pick?00What is the probability of choosing a red jelly bean on the first pick and then without replacing it, choosing a green jelly bean on the second pick? P(red) ? P(green after red) =17061386840000Boxplots(Box-and-Whisker Plots)A graphical representation of the five-number summary-303530262890LowerQuartile (Q1)LowerExtremeUpperQuartile (Q3)UpperExtremeMedianInterquartile Range (IQR)510152000LowerQuartile (Q1)LowerExtremeUpperQuartile (Q3)UpperExtremeMedianInterquartile Range (IQR)5101520Comparing BoxplotsComparing the heights (inches) of high school boys and girls306133520593050-704852716230027764591941384MedianMedian45173901729740MedianMedian47618659664700ScatterplotIllustrates the relationship between two sets of data.1344930585470xy00xyPositive Linear RelationshipPattern of points slopes from lower left to upper right.(Generally, as the x-coordinates increase in value, the y-coordinates increase in value)1308735509270xy00xyNegative Linear RelationshipPattern of points slopes from upper left to lower right(Generally, as the x-coordinates increase in value, the y-coordinates decrease in value)1496060394335xy00xyNo Linear Relationship no relationship exists between the x- and y-coordinates1463675598805xy00xyTerm2104390443865004344433434974003234690443865003x + 2y – 83 terms392715328257500220218030162500-5x2 + (-2x) 2 terms31019756089650023ab1 termConstant4805993643890004751070605790-12 020000-12 4394835542925004x – 12121475516510007 – 2y + x – 6x 23219137687070004904105471805004887595484505 89 020000 89 3(x + 3.9) + QUOTE 89 Like Terms3616012626110001255708652780004x – 3y + 6x – 7414179259055000156527558514800 2y 2 – 3y + 7y 22359973805815005072067-508000-5r 2 – 6 + 2r + 2-32766093599000Order of Operations4812030405130( ) { } [ ] 00( ) { } [ ] Grouping SymbolsExponents4726305129543Left to right00Left to rightMultiplicationor Division4764405146050Left to right00Left to right Addition Subtractioncenter781050Any set of ordered pairs00Any set of ordered pairsRelationOrdered Pairs{(-3,3), (0,3), (1,5), (1,-1), (2, -1)}511175-464185Table00Tablexy-3303151-12-14276725447040Graph00Graph316611096837500661035838199A relation between a set of inputs, called the domain, and a set of outputs, called the range, with the property that each input is related to exactly one output00A relation between a set of inputs, called the domain, and a set of outputs, called the range, with the property that each input is related to exactly one outputFunction{(-1,1), (0,1), (2,3), (4,1)}xy-1101234132896991341873004200525-2540020000DomainThe set of all the input values for the independent variable or x-values (first number in an ordered pair) {(-1,1), (0,1), (2,3), (4,1)}xy-11012331115-191833500413241675570865D: {-1, 0, 2, 4}00D: {-1, 0, 2, 4}33083501570355004200525-2540020000RangeThe set of all the output values for the dependent variable or y-values (second number in an ordered pair) {(-1,1), (0,1), (2,3), (4,1)}x-2794059690000y-110123413241675570865R: {1, 3}00R: {1, 3}33083501570355004200525-2540020000SlopeRepresents the rate of change in a linear function or the “steepness” of the line.24066521844010515601346203200324327525280035Slope = 2300Slope = 23slope =change in ychange in x=vertical changehorizontal changeSlope 3627120519539003327405321300016376656000115A horizontal line has a slope of zero (0).020000A horizontal line has a slope of zero (0).212090032645350032140422582545A line with a negative slope slants down to the right.020000A line with a negative slope slants down to the right.-126122566429A line with a positive slope slants up to the right.020000A line with a positive slope slants up to the right. Linear FunctionA linear function can be written as y = mx + b and its graph is a straight line. Its slope represents a constant rate of change. y = mx + b (slope is m and y-intercept is b)Example: y = -43 x + 53556635441325(0,5)-4300(0,5)-432180590226060Identifying Slope and 4753610840105+1020000+14038600843915+1020000+13238500848995+1020000+12495550847090+1020000+1y-Intercept4776470873125-3020000-339052501714502409825889004038600885190-3020000-3390525055054503267075894715-3020000-3314325056134102533650885190-3020000-32419350561341031337258890042043361945004y-intercept, b, is 2, located at (0,2).slope = m = -31 = -3y = -3x + 200y-intercept, b, is 2, located at (0,2).slope = m = -31 = -3y = -3x + 255784754026535004768850400812000465264552990304652645-31750357298477679023037423544211001089025-5080001088390107263800Dependent/Independent VariableDetermine the distance (d) a car will travel going 55 mph.hd0015521103165d = 55h4558030280670dependent020000dependent-289560318135independent020000independentIndependent Variable32886657810500y = 2x + 7 x represents the independent variable(input values or domain)Dependent Variable19817873365500y = 2x + 7 y represents the dependent variable(output values or range)Connecting RepresentationsA bike rents for $4 plus $1.50 per hour. 366747562223300276225173933c = 1.5h + 400c = 1.5h + 4hc0415.52738.5410511.5Multistep Equations2x – 5.7 = -3.4x + 11.0423 (n + 9) = - 56n25 = 6p - 5-4Multistep Equation1559560876303x + 5 = -3 – x0200003x + 5 = -3 – x4486910170815000487680017081500041021002188210004084320170815000219392511347450022066256959600017919701147445001804035720725001822450336550006769107378700066992511582400068262532956500Verbal and Algebraic Expressions and EquationsVerbalAlgebraicA number multiplied by five5nThe sum of negative two and a number-2 + nThe sum of half a number and two is five times the number12y + 2 = 5yNegative three times a number is one-fifth the difference of four times the number and ten-3x = 15(4x – 10) Inequality-3(n – 4) < 0-3n + 12 < 0-3n < -12n > 4317500190500 0 1 2 3 4 5 00 0 1 2 3 4 5 508264156037 0 1 2 3 4 5 0 1 2 3 4 5 ................
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