Middle School Math Vocabulary Word Wall Cards



Grade 7 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.Number and Number SensePowers of TenScientific NotationComparing Numbers in Scientific NotationRational Numbers Comparing Rational NumbersPerfect SquaresSquare RootAbsolute ValueComputation and EstimationProportionRatio TableScale FactorProportional Reasoning HYPERLINK \l "prop_reason_ex2" Proportional Reasoning: Using BenchmarksMeasurement and GeometryRectangular PrismVolume of a Rectangular PrismHYPERLINK \l "surface_area"Surface Area of a Rectangular PrismCylinderSimilar FiguresSimilar Figures and Proportions HYPERLINK \l "quad_rel" Quadrilateral RelationshipsParallelogramRhombusRectangleSquareTrapezoidLine of Symmetry HYPERLINK \l "reflection" ReflectionTranslationProbability and Statistics HYPERLINK \l "probability" ProbabilityTheoretical ProbabilityExperimental ProbabilityHistogramComparing Graphs: Histogram and Stem and Leaf GraphComparing Graphs: Histogram and Circle GraphComparing Graphs: Histogram and Line PlotPatterns, Functions and AlgebraSlope HYPERLINK \l "unit_rate" Unit Rate Proportional Relationship: y = mx HYPERLINK \l "prop_relation_ex" Proportional RelationshipAdditive Relationship: y = x + bAdditive RelationshipGraphing Linear Relationships HYPERLINK \l "connect_prop" Connecting Representations: Proportional Relationship HYPERLINK \l "connect_additive" Connecting Representations: Additive Relationship HYPERLINK \l "order_ops" Order of OperationsVerbal and Algebraic Expressions and Equations HYPERLINK \l "equation" EquationInequalityPowers of TenScientific Notation424053081280Exponent0Exponent1440180128905Coefficient0Coefficient36595056521440041833792349500197358090170a x 10n377380512700Base0Basea = Coefficient (a number that is greater than or equal to 1 and less than 10)10 = Base n = Exponent (a number that is an integer)Examples 17,500,000 = 1.75 x 107 0.0000026 = 2.6 x 10-6 5.3 x 1010 = 53,000,000,000 4,421.952 = 4.421952 x 103Comparing Numbers in Scientific NotationPlanet Diameter Table (km)PlanetDiameter (km)Scientific NotationMercury4,879 km4.879 x 103 kmVenus12,104 km1.2104 x 104 kmEarth12,756 km1.2756 x 104 kmMars6,792 km6.792 x 103 kmJupiter142,984 km1.42984 x 105 kmSaturn120,536 km1.20536 x 105 kmUranus51,118 km5.1118 x 104 kmNeptune49,528 km4.9528 x 104 km Numbers6327161682300The set of all numbers that can be written as the ratio of two integers with a non-zero denominatorExamples235 , -5 , 0, 0.3, 16 , , 137 Comparing Rational Numbers540728967945212002123609711596901200121245343176183-200-276195229749-5200-52296749174625005570468270869-533627361258Values for numbers get smaller as move further to the left on the number line00Values for numbers get smaller as move further to the left on the number line5410200321310Values for numbers get larger as move further to the right on the number line00Values for numbers get larger as move further to the right 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 > -52 or -52 < -2-2 < 212 or 212 > -2Perfect Squares02 = 0 0 = 012 = 1 1 = 122 = 2 2 = 432 = 3 3 = 942 = 4 4 = 1652 = 5 5 = 2521666208642350029972009525perfect square00perfect squareSquare 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.Absolute Valuedistance a number is from zero92 = 92 -92 = 92 3886835500380412 units00412 units1587500500380412 units00412 units332105047752000886460477520003289935800100055816501873250080835518351500-21145545085 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 600 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6Proportion a statement of equality between two ratios3069590237490 a:b = c:da is to b as c is to dExample45453302489202 is to 5 as4 is to 10002 is to 5 as4 is to 10 3075940184152:5 = 4:10002:5 = 4:10Ratio Tablea table of values representing a proportional relationship that includes pairs of values that represent equivalent rates or ratios ExampleTerry’s neighbor pays him $17 for every 2 hours he works. Terry works for 8 hours on Saturday. A ratio table represents the proportional relationship:Hours1936625424180?8.500?8.5749935168275002945515414655?8.500?8.57448551651000048Pay in $?1734?How much does Terry earn per hour?172=?1 Terry earns $8.50 per hourHow much will Terry earn in 8 hours?$ He will earn $68.00 in 8 hours.Scale Factora number which scales, or multiplies, a quantityFigures A and B are similar340233030416514514B0014514B7999491240683A0083AWhat is the scale factor (scaling up) from figure A to figure B?Scale factor =148=74=1.75What is the scale factor (scaling down) from figure B to figure A?Scale factor =814=47Proportional ReasoningAbout how many centimeters are in 2 feet if 1 inch is about 2.5 centimeters?39738301847854450080228602 feet = 24 inches02 feet = 24 inchesThere are approximately 60 centimeters in 2 feetAbout how many liters are in 3 gallons if 1 quart is approximately 0.95 liters?32575576203 gallons = 12 quarts003 gallons = 12 quarts218313016954500There are approximately 11.4 liters in 3 gallons.Proportional ReasoningUsing benchmarksA meal at a restaurant costs a total of $35.00. Sharon wants to leave a tip.PercentCost of mealPercentage or tip5%$35.00$1.7510%$35.00$3.5015%$35.00$5.2520%$35.00$7.00To find 10% of $35.00 calculate 0.10($35.00) = $3.50Using $3.50 as a benchmark, for example, we can then determine the 20% tip by doubling to $7.00 or the 5% tip by halving to $1.75.Rectangular Prisma polyhedron in which all six faces are rectangles 1662296580000Volume = area of the base times the heightV = BhSurface area = height times the perimeter plus twice the area of the baseS.A. = hp + 2BVolume of a Rectangular Prism794385391160002305052869565 Volume = length · width · heightV = lwhVolume = area of the base x heightmeasured in cubic units00 Volume = length · width · heightV = lwhVolume = area of the base x heightmeasured in cubic units95250760095height020000height15913102084705length020000length34417001574800width020000width407860576581000Surface Area of a Rectangular Prism288798045593000-123825368935h020000h2097405612140w020000w21653526035005130805956300200006781804073525S.A. = 2lw + 2lh + 2whS.A. = 2lw + 2lh + 2wh2249805255905000971551886585Surface Area (S.A.) = sum of areas of faces020000Surface Area (S.A.) = sum of areas of faces86487099695l020000l5572760457200020000Cylindera solid figure formed by two congruent parallel faces called bases joined by a curved surface 22720901856840029206277479rhrh1200151904365Volume = area of the base x heightV = r 2hS.A. = 2 r 2 + 2 r h020000Volume = area of the base x heightV = r 2hS.A. = 2 r 2 + 2 r hSimilar Figures27305063500ABDCEFGH2461200ABDCEFGH24612ABCD HGFEAnglesSidesA corresponds to HAB corresponds to HGB corresponds to GBC corresponds to GFC corresponds to FCD corresponds to FED corresponds to EDA corresponds to EHCorresponding angles are congruent.Corresponding sides are proportional.Similar Figures and Proportions352425152400ABDCEFGH2461200ABDCEFGH24612ABCD HGFEDCEF = ADHE42 = 126Quadrilaterals Relationships2134870265430Quadrilaterals00Quadrilaterals38829217039340018237828902871628085725000147828067564000687705239395No sides parallel00No sides parallel400984854847Trapezoid1 pair parallel sides00Trapezoid1 pair parallel sides17135252985446295734325804783925540304927035399772011916Rhombus4 congruent sides00Rhombus4 congruent sides28930901251600001840865560735Parallelogram2 pairs of parallel sides00Parallelogram2 pairs of parallel sides12004451979856Rectangle4 right angles00Rectangle4 right angles26593802134073Square00Square122487116351400025858381720200004563494135949111795453908500 Parallelogram7543804051300075608664467800191614664467700opposite angles are congruentopposite sides are parallel and congruentdiagonals bisect each otherRhombus1202055500380002148158726563001202055738505003022283340566004 congruent sides2 pairs of parallel sidesopposite angles are congruentdiagonals bisect each other at right anglesRectangle9455158959850093345090170000660552590086004 right anglesopposite sides are parallel and congruentdiagonals are congruent and bisect each otherSquare160224720794800184790741266600184790741266500455676020891501746064217330regular polygon4 right angles4 congruent sides2 pairs of parallel sidesdiagonals are congruent and bisect each other at right anglesTrapezoid 128834950819900exactly one pair of parallel sidesmay have zero or two right anglesmay have zero or one pair of congruent sidesLine of Symmetrydivides a figure into two congruent parts, each of which are mirror images of the other-13132234593 100614888375003990226888868Reflectiona 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)135445541275yxDFEDEF00yxDFEDEF2145157317037445799531315800PreimageImageD(1,-2)D(-1,-2)E(3,-2)E(-3,-2)F(3,2)F(-3,2)21483073777529179912549644664613679136975872260810204451246505The 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 3055620144476yy3402330251934ACBD00ACBD15645281373910BADC00BADC18421351448379001843551216315200291883721651332918404145542036573701091921473231310810073646170372278472642336386252254151684655xxPreimageImageA(1,2)A(-4,-1)B(4,2)B(-1,-1)C(4,4)C(1, 1)D(1,4)D(-4, 1)363855133985The 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’Probabilityif all outcomes of an event are equally likely, the probability of an event occurring is equal to the ratio (between 0 and 1) of desired outcomes to the total number of possible outcomes in the sample space 20688306858000ABABA CC P(A) = 373571875323850likely020000likely1728470316865unlikely020000unlikely128587556832500 264668024066500242252510414037020000374501515819785certain020000certain588645846455impossible020000impossible 0 12 1Theoretical Probabilitythe expected probability of an event18313408826500Theoretical probability of spinning the spinner and landing on blue (B) =Experimental Probabilitythe probability of an event determined by carrying out a simulation or experiment18764253048000Jane spun the spinner 20 times. Her result is shown in the table. ColorNumberYellow (Y)4Green (G)6Blue (B)10Experimental probability of spinning the spinner and landing on blue =Histograma graph that provides a visual interpretation of numerical data by indicating the number of data points that lie within a range of values, called a class or a bin (the frequency of the data that falls in each class or bin is depicted by the use of a bar)8669245841300 4468276166702700337645515714920047412321066525frequency00frequency112457541509180010016894068777-2947924328340intervals00intervalsComparing Graphs4558351688000870053759863The histogram provides a visual interpretation of numerical data.The stem and leaf chart shows all the data in a set.The stem and leaf chart can be used to find the mean, median or mode.00The histogram provides a visual interpretation of numerical data.The stem and leaf chart shows all the data in a set.The stem and leaf chart can be used to find the mean, median or mode.-389758169890900-2159089220300Comparing Graphs277595421531200-627811808082Neither chart displays the entire data set.The mode and the median can not be found without knowing all the data in a set.The histogram displays trends. The circle graph shows parts to the whole. 020000Neither chart displays the entire data set.The mode and the median can not be found without knowing all the data in a set.The histogram displays trends. The circle graph shows parts to the whole. 932189918456Comparing Graphs578428206442001419371549969The histogram provides a visual interpretation of numerical data.The line plot displays all data in the set.The line plot can be used to find the mean, median, or mode.020000The histogram provides a visual interpretation of numerical data.The line plot displays all data in the set.The line plot can be used to find the mean, median, or mode.Slopea rate of change in a proportional relationship between two quantities 16923222621200Slope=change in ychange in x=vertical changehorizontal changeUnit Rate number of units of the first quantity of a ratio compared to 1 unit of the second quantity (also called the constant of proportionality) A student walks 2 miles per hourUnit rate = 12128501841500Proportional Relationshipy =mx (m is the slope)Example: y = 43 x267017538036500191506161793m = 4300m = 43Proportional RelationshipPoints representing a proportional relationship: {(0, 0), (6, 1.5), (10, 2.5),(20, 5), and (24, 6)}.The slope, rate of change, or ratio of y to x isyx? = 1.56 = 2.510 = 520? = 624? = 14? = 0.25The equation representing the proportional relationship of y to x is y =mx or y = 14?x or y = 0.25x.Additive Relationshipa relationship between two quantities in which one quantity is a result of adding a value to the other quantityy =x+b(b is the y-intercept)4356735161290b = -200b = -2Example: y = x + (-2)2656205340360-140970481965xy-3-5-2-4-1-30-21-1203100xy-3-5-2-4-1-30-21-1203137445951143000350652790862(0,-2)00(0,-2)43154602794000Additive RelationshipTomas is three years younger than his sister, Maria. The table represents their ages at various times.Maria (x)456698347162888–3 –3 46926520955011Tomas (y)1238The difference in their ages is always -3.The equation representing the relationship between their ages is y = x + (-3) or y = x - 3Graphing Linear Relationships3545205160655Graph the line representing the additive relationship with slope of 2 and passing through the point (0,4).020000Graph the line representing the additive relationship with slope of 2 and passing through the point (0,4).-102869151130Graph the line representing the proportional relationship with slope of 2 and passing through the point (2,4).020000Graph the line representing the proportional relationship with slope of 2 and passing through the point (2,4).3907790233299022395329714249240395032620696551139483482749641(0,4)(0,4)392534027423433632662528336xy0xy411670536245801 2 3 4 5 6 71 2 3 4 5 6 7364045512433301 2 3 4 5 6 7 8 9 101 2 3 4 5 6 7 8 9 10116332014160500259080530225xy1 2 3 4 5 6 71 2 3 4 5 6 7 8 9 10(2,4)21xy1 2 3 4 5 6 71 2 3 4 5 6 7 8 9 10(2,4)216083304690745Slope = 2 = vertical changehorizontal change=2100Slope = 2 = vertical changehorizontal change=21Connecting RepresentationsProportional Relationship1638301078865The scale on the x-axis needs to be moved over a little to the right. 00The scale on the x-axis needs to be moved over a little to the right. 167640108267500The total distance Sam walks depends on how long he walks. If he walks at a rate of 2.1 mph, show multiple representations of the relationship.6197601028701 2 3 4 5 6 7 8 9 10001 2 3 4 5 6 7 8 9 10104349523247351 2 3 4 5 6 7001 2 3 4 5 6 7Connecting RepresentationsAdditive RelationshipJanice started with $5 in her piggybank. If she adds $1 each week, show the total amount in her piggybank any week using multiple representations.wa0516275105727704838701 2 3 4 5 6 7 8 9 10001 2 3 4 5 6 7 8 9 10107950029051251 2 3 4 5 6 7001 2 3 4 5 6 732588203838575a = w + 54000020000a = w + 527813081915wa00wa35998845032900Order of Operations-323850344170004812030405130( ) [ ] 00( ) [ ] Grouping SymbolsExponents4726305129543Left to right00Left to rightMultiplicationor Division4764405146050Left to right00Left to right Addition SubtractionVerbal and Algebraic Expressions and EquationsVerbalAlgebraicA number multiplied by 55nThe sum of negative two and a number-2 + nThe sum of five times a number and two is five5y + 2 = 5Negative three is one-fifth of a number increased by negative three fifths-3 = 15x + (-35)Equationa mathematical sentence stating that two expressions are equal5559161949456 + 2x = 10006 + 2x = 102.76 + 3 = n + 2.763x + (-5.1) = 334-274320982345Example 1 -3r≤7.5-3r-3≥7.5-3r≥-2.5400000Example 1 -3r≤7.5-3r-3≥7.5-3r≥-2.5Inequality224028016446500-312420254635Example 2 -3(n-4)<0-3n+12<0-3n+12-12<0-12-3n<-12-3n-3>-12-3n>400Example 2 -3(n-4)<0-3n+12<0-3n+12-12<0-12-3n<-12-3n-3>-12-3n>4235458048476100447675206375Example 3 x-7-3≥4-3?x-7-3≤-3?4x-7≤-12x-7+7≤-12+7x≤-500Example 3 x-7-3≥4-3?x-7-3≤-3?4x-7≤-12x-7+7≤-12+7x≤-525069801902460 ................
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