8th Grade Summer Math Packet - Millsboro Middle School

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Name:8th Grade Summer Math PacketDear Future 8th Grader,This summer math packet is designed to help you keep your math skills strong before returning to 8thgrade in the fall. We want you to feel confident on the following skills and problems when you begin 8thgrade. If you get to a problem you are confused on, here are some ideas to help: Ask a parent/guardian, family member, or friendGo to www.khanacademy.org and search for a video to help you remember that conceptPractice that skill on Khan Academy and try to improve your scoreLook at your math notes or SpringBoard book from 7th gradeMark that problem with a “?” to remember to ask your 8th grade teacher in the fallUp first, we’d like you to practice your math facts over the summer andreturn to 8th grade strong. Please work on the following:ooMultiplication Facts (1-12’s)Division Facts (1-12’s)You can find flash cards for these at any dollar store, or you can search“Math Facts Flash Cards” online to download and print a set. Practice,practice, practice – we want you to have these memorized!The rest of the packet is review problems from 6th and 7th grade math. Do your best to complete themall and show your work! You should not use a calculator unless you see the calculator icon next to aproblem. Bring your completed math packet to your 8th grade math teacher in the fall – and happysolving!1. 3.175 12.82.257.4 94.253. 325.9 1.024.4.3 0.121

Name:5. 1,407 ( 12.65)6.5,387.25 14.0417. 1.75 3.18.4.636 0.389.10.2

Name:11.12.13. Give three fractions that are equivalent to14.16.2356 58 141420. Show your work!15.17.913 4511 216 33

Name:18.20.22.24.57 1112119.9 143253 2 921.2 2 5 823 361620 25217 3 223. 425.6 3118426. Convert each fraction into a decimal using long division. Decide whether each decimal is aterminating or repeating decimal:45891120464

Name:27. Which fractions below are equivalent toa.b.c.d.e.2432? 2432 24 321216 6 8 3428. Find the value of each of the integer expressions below: 24 9 ( 6) 22 4(330 10) ( 17) 2 8 532 78(6)( 3)( 2)225 5 56 8 707( 45) ( 60)(13) ( 6) 4 10 2 14 729. Apply the Distributive Property to each expression to create an equivalent expression:4(𝑟 6)3(6𝑎 2𝑎 1)(𝑚 𝑛) 310𝑥 4𝑥 8(𝑥 2)5

Name:30.31.32.6

Name:33.34.35.36.7

Name:37.38.39. Solve each multi-step equation:4𝑥 3 1912(𝑚 1) 248𝑏 2𝑏 6 208

Name:40a. For each order, a T-shirt company charges a 50 setup fee and 4 per T-shirt. Write an equationthat represents the situation using C for total cost and t for the number of t-shirts sold.40b. Complete the table of values to show thetotal cost for up to 10 t-shirts sold.C (total cost) 54.00 78.00 90.0040c. Create a graph of the data. Be sure tolabel both your axes and choose your scalecorrectly.t (number of t-shirts sold)1234567891040d. Identify the independent and dependent variables in this situation. Explain why each variableis either independent or dependent.40e. How much would it cost to order 35 t-shirts? How many t-shirts could you order with a budgetof 140? Use your equation to answer each question and show your work.9

Name:41.42.43.44.10

Name:45.46. Graph and label each ordered pair on the coordinate plane:A (0, 0)B (3, 8)C (-2, 7)D (-5, -5)E (6, -4)F (3, 0)G (0, -5)H (-1.5, -9)What is the distance between Point Band Point F?What are the coordinates of thereflection of Point C across the y-axis?Which point is located at the origin?Which Point lies on the x-axis?Which Point lies on the y-axis?11

Name:47.48.49.12

Name:50.51.Write a ratio comparing the amount of sugar and the amount of water in the fruit punch recipe.13

Name:52. Stephanie walked 6 miles in 2 hours. The graph represents her pace.What is her unit rate?What is the constant of proportionality?Write a linear equation to represent the situation and the graph.Use y for number of miles walked and x for the number of hours.53.54. A painter is paid a standard hourly rate and makes 41.25 for five hours of painting. How much isthe painter paid for eight hours of painting?14

Name:55. The following table shows the money a different painter earned. What is this painter’s hourly rate(constant of proportionality)? What does this mean in this situation?Hours345Money Earned 29.25 39.00 48.7556.Explain what the constant of proportionality means in this situation.57.15

Name:58.59.16

Name:60.61.62.63.17

Name:64. Complete the /51100%200%65%13/201/987.5%65. What is 25% of 80?66. What is 72% of 18?67. 60% of 320 is what?68. What percent is 20 out of 25?69.70.71.72.18

Name:73.74.75.19

Name:76.77.78.20

Name:79.80.81. Evaluate each expression:23 4142 3( 3.4)2 259017121

Name:82. Simplify each expression using PEMDAS:(4 1)2 5 3 710 4(24 12) 7 753 (25 3) 8283. Complete each blank to show equivalent units of measurement:a. 1 foot inchesb. 1 yard feet inchesc.d. 1 centimeter millimeters (mm)1 meter cm84.22

Name:85.86.87.88.23

Name:89.90.𝐴 𝜋 𝑟291.92.93.24

Name:94.95.96.Complete the table:AfternoonEveningMeanMedianModeRange25

Name:97.98.99.26

Name:Mathematics Vocabulary ReviewFor each mathematics vocabulary term: Read the word, read the meaning in math class, andread the related words. Then, give a description or example of the word (look through thispacket for ideas!). Draw a visual representation of the word if you know one. Finally, add anymore synonyms for the word that you know.WordMeaning(in d Words(synonyms)To find the value of anexpression.SolveSimplifyAnswerAnalyzeExamining parts tounderstand how theywork together.Break downLook for patternsMake predictionsDraw conclusionsSimplifyTo break down into asimpler form usingproperties ofoperations.ReduceBreak downSolveEvaluateReduceSolutionEquivalentThe process ofconverting a fraction ormixed number to anequivalent fraction ormixed number, in whichthe greatest commonfactor of the numeratorand the denominator ofthe fraction is one.The answer to aproblem or the valuethat makes an equationtrue.SimplifySimplest formQuantities, numbers orexpressions that havethe same value.EqualSameAnswer27

Name:ClassifyTo sort into categoriesor to arrange intogroups by attributes Compare/contrastApproximateA value that is close toan exact value. Toestimate or come closeto an exact value.EstimateRoundA step by step methodfor solving a problem.RuleProcessMethodThe math processes ofaddition, subtraction,multiplication, divisionand manipulatingnumbers with otheroperators (exponents,grouping symbols,roots).An unknown or varyingquantity. A symbol(usually a letter) thatrepresents a EquationUnknownVarying amountMissing valueA mathematical phrasethat can containnumbers, variables (likex or y) and operators(like add, subtract,multiply, and divide).Does not containan equal ( ) sign.Number phraseNumber sentenceA statement ofequivalence of twomathematicalexpressions. Amathematicalstatement that showsthat two quantities orexpressions have anequal value.Contains only ONEequal ( ) sign.EqualEquivalentEqual values28

Name:TermsConstantRatioRateSlopePartsPiecesParts of a mathematicalexpression, separatedby addition orsubtraction operators.A number having afixed value that doesnot change or vary.Contains NOvariables.NumberComparisonFractionA comparison of twoquantities using acolon, written as afraction, or with theword “to”.A ratio that comparesquantities measured indifferent units.Rate of changeConstant rateUnit rateSpeedConstant ofproportionalitySlope (on a graph)The ratio of change inthe vertical axis (y‐axis)to change in thehorizontal axis (x‐axis);the steepness of alinear graph.Rate of changeConstant ofproportionalityConstant rateSteepness of agraphUnitA quantity of one.A label used to identifya mathematicalquantity or amount.Answers shouldalways be labeledwith units, ifpossible.OneLabelCompositeA number that has 2 ormore whole numberfactors – factors otherthan itself and 1.*Composite hastwo differentmeanings in math!*ComplexCompoundA figure that is made bycomposing smallershapes or figures.29

Name:PrimeA number that has onlytwo whole numberfactors – 1 and itself.RationalAny number that can bewritten as a fraction orratio.RatioFractionRadicalThe symbol , whichis used to represent thesquare root or nth rootof a number.RootSquare rootBaseA number in a powerthat is multiplied byitself – how many timesis indicated by theexponent.Prime numbers areonly evenlydivisible by 1 andthe number itself.*Base has MANYdifferent meaningsin mathematics!*BottomThe “big” numberin a powerThe “bottom” of a 2-Dshape.The dimension on a 2-Dshape that isperpendicular to theheight.ExponentThe bottom face (flatsurface) of a 3-D shape.A number that indicateshow many times a basenumber should bemultiplied by itself.PowerThe number of timesthe base number is tobe multiplied by itselfwhen working withexponents.TableA chart used toorganized informationor data.The “little”number in apowerSquaredCubedTwo-way tableInput-output tableChart30

Name:ContinuousData that can take anyof an infinite number ofvalues between wholenumbers. A graph inwhich there are no gapsor holes (e.g., a linegraph).ConnectedLine graphDiscreteDistinct values that arenot connected byintermediate valuesand are a finite set ofvalues. A discretegraph is a series ofpoints that are notconnected by acontinuous line.DisconnectedPointsNo in-betweenvaluesOriginThe point ofintersection of thex‐ and y‐axes in acoordinate plane,where the x‐coordinateand y‐coordinate areboth zero (0, 0).(0, 0)The “center” ofthe coordinateplaneNetA two‐dimensionaldiagram that can befolded or made into athree‐dimensionalfigure; typically used tofind the surface area ofa 3-D figure.UnfoldedFlatSurface areaA transformation inwhich every point in afigure is moved in thesame direction and bythe same distance.SlideShiftTranslation31

Name:ReflectionA flip of a flat figureacross a line ofsymmetry that createsa mirror image.Reflections aresometimes across the xaxis or y-axis on thecoordinate plane.FlipMirror imageRotationA transformation of afigure by turning itabout a point or axis.The amount of rotationis usually expressed inthe number of degrees(e.g., a 90 rotation).The direction of therotation is usuallyexpressed as clockwiseor counterclockwise.TurnMeanThe average.A measure of center ina set of numerical data,computed by addingthe values in a list andthen dividing by thenumber of values in thelist.AverageMedianThe middle value of aset of data that arearranged in order ofsize.MiddleIntervalDistance between twopoints, amount of timebetween two events, ora range of numbers ona graph (ex: histogram).GroupRangeBucket32

8th Grade Summer Math Packet Dear Future 8th Grader, This summer math packet is designed to help you keep your math skills strong before returning to 8th grade in the fall. We want you to feel confident on the following skills and problems when you begin 8th grade. If you get to a problem you are confused on, here are some ideas to help:

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