Sixth Grade Summer Math Packet

Students EnteringSixth GradeSummer Math PacketName--------------

Dear Parents,The attached packet provides a range of activities that reviewand e:xp-a-nd on the math concepts yourchi·ld has learned inschool this past year. It is designed to be worked on for 15 to30 minutes a day throughout the summer, rather thancompleted in just a few days at the beginning or end ofsummer. The goal is to keep skills sharp to be ready to moveforward into the n.e?d school year. 'lYe .have provi d answers .for grades 3 6 and ask you to please review the work with yourchild as it is completed. Students will be asked to hand in theircompleted work the first week of school.Have a great summerlThe SeacrestStaff

Table of Contents41)Adding and Subtracting Decimals41)Multiplying with Decimals41)Dividing with Decimals41)Interpreting Data41)Geometric Ideas41)Measuring and Drawing Angles41)Adding and Subtracting Fractions41)Adding Mixed Numbers41)Subtracting Mixed Numbers41)Multiplying Fractions41)Multiplying Mixed Numbers41)Problem Solving Strategies41)Measurement- Customary & MetricePerimeter41)Area41)Ratio and Proportion41)Fractions, Decimals, and Percents41)Probability

2Adding and Subtracting DecimalsFind 1.7 2.45.Find 36.57 - 4.6.Line up the decimal points.Line up the decimal points.tt11.7 2.451.70 2. 4 5- Write zeros toshow place value.4.15t5 1536.573 . 7- 4. 6- 4. 6 031 9 7- Write zeros toshow place value.DtPlace decimal pointin answer.Place decimal pointin answer.Find each sum or difference.t1.2.65 13.302.8 .976.5. 669."15.4III 1 000.228 11. 1.34 4.113. 448t1 4.1 0- 3.05 1.75 80.3 3. 7.6.8 237.2912. 133.01 - 5.6" 8.0.5- 0.23 14. 12.3 0.61 100 co. I .a Vi ·1I9- 0.610. "3 -2.54 II4.74436.2c15. On the 3-days of their vacation, the Davis familytravel d 417 mi, 45.3 mi, a'nd 366.9 mi. How far'did they travel. all together?0CI)'6\J«c1\1EII)e0u.t::0016. Etta bought a calculat.or for 15. Glenn .found th'E} .s me model for 9.79. How much more did Etta.pay than Glenn did?(J')0t.))!

,:NameFind 4.3 x 2.7.Co.unt the number of decimal places in both factors.The total is the number of decimal places in the product.Multiply as you wouldwith whole numbers.24.32.711 . 614.3xx 2.7301- - - 1 decimal placE?1 decimal place2 decimal places8601 1 61Find e.ach product.141.2.8.81121120X5.9. 23 X 0.47x.9X3.30.1 26.2.1 5x. 8.3 ---3.1.610. 0.9 X 57 0.4x 3.24.0 .51x 4.28 .0 .05x 0.31 .35X1311 . 168 X 2.25 1co.loll')8 "("\Qvf\11VoV /'-.V.I 1 -if)Ii) c·0U):a"0 CroEU)15. A roll of paper towels contained 250 sheets.Each sheet was 8.75 inches long . How long was the roll? 0LLt:lg-(f)@1Tania bought 3 new sweaters, Each sold for -19.99.How much did she spend?.UI

-NameReview6,Dividing with Decimals1-"'\I,} )Find 36.8-7-16.t2.31 6)3 6 . 8-324 8Place the decimal point.2.21 6)3·6 . 8- Think: 20)40Multiply 2 x 16.Subtract. Bring down 8.Multiply 3 x 16.Subtract.- Try 2 in the quotient.oFind each quotient.2.3. 9)1 4 1 . 32. 6)1 3 1 .41. 6)1 3.84. 5)388 . 5- @JTID-DO0))))5. 7)6.6 9 .-29. 269.12-7-7.41)274.76.2 8)2 6 3 . 210. 311.568 -7-8. 7)34.2.34 co5 'Ci)11.2,229.62 -;- 46 '12. 1,449.09-7-81 : f.!I : !c:0II/):a1:J ICien'1;3. A photographer bought 36 rollsWhat was the price of one roll?of film for 136.44.'14. Four students each ran' 100 m in a AOO-m relay race.The' t am's total time was 49.44 sec. Find the averagetime of each runner.'E1/),i iI :t::00en@,,

·1!·NameThe bar 'graph shows the lengthsin miles of the Great Lakes. Lengthsof 'bars represent lengths of lakes.Which 'is the shortest Great Lake?The shortest lake is Lake Ontario.lengths of the Great lakes500r.·· .·.·.·.······.·.·. .·.·.··.·· . . ··.-., 4001-·.·.·.·.·. ·.···· .·:······.····. ·· .· ·. ·.·.··.,g.c300g 200.J100Q)oSuperior MichiganErieLakeHuronOntarioUse the graphs to answer each question.1 How fllany archers scored 4 buli's eyes?Archery Resultsaxxx(Iffi ::. -:::--[· I.:··;r I ·:I l :::f:]i : ,: :l ! : ;: : I :: F jb i. IilJan Feb Mar Apr May Jun Jul Aug.MonthIIxxxxxxxxxI»II30 1 ·24 5 6Number of Bull's-eyes Scored2. What was the most common numberof bull's-eyes scored?Number of Houses Soldxxxx.13. In which month were the most housessold?4. In which. month were about the sam.enumber soid as were said in August?r'iIiIiCD 5a Which grades raised about the same'amount for the school book drive?. I;I cSchool Book Fund Driveo500.·.· .··.· · ·--·.· . . ·. .·.· ·.·· ·.·. ,. 2'0 400 r--.·. ·.· ··.- . · . · E{Ii(/)-- 300. 6aThe school's goal was to raise 1 ,500.About how much did they raise in all?.'0 200t::'o.0C/)o@100o 0u.1st2nd3rd' 4thGrade5th

,Name---------------------- ----------------------------------Geometric Ideas A line is a straight path of pointsthat goes on forever in twodirections. Examples: AS"GK. A A ray is a part of a line withone endpoint, extending foreverin only one direction.Examples: FD, FB.B A· line seg ent is part of a linewith two endpoints.Examples: CF, MQ. A midpoint is the point halfwaybetween the endpoints of a linesegment. Example: Point L is halfwaybetween points J and M on JM. Congruent line segments are ·Iine segments that have the same length.Example: OR is congruent to.ST. Parallelli s are in the sa(m plane but do not intersect.Example: AS is parallel to 8'T.mw1&[rowis PTmet1no"yas!Use the diagram. at the right. Name t.he following 1. three line segments2. two parallel lines 3. two lines that intersect DTwd.5c:o1ao.4. two congruent line segments·:J Co. 5. two lines perpendicular to BR@.,-.:' .6. two midpoints of line segmentsI

\ "j'How to measure nan angle:angle:Step 1 Place the protractor's center on the angle'svertex.Draw an angle of 52 .Step 1 Draw a ray.· Jis.tep 2 Place the 0 mark on one side of theangle.Step 2 Place the protractor's center on theendpoint. Line up the ray with the 0 mark.Step 3 Using the scale with the 0 mark, place a'point at 52 .Step 4 Draw the other ray.NLMN 60 Step 3 Use the scale beginning with ttie 0 markto read the measurement where the other side ofthe angle crosses the protractor. ---- ------------------ CILABe 52 Classify each 'angl'e as acute, right, obtuse, or straight. Then measure the angle.1./L2.Draw an angle with each measure.coo.ECo o::l"0Wc:oe!ro Dn.

Name Review-:'" I.': I10.I 'Adding and SubtractingF:ra.ctions' d2 1FIn3 6'al@ 9 12 15I(a) 12 18 24 301F·In d 4"-s'1Multiples of 3. 4. 8,1216@ Multiples of 4Multiples of 65.10' 15@ 25 Multiples of 5The least common denominator is 6.The least common denominator is 20. Write equivalent fractions.11 '6 '6Add.1514Write equivalent fractions.4" 20Subtract.'5 2551620Find each sum or difference.1I1.')114 3 ---2.k12 - - - -3.143' 9 ---j'I: II II4.37 27 - -I II I I1155. 12 - 12.33 --6.1112':2 3' - -9. '5 10' - - 10. :2 '5 - -12. Meg practiced the- piano' .f.or 1 hr. She did ho eworkfor' hr. How much longer dId she do 'homework thanshe practiced the piano?JII118213-4 --

To add mixed numbers, you can add the fractional parts to the wholenumber parts, and then simplify.FIn d 24"2 3 1,4The fractions have acommon denominator.Add the fractions. Thenadd the whole numbers.2 Find 3% 4t·Write equivalent fractionswith the LCD.323- 3&.9 4 1 94 3 4419Find 4Add the whole numbers;then add the fraction.4 3 57 5Add the Iwhole numbers.Add the fractions.Simplify if possible.5 4 3 .3&.9111 "797L9Find each sum. Simplify your answer.2. 4i 1i4. 8 1 152c.,;I.a.14V3 118--L -11I6. 7 Si .-----'------ 7. In 2001, the men's indoor pole vault record was 20i ft.The women's record for the indoor pole vault was 15 1b2 ft.What is the combined height of the two records?1.00EC0:g()::J-0WC0 1lQ)a. 8. Writing in Math How high is a stack of library books if one bookis .it in. high, the second book is 1 in. high, and the third is2 in. high? Explain how you soived this problem.

: I' i Subtracti.ng Mixed NumbersSubtract 3213 - 26,Write equivalent fractions.2. Subtract the fractions.24Subtract the wholenumbers.Simplify.2433 3(3433 3611-26 2633 36i12ij 2611-2(3 2(33316 6The LCD of 3 and 6 is 6.112Find each difference. Simplify.3.2.1.4.-i- 2-'8-J)5.3710- 19529. 231- 14 6.7Z8- 2 3 47.8.- 21- 1186410.352.6244 - 45 (0 'ii3111. 232- 13 3513. 38 - 2(3 .4212. 49 -33 15·14. 53'·- 28 c0en'0"0«ctilECI)' 0u.150enI 1II()15. Greg found two rocks for his collection. One weighed 41lbarid the other weighed 2 lb. Find the· difference in weights.I

.32Fmd Lf x J"OneWayDraw a picture. Simplify ifpossible.Another WaySimplifyMultiply the numeratorsand denominators.Simplify if possible.Find the GCF of anynumerator and anydenominator. x. 4 73 x 264 x 7- - 1428The GCF of 2 and 4 is 2.Divide 2 and 4 by the GCF.13Z·3.% x 7" 142'-----y--"346 of the 28 squares haveoverlapping shading.326So, "4x7" 28'6Simplify 2 8 to1 'Write an equation for each picture . 1'.Find each product. Simplify if possible.3 . '§'x1.83.! ;6. x , !7. Number Sense Can you simplify before multiplying 14x ? Explain.

.NameI"'.,.-------- -Multiplying Mixed Numbers!How to find the product of two mixed numbers:Find 3 x 4 .Step 1Step 3Step 2Estimate by rounding.Look for commonfactors and simplify.Multiply. Write the productas a mixed number.3 x 4.1321 x 1 4520116"2 is close to 20, so theThen write each mixednumber as an improperfraction.answer.is reasonable.3 x 4.1'/1x 1)131132I 2Find each product. Simplify if possible.3. 6 x 3t5. 4t x 16 2. 2t x 2i 4. 1 i x 3t 6. 1 t x 2 7 Number Sense Is 2 x 17% greater than or less than 36? Explain.:.1

Name ,A computer store has 25 printers and computers.There are 7 more printers than computers.How many of e ch are there?PrintersComputers2014165119Guess 1Guess 2Guess 3Check2.0 - 5 114-11 316 --'- 9 7/Solution: There are 16 printers and 9 computers.Pr:oblem Solving Strategies Act It Out Draw a Picture Look For a Pattern Try, Check, and ReviseMake an Organized List Make a Table Solve a Simpler Problem, Work Backward&)Use any strategy to solve.1. At the veterinarian's office, Terri learned that her dog weighed4 times as much as her cat. Together the pets weighed 40 Ibs.How much did the dog weigh?2s Yasmin arrived home .from play practice at 4:25 P.M. The walk, home took 15 m.inutes. Practice began 20 min"t.Jtes after thefinal bell and la ted for a h,alf hour. When 'did school end?3sVaness ,pieg ; , Rose, an Randystood in line for Iw.nch. Rose was justbei1.ind Va:nessa. Diego, was not" nextto Rose or R npy.· Wri,e ,the lin'e order.'(04,. tudents playe9' p. 'g,e .P .! nd vOHky a:1I for 45 ,minut s.Th.ey played doc;:fge ball for 11 more minutes than they playedvOlleYball.J:-1ow long did they play dodge ball?'.' (j)' ,t:.g'0., t:t13.Een ou.Mr. Jones has A: hirt , 2 ties, and3 pair of p :nt. .'I -iqw,:.rnahy,'day '·in,wear'' .a'different. row can:''.'.'. outfit?ahe'.':g:,S@.'. :.'--,'",{i

-------R 10. 1Customary MeasurementUnits of CapacityUnits of length,!.)!i';itl![ft if1 yd 3 ftpint (pt)1 pt 2 c1 yd 36 in.quart (qt)1 qt 2 ptgallon (gal)1 gal 4 qtyard (yd)II;HIii!ii1 c 8 fluid ounces (oz)1 ftmile (mi)!cup (c)foot (ft) 12 in.1.mi 5,280 ft1 mi How to change from one unit of measurement to another:To change from larger units to smallerunits in the customary system, you haveto multiply.To change from smaller units to largerones, you have to divide.120 yd1 c 80zft Ii:1 yd 3 ft[)120 X 3 ft 360 ftIIIj1,760 yd2560z c256 -;- 8 32120 yd 360 ftComplete.1. 36.in.3. Sib I'IIt,!5. 1.5 miroz9. 640z l11. 4 gal I:[; :f 1f'. v.",I,. rIL0.0 ID 15. 4.5 qt 2. 4 qt c4. 39 ft yd6. 3.5 galIbptOZ10. 3ydqt 8. 16 pt Ib!t!Ift 7. 2T 'II,ft qtin.12. 55yd ft14. 20 pt gal 00.sc16. 205 yd ftc0 0:::J"0W17. Reasoning A vendor at a festival sells soup for 1.25 per cup or 3.75 per quart. Which is the better buy?C0 «JQla.@(.I