STUDENT/PARENT INFORMATION LETTER SUMMER MATHEMATICS PREPARATION PACKETS Summer 2014
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1 MONROE TOWNSHIP PUBLIC SCHOOLS Mnre Twnship Middle Schl 1629 Perrineville Rad Mnre Twnship, NJ Telephne (732) Fax (732) Chari R. Chanley, Ed.S. James F. Higgins, Jr. Sctt Sidler Principal Assistant Principal Assistant Principal STUDENT/PARENT INFORMATION LETTER SUMMER MATHEMATICS PREPARATION PACKETS Summer 2014 Dear Students and Parents/Guardians, Welcme t summer preparatin with Mnre Twnship Middle Schl Mathematics! In preparatin fr a successful new schl year, each student wh was enrlled in a grades 5 7 math curse this year is required t cmplete a summer review packet. These packets are available n the MTMS website. Crrelated t the Cmmn Cre State Standards (CCSS), the summer packets were designed specifically with the prerequisite cncepts and prcedures in mind that are necessary fr success in each math class. Cmpleting the prblems included will help the student find a strnger start t ur middle schl mathematics curses: grade 6 Mathematics, grade 7 Mathematics, grade 8 Mathematics, Middle Schl Algebra I and Middle Schl Gemetry. The students wrk n these review packets will als ffer their new teachers valuable insight that will impact instructin at the beginning f the schl year. We recmmend that when wrking thrugh the review packet students shuld fllw these helpful hints t make their wrk cunt: Shw ALL steps used t arrive at yur final answer. Use the many resurces available n the Internet as references when yu get stuck. Dn t rush! Wrk steadily thrugh the summer. Well-meaning students may want t finish the entire packet at the beginning f the summer r even befre the schl year ends. Other students may try t put ff the packet entirely until a few days befre schl. Either apprach (t sn r t late) defeats ne f the main bjectives f this packet: maintaining students mathematical skills thrughut the summer. During the first week f schl, students will turn in their cmpleted preparatin packets, have the pprtunity t ask fllw-up questins and then take a diagnstic assessment. We wish yu and yur family a very happy, healthy and mathematical summer! Thank yu, Yur Grades 6 8 Math Teachers Susan Gask Supervisr f Mathematics Mnre Twnship Schls Chari Chanley Principal Mnre Twnship Middle Schl
2 Mnre Twnship Middle Schl Mnre Twnship, New Jersey Preparing fr Middle Schl 8 th Grade *PREPARATION PACKET* (MODIFIED FOR RESOURCE Classes) Summer 2014 Welcme t 8 th Grade Mathematics! Our 8 th Grade Mathematics Curse is a cmprehensive survey curse that will prvide yu with the fundamental tls f mathematical understanding that will supprt yu in all yur high schl curses. Since yu will be taking 8 th Grade Mathematics after successful cmpletin f 7 th Grade Mathematics, the Mnre Twnship Middle Schl 8 th GRADE PREPARATION PACKET cntains review material f the 7 th grade cncepts, skills, and prcedures that shuld be mastered BEFORE entering 8 th grade in the fall. Essentially, this packet prvides a review f the majr 7 th grade tpics as well as a preview f 8 th grade tpics. The sectins are based n the Cmmn Cre State Standards (CCSS). See ur twnship website fr great web- based resurces if yu need a refresher n any f the prblems encuntered here in this packet. This cllectin f prblems will identify thse cncepts that yu have mastered as well as thse yu will need t practice and review. Yu are expected t seek extra help immediately n thse cncepts with which yu have nt demnstrated prficiency. Be resurceful use the nline resurces! Here are sme websites yu might find particularly useful: ***SOLVE THESE PROBLEMS WITHOUT THE USE OF A CALCULATOR AND SHOW ALL WORK*** Yu will be respnsible fr handing in the cmpleted packet with all wrk shwn ON THE FIRST DAY OF SCHOOL. The prblems here are very representative f the types f items yu will need t have mastered BEFORE 8 th Grade Math s we strngly encurage that yu include this packet in yur summer festivities! Gd luck and enjy! J 8 th GRADE PREPARATION PACKET SCORE: f 4 Page 1
3 REVIEW: COMMON CORE STATE STANDARDS (CCSS): Grade 7 Ratis and Prprtinal Relatinships 7.RP Analyze prprtinal relatinships and use them t slve real- wrld & math prblems The Number System 7.NS Apply and extend previus understandings f peratins with fractins t add, subtract, multiply, and divide ratinal numbers Expressins & Equatins 7.EE Gemetry 7.G Use prperties f peratins t generate equivalent expressins Slve real- life and mathematical prblems using numerical and algebraic expressins and equatins Draw, cnstruct, and describe gemetrical figures and describe the relatinships between them Slve real- life and mathematical prblems invlving angle measure, area, surface area, and vlume Statistics and Prbability 7.SP Use randm sampling t draw inferences abut a ppulatin Draw infrmal cmparative inferences abut tw ppulatins Investigate chance prcesses and develp, use, and evaluate prbability mdels PREVIEW: COMMON CORE STATE STANDARDS (CCSS): Grade 8 The Number System 8.NS Knw that there are numbers that are nt ratinal & apprximate them Expressins & Equatins 8.EE Functins 8.F Gemetry 8.G Wrk with radicals and integer expnents Understand the cnnectins between prprtinal relatinships, lines, and linear equatins Analyze and slve linear equatins and pairs f simultaneus linear equatins Define, evaluate, and cmpare functins Use functins t mdel relatinships between quantities Understand cngruence & similarity using physical mdels, transparencies, r gemetry sftware Understand and apply the Pythagrean Therem Slve real- wrld and mathematical prblems invlving vlume f cylinders, cnes, and spheres Statistics and Prbability 8.SP Investigate patterns f assciatin in bivariate data Page 2
4 Ratis and Prprtinal Relatinships 7.RP (*Use fr #1) In a survey, Eric, the team manager, asked the 120 sccer players in the league which drink they preferred during and after the game. Drink During Game % During Game After Game Gatrade Ocean Spray Evian Water % After Game 1. Ricard, the sccer league directr, made the fllwing statements based n Eric s survey. (Hint: Calculate the percentage f students wh preferred each drink befre the game and after the game.) Which statements are accurate? Explain hw yu made each decisin. a. During the game, players prefer Ocean Spray t Evian Water by a rati f 4 t 1 Circle: ACCURATE r INACCURATE because: b. 25% f the players prefer Evian Water after the game. Circle: ACCURATE r INACCURATE because: c. Mre than half f the players prefer Gatrade during the game. Circle: ACCURATE r INACCURATE because: Page 3
5 Directins: Fr #2 & #3, use the map belw. Take ntice f the scale that is prvided. 2. The cartgrapher wuld like t add Dallas, Texas t the map. If it is 1546 miles between New Yrk and Dallas, Texas, then hw many centimeters shuld they be apart? (Hint: Set up a prprtin.) 3. Hw many miles apart is it frm Ls Angeles t New Yrk? 4. Which rectangles belw are similar? Hw d yu knw? Shw yur wrk! (Hint: Set up a prprtin r find the scale factrs.) Page 4
6 5. Belw is a triangle and its image. a. Write an algebraic rule t shw hw t transfrm a pint (x, y) frm the triangle pre-image t its image. ( x, y ) b. What is the scale factr frm the triangle t its image? (Hint: Set up a prprtin.) c. Calculate the area f each triangle (riginal and image). Original Area: Image Area: 6. At a math bake sale, 3 5 f the baked gds are Pi pies. The rest f the baked gds are baskets f muffins. There are 24 baskets f muffins. a. Find the fractin f baked gds that are muffins. b. Find the TOTAL number f baked gds. c. One third f the pies are blueberry. Hw many pies are NOT blueberry? Page 5
7 7. On a trip t New Yrk City, yu eat at a lcal restaurant with yur family. The fd bill fr yur meal was $75. The sales tax is 4.5% and yu leave a 15% tip. Calculate the fllwing: a. Find the amunt f sales tax (befre the tip is applied). b. Find the amunt f tip (after the tax is added). c. Calculate yur TOTAL bill (adding tax and tip). 8. A sign at the fair advertises ticket prices fr the carnival games. Find the unit price fr each ticket clr. Red Tickets: Blue Tickets: Yellw Tickets: 9. An imprtant categry f percentage prblems is markup & markdwn prblems. Slve the fllwing: a. A sprting gds stre pays its whlesaler $50 fr a certain baseball glve and then sells the glve t custmers at a retail value f $90. What is the markup rate? b. A sweater riginally priced at $44 is marked dwn 25%. What is the sale price? c. A DVD player that regularly sells fr $325 is marked dwn t $ What is the discunt rate? Page 6
8 10. If 4 f a gas tank can be filled in 2 minutes, then hw many minutes will it take t fill the 9 whle gas tank? (Hint: Set up a prprtin.) The Number System 7.NS 11. Fill in the missing fractin/decimal/percent cnversins belw. FRACTION DECIMAL PERCENT % % Describe a real life situatin that invlves integers. Fr example, a hydrgen atm has 0 charge because its tw parts have ppsite charges: +1 and Use the distributive prperty t write an equivalent variable expressin. a. 3( x + 4) b. 7(2x 5) 14. Evaluate each pwer. 3 a. 2 b. 2 4 c Page 7
9 15. Find the sum r difference. (Hint: Find the cmmn denminatrs first.) a b c Find the qutient r prduct. 21 a. 38 g b. 1 4 (20) 5 c d Simplify and shw all steps f wrk: (5 + 3) Simplify and shw all steps f wrk: 2 3 x Simplify and shw all steps f wrk: 2 (3 + 10) Simplify and shw all steps f wrk: 10 [50 ( 2 25) + 7] 2 2 Page 8
10 Expressins & Equatins 7.EE 21. Simplify 2a+ 0.5a 22. The perimeter f a rectangle is 54 cm. Its lengths are 6 cm. What is its width? (Hint: Fill in the knwn measurements first.) P = Evaluate the expressin m nwhen denminatrs, then slve.) 3 m = and 4 5 n =. (Hint: First find the cmmn Slve the prprtin: = 42 c 25. Is x = 0 is a slutin f 7x 4> 3x+ 1? Shw yur wrk t supprt yur answer. (Hint: Plug 0 in fr x and slve.) 26. Slve: 2x + 17 = Which f the fllwing is the crrect equatin fr: The qutient f a number and ten is thirteen. n a. n 10 = 13 c. = b. 10 n = 13 d. 13 n = Page 9
11 Gemetry 7.G 28. Define the fllwing terms and draw an example f each: a. Supplementary angles: b. Cmplementary angles: c. Vertical angles: d. Adjacent angles: 29. Classify the 3-dimmensinal figure belw. Page 10
12 30. Belw is a grid with fur quadrants. Plt the fllwing pints, and cnnect them with line segments. Classify the type f triangle yu see. Pint A (-2, -4) Pint B (3, 4) Pint C (3, -4) This shape is a triangle. 31. On the same grid paper abve, transfrm yur figure ABC using the rule (2x, 2y). Write the new c crdinates belw. Pint A Pint B Pint C 32. The frmula fr finding the vlume f a rectangular prism is V = l w h. Belw is made frm centimeter cubes. What is the VOLUME f the prism? (Hint: Cunt the blcks t find the length, width, and height befre using the frmula.) 33. The frmula fr finding the surface area f a rectangular prism is: SA = (2 l w ) + (2 l h) + (2 w h). What is the SURFACE AREA f a rectangular prism with the dimensins f 3 inches in height, 4 inches in width, and 5 inches in length? Page 11
13 34. In the diagram belw, find the measure f the exterir angle. 35. The scale drawing f a sccer field is 1 inch = 10 yards. The drawing f a sccer field is 12 inches by 7.5 inches. Find the dimensins f the actual sccer field. Remember that 1 inch equals 10 yards. 7.5 in 12 in 36. Find the circumference f a circle with a radius f 2 cm. c =Π d 37. Find the area f a circle with a radius f 2. A = 2 Π r 38. Describe a real-wrld situatin that wuld invlve finding the vlume and/r surface area f a 3-dimensinal bject. Page 12
14 Statistics and Prbability 7.SP Define the fllwing terms: 39. Prbability: 40. Randm sample: 41. Mean: 42. Median: 43. Mde: 44. Each letter f the wrd MATHEMATICS is written n a separate slip f paper and placed in a hat. A letter is chsen at randm frm the hat. What is the prbability f chsing M n yur first try? 45. Find the mean, median, and mde f the fllwing set f numbers: 3, 5, 2, 5, 8, 10, 1, 5 Page 13
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