SECOND EDITION STUDENT BOOK GRADE

SECOND EDITION STUDENT BOOK GRADE 5

Bridges in Mthemtics Second Edition Grde 5 Student Book Volumes 1 & 2 The Bridges in Mthemtics Grde 5 pckge consists of: Bridges in Mthemtics Grde 5 Techers Guide Units 1 8 Bridges in Mthemtics Grde 5 Assessment Guide Bridges in Mthemtics Grde 5 Techer Msters Bridges in Mthemtics Grde 5 Student Book Volumes 1 & 2 Bridges in Mthemtics Grde 5 Home Connections Volumes 1 & 2 Bridges in Mthemtics Grde 5 Techer Msters Answer Key Bridges in Mthemtics Grde 5 Student Book Answer Key Bridges in Mthemtics Grde 5 Home Connections Answer Key Bridges in Mthemtics Grde 5 Components & Mnipultives Bridges Eductor Site Work Plce Gmes & Activities Digitl resources noted in itlics. The Mth Lerning Center, PO Box 12929, Slem, Oregon 97309. Tel 1 (800) 575-8130 www.mthlerningcenter.org 2017 by The Mth Lerning Center All rights reserved. Bridges nd Number Corner re registered trdemrks of The Mth Lerning Center. Prepred for publiction using Mc OS X nd Adobe Cretive Suite. Printed in the United Sttes of Americ. To reorder this book, refer to number 2B5SB5 (pckge of 5). QBB5901 (1 & 2) Updted 2016-06-27. Number Corner Grde 5 Techers Guide Volumes 1 3 Number Corner Grde 5 Techer Msters Number Corner Grde 5 Student Book Number Corner Grde 5 Techer Msters Answer Key Number Corner Grde 5 Student Book Answer Key Number Corner Grde 5 Components & Mnipultives Word Resource Crds The Mth Lerning Center grnts permission to reproduce nd shre print copies or to shre electronic copies of the mterils in this publiction for use in the clssroom for which the publiction ws purchsed. Licensed users my shre print or electronic copies of the mterils with other district stff nd techers nd with students nd their fmilies in support of implementtion in the clssroom for which the mterils were purchsed. All other uses nd distribution of the mterils re expressly prohibited, nd you my not mke print or electronic copies of the mterils vilble for public ccess. For usge questions, plese contct The Mth Lerning Center. Bridges in Mthemtics is stndrds-bsed K 5 curriculum tht provides unique blend of concept development nd skills prctice in the context of problem solving. It incorportes Number Corner, collection of dily skill-building ctivities for students. The Mth Lerning Center is nonprofit orgniztion serving the eduction community. Our mission is to inspire nd enble individuls to discover nd develop their mthemticl confidence nd bility. We offer innovtive nd stndrds-bsed professionl development, curriculum, mterils, nd resources to support lerning nd teching. To find out more, visit us t www.mthlerningcenter.org. ISBN 978-1-60262-535-8 Bridges in Mthemtics Grde 5 Student Book

Bridges Grde 5 Student Book Volumes 1 & 2 Unit 1 Expressions, Equtions & Volume Work Plce Instructions 1A The Product Gme... 1 You Choose... 2 Product Gme Problems... 3 More Product Gme Problems... 4 Fcts & Boxes... 5 Fct Connections... 6 Are They Equivlent?... 7 Smller Boxes... 8 Clculting Crdbord... 9 Zck s Strtegies...10 How Mny Boxes?... 11 Work Plce Instructions 1B The Multiple Gme...12 Milo s Multiples...13 Thinking About The Multiple Gme...14 Pricing Brd s Bseblls...15 Lily s Lcrosse Tem...17 Sm s Sewing Supplies...18 Chrlie s Chocoltes...19 Work Plce Instructions 1C Bet the Clcultor...20 Expressions & Equtions...21 Multipliction & Division...22 Mthemticl Thinking...23 Division Story Problems...24 Wht Should You Do with the Reminder?...26 Rce Cr Problems...27 Quotients Win, Gme 2...28 Work Plce Instructions 1D Quotients Win...29 Multipliction & Division Problems...30 Using Bsic Fcts to Solve Lrger Problems...31 Unit 2 Adding & Subtrcting Frctions Money & Frctions...32 Frctions & Mixed Numbers...33 Frctions on Clock Fce...34 Clock Fce Frctions...35 Clock Frctions Problem String...36 Work Plce Instructions 2A Clock Frctions...37 Adding Frctions...38 Equivlent Frctions on Clock...39 Adding Frctions...40 Work Plce Instructions 2B Rcing Frctions...41 Frction Story Problems...42 Double Number Line...43 Another Double Number Line...45 Add or Subtrct Frctions...46 Work Plce Instructions 2C Trget Prctice...47 Better Buys...48 Frction Estimte & Check...49 Buying Grnol...50 Buying Apples...52 Rewrite & Clculte...53 More Equivlent Frctions...55 Frction Story Problems...56 Rtio Tbles to the Rescue!...57 Adding Frctions & Mixed Numbers...58 Frction Addition & Subtrction Review...59 More Frction Problems...60 Frction Equivlents...61 Which Is Bigger?...63 Using the Gretest Common Fctor to Simplify Frctions...64 Simplifying Frctions...66 Problem Solving with the LCM & GCF...67 Evn s Turtle...69 Bridges in Mthemtics Grde 5 Student Book

Unit 3 Plce Vlue & Decimls Frction Problems...70 Work Plce Instructions 3A Bet the Clcultor: Frctions...71 Frction & Deciml Equivlents...72 Plce Vlue Ptterns...73 Adding & Subtrcting Decimls...74 Wht s the Shre?...75 Deciml Color & Order...76 More Deciml Color & Order...78 Deciml Grid...79 Thinking About Thousndths...81 Work Plce Instructions 3B Drw & Compre Decimls...82 Plying Drw & Compre Decimls...83 Work Plce Instructions 3C Round & Add Tenths...84 Model, Add & Subtrct Decimls...85 Work Plce Instructions 3D Trget One...86 Working with Decimls...87 Frctions & Decimls Chrt...88 Deciml Grid...89 Frctions, Decimls & Money...91 Deciml Prctice...92 Decimls on Number Line...93 Round, Add & Subtrct Decimls...94 Memory Bytes...95 Olympic Story Problems...97 Verticl Problems...98 More Memory Bytes... 100 Equivlent Mesures...101 Different Mesures... 102 Meters & Meters... 103 Mesurements... 104 Rounding & Division Prctice... 105 Bse Ten Grid Pper... 106 Division Prctice... 108 Work Plce Instructions 3E Division Showdown... 109 Metric Conversions...111 More Rounding & Estimtion Prctice...112 Unit 4 Multiplying & Dividing Whole Numbers & Decimls Frction & Deciml Review...113 Work Plce Instructions 4A The Product Gme, Version 2...114 Product Problems...115 Cllie s Cke Pops...116 Multipliction Strtegy...117 Box Puzzle Chllenges...118 Work Plce Instructions 4B Multipliction Bttle...119 Find the Product...121 Cllie s Soccer Clets... 122 Multipliction Bttle...124 More Plnning for Cllie... 125 With or Without... 128 Over & Under... 129 Mking Cupckes... 130 Double-Digit Multipliction Sketches...131 Work Plce Instructions 4C Bet the Clcultor: Multipliction...133 More About Qurters... 134 Double-Digit Multipliction...135 Resonble Estimtes & Prtil Products...137 Moving Towrd the Stndrd Algorithm... 138 Bottom to Top, Right to Left... 140 Understnding the Stndrd Algorithm...141 Al s Prctice Sheet... 143 Fill in the Boxes... 144 Solving Problems with the Stndrd Algorithm... 145 Alex & the Algorithm...147 25 64... 148 Story Problems... 149 Leh s Problems...152 Which Estimte Mkes the Most Sense?...153 Work Plce Instructions 4D Estimte & Check... 154 2- by 3-Digit Multipliction...155 Story Problem Pper... 156 Division on Bse Ten Grid...157 Wter Conservtion... 158 Wter Conservtion Chllenge... 160 Division with Tbles & Sketches...161 Work Plce Instructions 4E Lowest Reminder Wins... 162 Divisibility Rules... 163 Multipliction Problems & Mzes... 164 Bridges in Mthemtics Grde 5 Student Book

Unit 5 Multiplying & Dividing Frctions Mike s Mesurements... 165 Work Plce Instructions 5A Trget One Frctions... 166 Trget One Frctions... 167 A Frction of Whole... 168 Frctions of Wholes...170 Thinking About Strtegy...171 Ryn s Bsebll Crds...172 More Geobord Perimeters...173 More Geobord Perimeters, Chllenge...174 Reviewing the Stndrd Algorithm for Multipliction...175 Frction Multipliction Grids...176 Simplifying Frctions...177 Are of the Addition Key...178 Multiplying Frctions with the Are Model...179 Missing Frctions...181 Brin s Boxes & Kevin's Pictures... 182 Find the Product... 183 Picturing Frction Multipliction... 184 Modeling Frction Multipliction... 185 Resoning About Multiplying with Frctions... 186 More Frction Multipliction... 187 Work Plce Instructions 5B Tic-Frc-Toe... 188 Tic-Frc-Toe Moves... 189 Grouping or Shring?... 190 Skills Review 1...192 Skills Review 2... 193 Do-It-Yourself Story Problems... 194 Skills Review 3...197 Skills Review 4... 198 More Do-It-Yourself Story Problems... 199 Skills Review 5... 202 Frction Estimte & Check... 203 Unit 6 Grphing, Geometry & Volume Frction & Deciml Story Problems...204 Zero Ptterns Review... 205 Grphing the Cube Sequence...206 Coordinte Dot-to-Dots... 207 Grphing Another Cube Sequence... 208 Short & Tll Towers... 209 Exploring New Sequence...211 Tile Pools...212 Tile Pools Chllenge...214 More Coordinte Dot-to-Dots...216 Anthony's Problem...217 Grphing the Two Pyment Plns...219 Mirnd s Number Ptterns... 220 Work Plce Instructions 6A Drgon s Tresure... 221 Rit's Robot... 222 Tringles Record Sheet... 223 More Geobord Tringles... 224 Thinking About Qudrilterls... 225 Perimeters & Trpezoids... 227 The Logic of Qudrilterls Chllenge... 228 Qud Construction... 229 Properties of Prllelogrms... 230 Bsebll Box Lbels... 231 Bseblls Pcked in Cube-Shped Boxes... 233 Pcking Mtt s Mrbles...234 Grphing & Geometry Review... 235 Work Plce Instructions 6B Polygon Serch... 236 Finding Volume... 238 Volumes Record Sheet... 239 Tnk Volume... 240 Work Plce Instructions 6C Volume Bingo...241 Volume Problems... 242 Pet Sncks... 245 More of Cleb s Flgs... 246 Aron s Arrys... 248 Thinking About Flgs... 249 Cleb s U.S. Themed Flgs... 250 Sophi s Work... 252 Design--Flg Chllenge... 253 Boxes & Bnners... 255 Simplifying Frctions Review... 256 Bridges in Mthemtics Grde 5 Student Book

Unit 7 Division & Decimls Rob s Review... 257 Arry Work... 258 Work Plce Instructions 7A Roll Five... 259 Roll Five & Rtio Tbles... 260 Fruit Pizz... 261 Thinking About Division... 262 Food Project... 263 Division with Frctions...264 Story Problems... 265 Thinking About Money... 267 Multipliction Round & Check... 268 Frction Division on Clock... 269 Work Plce Instructions 7B Quotients Rce to One Hundred... 270 Dividing Frctions & Whole Numbers... 272 Dividing Mrbles... 273 Deling with Reminders...274 Story Problems: Division with Reminders... 277 Division Prctice... 278 Exponents & Powers of Ten... 279 Ptterns in Multiplying by Powers of Ten... 280 Multiplying by Powers of Ten Prctice... 282 More Exponents & Powers of Ten... 283 Ptterns in Dividing by Powers of Ten...284 Dividing by Powers of Ten Prctice... 287 Multiplying & Dividing by Powers of Ten... 288 Using the Are Model to Multiply Deciml Numbers... 289 Multiplying Two Deciml Numbers...290 More Decks... 291 Decimls, Powers of Ten & Exponents... 292 Deciml Division with Money... 293 Compring & Multiplying Frctions & Decimls... 295 Using Models & Strtegies... 296 Common Division Mistkes... 297 Reviewing Deciml Addition & Subtrction... 298 Unit 8 Solr Design Temperture Conversions... 299 Absorbing & Reflecting Solr Energy...300 Reding Line Grph... 303 Concentrting Solr Energy...304 Solr Concentrtion... 307 Collecting Solr Energy...308 Solr Collection...311 Solr Boxes...312 More Solr Boxes...314 Chnging Surfce Are...315 Erth Mterils...316 Erth Mterils in Boxes...318 Erth Mterils Questions...319 Erth Mterils Experiment... 320 Window Orienttion... 321 Mking Windows... 323 Insultion Mterils... 324 Amount of Insultion Mterils... 327 Insulting Our House... 328 Buying Window Mterils... 329 Testing Our House... 330 Insultion Experiment... 332 Insultion Grph Questions... 333 Using Energy... 334 Solr Devices... 335 Solr PV Cells... 338 Solr Collector Experiment... 339 Choosing Our Mterils...340 Another Solr House... 342 Determining House Mterils... 343 Testing Our Finl Houses...344 Floor Pln... 347 Room Volume... 349 More Solr Fetures... 350 Bridges in Mthemtics Grde 5 Student Book

Unit 1 Module 1 Session 1 Work Plce Instructions 1A The Product Gme Ech pir of plyers needs: 1A The Product Gme Record Sheet to shre 2 gme mrkers pencils 1 Plyers decide who is going first. Plyer 1 is O nd Plyer 2 is X. 2 Plyer 1 plces one of the gme mrkers on ny fctor. 3 Plyer 2 plces the other gme mrker on fctor. Then, he multiplies the two fctors, drws n X on the product, nd writes n eqution to mtch the combintion. Plyer 1 I choose 5. Plyer 2 I choose 7. Let s see, 5 7 is 35, nd I m X, so I ll put my X on 35. 5 7 = 35 4 Plyer 1 moves one gme mrker to get new product. She cn move either of the mrkers. Plyer 1 I ll move the fctor mrker from the 5 to the 3. Since 7 3 is 21, I get to put n O on 21. 7 3 = 21 5 7 = 35 5 Ply continues until plyer gets four products in row cross, up nd down, or digonlly. Only one fctor mrker cn be moved during plyer s turn. Plyers cn move gme mrker so tht both re on the sme fctor. For exmple, both mrkers cn be on 3. The plyer would mrk the product 9 becuse 3 3 = 9. If the product plyer chooses is lredy covered, the plyer loses tht turn. Gme Vrition A Plyers ply for five in row. Bridges in Mthemtics Grde 5 Student Book 1

Unit 1 Module 1 Session 1 You Choose 1 Choose 15 of the problems below to solve. 8 5 = 7 7 = 4 6 = 3 8 = 4 7 = 4 9 = 6 7 = 6 8 = 8 4 = 3 6 = 10 4 = 8 10 = 8 9 = 6 11 = 12 10 = 15 4 = 40 6 = 50 8 = 10 9 = 14 9 = 25 4 = 11 9 = 6 12 = 12 9 = 7 60 = 30 6 = 13 8 = 11 5 = 25 8 = 12 8 = 2 Explin how you decided which problems to solve. Bridges in Mthemtics Grde 5 Student Book 2

Unit 1 Module 1 Session 2 Product Gme Problems ex Chloe nd Av were plying The Product Gme. Their fctor mrkers were on 4 nd 5. Av decided to move the mrker from 5 to 7. Write numericl expression to represent her move. 4 7 1 Chris nd Ktie were plying The Product Gme. Their fctor mrkers were on 9 nd 2. Chris decided to move the mrker from 2 to 6. Write numericl expression to represent his move. 2 Eric nd Willim were plying The Product Gme together. Willim put n X on 42. One fctor mrker ws on 6. The other fctor mrker ws on. 3 Cindy plced n X on the product 36. Wht re ll the possible loctions of the two fctor mrkers? 4 Eli plced n O on the product 24. Wht re ll the possible loctions of the two fctor mrkers? 5 Hnnh nd Sen were plying The Product Gme. Hnnh needed to lnd on the product 18 to win the gme. The mrkers were on 4 nd 6. Which fctor mrker should Hnnh move? b Where should she plce it? 6 Solve the following problems. 8 10 8 5 4 6 8 6 6 12 12 8 96 32 Bridges in Mthemtics Grde 5 Student Book 3

Unit 1 Module 1 Session 3 More Product Gme Problems 1 Jck nd Connor re plying The Product Gme. They re using light nd drk mrkers insted of X s nd O s to cover their products on the gme bord. Jck is using the light mrkers. Wht move should he mke next? Tell why. b Connor is using the drk mrkers. Wht move should he mke next? Tell why. 2 Melnie nd Jsmine re lso plying The Product Gme. Melnie is using the light mrkers. Wht move should she mke next? Tell why. b Jsmine is using the drk mrkers. Wht move should she mke next? Tell why. 3 Solve the following. 11 8 11 9 9 3 6 4 44 21 42 45 9 9 Bridges in Mthemtics Grde 5 Student Book 4

Unit 1 Module 1 Session 4 Fcts & Boxes 1 To multiply numbers by 5, Kylee first multiplies by 10 nd then finds hlf the product. Write n expression with prentheses to show how Kylee would solve 9 5. b Wht is 9 5? c Mrshll sys he would rther use 10 5 to find 9 5. Write n expression with prentheses tht uses 10 5 to find 9 5. Mtch ech expression with the correct box. 2 4 lyers of 3-by-5 cubes (3 5) 4 3 4 lyers of 3-by-2 cubes (3 2) 4 b 4 4 lyers of 3-by-4 cubes (3 4) 4 c 5 Fill in the dimensions of this box: ( ) dimensions of ech lyer number of lyers 6 Solve the following problems. 8 4 8 8 12 10 12 5 3 7 7 6 6 42 Bridges in Mthemtics Grde 5 Student Book 5

Unit 1 Module 1 Session 5 Fct Connections 1 Fill in the fcts. Look for reltionships. 3 3 3 6 6 6 2 4 8 2 4 8 2 Use the bove informtion to help you fill in the blnks. 3 4 = (3 2) = b 3 8 = (3 4) = c 6 2 = (3 2) = d 6 4 = 2 (6 ) = e 2 (6 4) = 8 = 3 Fill in the fcts. Look for reltionships. 4 4 4 8 8 8 2 4 8 2 4 8 4 Use the bove informtion to help you write n eqution tht includes prentheses. ex 8 4 = 2 (8 2) To find 8 4, I cn double 8 2. 4 6 = b 4 12 = c 8 8 = 5 CHALLENGE Complete the following equtions. 4 67 = (2 67) b 8 198 = 2 ( 198) c 3,794 = 2 (4 3,794) Bridges in Mthemtics Grde 5 Student Book 6

Unit 1 Module 2 Session 1 Are They Equivlent? 1 Mrk ech of the following equtions true or flse nd tell how you know. 12 6 = 24 3 b 7 4 = 28 2 c 48 6 = 24 3 d 16 4 = 2 32 e (22 7) 59 = 22 (7 59) 2 Fill in the blnk to mke ech eqution true. 6 = 3 14 b 8 5 = 4 c 12 16 = 8 d 8 = 16 2 e 4 = 2 26 3 CHALLENGE Tho sys she cn find the nswer to 8 90 by hlving the 8 nd doubling the 90 gin nd gin until she gets down to 1 720. Is she correct? Prove your nswer. Bridges in Mthemtics Grde 5 Student Book 7

Unit 1 Module 2 Session 2 Smller Boxes Brd needs some boxes to hold his smller orders of 12 bseblls. 1 List ll the possible boxes tht could hold 12 blls, if ech bll tkes up 1 1 1 spce. You cn use numbers, lbeled sketches, or words to show, but try to use system where you cn be sure you ve found ll the different boxes. 2 Mtch ech expression with the correct box below. The numbers in prentheses represent the dimensions of the bse nd the third number represents the height (number of lyers). (2 3) 5 b (3 5) 2 c (2 5) 3 Bridges in Mthemtics Grde 5 Student Book 8

Unit 1 Module 2 Session 3 Clculting Crdbord Below is list of six possible box designs for Brd s 24 bseblls. Determine how mny units of crdbord re needed to construct ech box. Brd s Bseblls Box Design Squre Units of Crdbord Needed (1 1) 24 (1 2) 12 (1 3) 8 (1 4) 6 (2 2) 6 (2 3) 4 Bridges in Mthemtics Grde 5 Student Book 9

Unit 1 Module 2 Session 3 Zck s Strtegies Zck hs been working with vriety of multipliction strtegies. 1 Write n expression to describe ech of the sttements Zck mde. To solve 24 15, I double nd hlve. b To solve 14 8, I find 14 10 nd remove 2 groups of 14. 2 Evlute the two expressions bove (in other words, find the vlues). b 3 Fill in the blnks. (2 3) = 30 b 4 ( 4) = 48 4 True or Flse? 4 9 = (4 10) 1 b 9 13 = (10 13) (1 9) 5 Solve the following. 9 3 = 9 30 = b 15 4 = 15 40 = Bridges in Mthemtics Grde 5 Student Book 10

Unit 1 Module 2 Session 4 How Mny Boxes? 1 Shne is mking boxes to hold bseblls. He wnts the dimensions to be 3 5 7 units. How mny blls cn one of Shne s boxes hold? 2 Riley is lso mking boxes to hold bseblls. She wnts the dimensions of her boxes to be 4 6 3 units. How mny blls cn one of Riley s boxes hold? 3 Rquel found two boxes in her storeroom. One box hs the dimensions 6 2 3 nd the other is 2 3 6. Which box holds more blls? Explin your thinking. Bridges in Mthemtics Grde 5 Student Book 11

Unit 1 Module 2 Session 5 Work Plce Instructions 1B The Multiple Gme Ech pir of plyers needs: 2 colored pencils of different colors 1B Multiple Gme Record Sheet to shre 1 Plyer 1 circles trget multiple on the gme bord. The number must be multiple of other numbers (not only itself). In the first turn, ny number except 1 cn be chosen. 2 Plyer 2 circles ll the fctors of the trget multiple, not including the trget multiple itself. For exmple, if Plyer 1 chooses 12 s trget multiple, Plyer 2 circles 1, 2, 3, 4, nd 6 becuse 12 is multiple of ech. Michelle Mli The Multiple Gme Michelle circled 12, so Mli circles 1, 2, 3, 4, nd 6. 3 Then, Plyer 2 chooses nd circles new trget multiple, nd Plyer 1 circles ll the vilble (uncircled) fctors of Plyer 2 s trget multiple. Once number on the gme bord hs been circled, it my not be used gin. Michelle Mli The Multiple Gme Mli circled 20, so Michelle circles 5 nd 10. Michelle cn't circle 2 or 4 becuse they hve lredy been used. 4 Plyers tke turns choosing trget multiples nd circling fctors. When the numbers remining re not multiples of ny uncircled numbers (i.e., when no further plys cn be mde) the gme is over. If plyer chooses trget multiple for which there re no fctors tht cn still be circled, the chosen trget multiple must be crossed out nd the plyer loses their turn. 5 Ech plyer finds the sum of the numbers tht re circled with their color. The gretest totl wins. Gme Vritions A A pir of plyers my ply ginst nother pir. B Plyers my crete gme bord tht contins numbers greter thn 30. Bridges in Mthemtics Grde 5 Student Book 12

Unit 1 Module 2 Session 5 Milo s Multiples 1 Help Milo find t lest three multiples for ech number below. 12:,, b 16:,, c 23:,, 2 Help Milo find the fctors of ech of the numbers below. 12:,,,,, b 16:,,,, c 23:, d 36:,,,,,,,, 3 Wht fctors do 16 nd 24 hve in common? 4 Wht re two multiples tht 8 nd 16 hve in common? 5 CHALLENGE Frh's mom told her she's thinking of number tht is multiple of 12. Wht else cn Frh sy with certinty bout the number her mom is thinking of? Bridges in Mthemtics Grde 5 Student Book 13

Unit 1 Module 2 Session 6 Thinking About The Multiple Gme 1 List the fctors for ech number below. Write P next to numbers tht re prime nd C next to numbers tht re composite. 29: b 25: c 24: d 23: 2 Which of the bove numbers would you choose if you were going first in The Multiple Gme? Why? 3 In The Multiple Gme, when would be good time to choose the number 30? 4 Write n expression for ech of the clcultions below. Multiply 3 by 6, nd divide by 9. b Subtrct 10 from 30, nd then multiply by 20. c Add 13 nd 17 nd 21, nd multiply the sum by 25. d Divide 36 by 4, then dd 45. Bridges in Mthemtics Grde 5 Student Book 14

Unit 1 Module 3 Session 1 Pricing Brd s Bseblls pge 1 of 2 Brd is tking inventory of the blls in the storeroom nd deciding how to price them to sell. Solve ech problem nd write n expression or eqution to represent it. 1 There is box of 100 miscellneous blls tht Brd wnts to sell. Wht re one or two possible sets of dimensions for the box? b Wht is the totl price for the box of blls if Brd chrges $20 per bll? c Wht if he chrges $19 per bll? d Wht if he chrges $21 per bll? 2 Brd noticed there re ctully only 99 blls in the box. Wht is the totl price if Brd chrges $20 per bll? b Wht if he chrges $19 per bll? c Wht if he chrges $21 per bll? (continued on next pge) Bridges in Mthemtics Grde 5 Student Book 15

Unit 1 Module 3 Session 1 Pricing Brd s Bseblls pge 2 of 2 3 Brd keeps chmpionship blls on rck, s shown in the picture of Brd s Bsebll Storeroom. How mny blls re on the chmpionship rck? b Write n expression to represent how you could quickly find the number of blls on the chmpionship rck without counting every one. c Wht is the totl price if Brd chrges $25 per chmpionship bll? 4 Brd hs box of 72 brgin bseblls. Wht is the totl price for ll the brgin bseblls if ech bll is $10? b Wht is the totl price for the brgin bseblls if ech bll is $9? c If Brd chrges $792 for the whole box, how much is ech bll? d If Brd chrges $648 for the whole box, how much is tht for ech bll? 5 CHALLENGE There is box of Blue Bombers tht contins 72 bseblls. Wht re the dimensions of ll of the possible boxes tht contin 72 bseblls? Which one do you think is pictured in the storeroom? Bridges in Mthemtics Grde 5 Student Book 16

Unit 1 Module 3 Session 1 Lily s Lcrosse Tem Lily is the mnger of her school s lcrosse tem. Help Lily keep trck of the tem s equipment. Show your work using numbers, sketches, or words. 1 Lily brought this box of lcrosse blls to prctice on Mondy. How mny lcrosse blls does the box hold if one lcrosse bll fits in 1 unit 1 unit 1 unit spce? b How much crdbord does it tke to mke the box? 2 Lily needs to buy 110 new lcrosse blls for the tem. The blls come in sets of 22. How mny sets of lcrosse blls should Lily buy? b If one set of 22 lcrosse blls costs $20, how much will 110 lcrosse blls cost? 3 Is ech eqution true or flse? 98 34 = (100 34) (1 34) b 46 28 = 23 56 Bridges in Mthemtics Grde 5 Student Book 17

Unit 1 Module 3 Session 2 Sm s Sewing Supplies 1 Sm needs more thred for sewing project. One spool of thred costs 72 cents. Fill out the rtio tble below to find out how much 12 spools of thred cost. Spools of thred 1 2 10 12 Cost 72 How much do 12 spools of thred cost? b How would you figure out how much 24 spools of thred cost? c Write n expression with prentheses to show how you would figure out how much 24 spools of thred cost. 2 Sm sw sign dvertising thred on sle. The sign sid, Thred Sle! 12 spools for 840 cents, 15 spools for 900 cents, nd 18 spools for 990 cents. Which is the best del? Why? Show your thinking. 3 Write n expression for the clcultion. ex To find 18 times 35, I double 35 nd hlve 18: (35 2) x 1 2 (18) or (35 2) (18 2) To find 38 times 14, I multiply 30 times 14 nd 8 times 14 nd dd the two products together. Bridges in Mthemtics Grde 5 Student Book 18

Unit 1 Module 3 Session 3 Chrlie s Chocoltes Chrlie is filling boxes with hndmde chocoltes. She strts with the following boxes. 1 Chrlie fills box with 5 lyers. Ech lyer hs 3 rows of 5 chocoltes. Write n expression tht shows how mny chocoltes re in the box. b Write n eqution shows how mny chocoltes re in the box. c Chrlie s brother dropped his bsebll on the box nd broke 6 chocoltes, which hd to be removed. Write n expression tht shows how mny chocoltes re in the box now. d Write n eqution tht shows how mny chocoltes re in the box now. 2 Chrlie fills 2 more boxes with chocoltes. These boxes hve 7 lyers of chocoltes with 12 chocoltes in ech lyer. Then, Chrlie puts both boxes together in lrger box. Write n expression tht shows how mny chocoltes re in the lrger box. b Write n eqution tht shows how mny chocoltes re in the lrger box. Bridges in Mthemtics Grde 5 Student Book 19

Unit 1 Module 3 Session 4 Work Plce Instructions 1C Bet the Clcultor Ech pir of plyers needs: set of Bet the Clcultor Crds to shre scrtch pper nd pencil (optionl) 1 clcultor to shre Some clcultors will not work for this gme. Check the clcultor you wnt to use by entering 1 + 3 2 =. If the nswer shown is 7, tht clcultor will work for this gme. If the nswer shown is 8, you ll need to find different clcultor. 1 One plyer shuffles the crds nd plces the deck fce-down. Plyers decide which of them will strt with the clcultor, nd they decide on the number of rounds they will ply. 2 The plyer with the clcultor turns over crd so both plyers cn see it. 3 The plyer with the clcultor enters the problem exctly s it is written on the crd. If the clcultor doesn t hve prentheses, the plyer should enter the prts in prentheses first, then = to get result. They must then cler the clcultor nd enter the rest of the problem using the result in plce of the prt in prentheses. 4 At the sme time, the other plyer evlutes the expression using n efficient strtegy, either mentlly or with pper nd pencil. 5 The plyer who gets the correct nswer first keeps the crd. 6 Plyers compre nswers nd shre strtegies for evluting the expression. 7 Plyers switch roles nd drw gin. (The plyer who didn t hve the clcultor hs it now.) 8 The gme continues for n greed-upon number of rounds. The plyer with the most crds t the end wins. Gme Vritions A Plyers write their own problems on crds, mix them up, nd then choose from those problems. B C D Insted of rcing the clcultor, students rce ech other to find the nswer mentlly, nd check the nswer to be sure it s correct using clcultor if necessry. Plyers ply coopertively by drwing crd nd discussing their preferred mentl strtegy. Plyers spred the crds fce-down on the tble. Ech student chooses different crd t the sme time nd then rces to see who gets the correct nswer first. Bridges in Mthemtics Grde 5 Student Book 20

Unit 1 Module 3 Session 4 Expressions & Equtions 1 Write numericl expression tht includes grouping symbols for ech: To find 8 17, I double nd hlve. b To find 36 19, I find 36 times 20 nd remove 1 group of 36. c To find the volume of box tht hs 19 by 22 bse nd 27 lyers, I multiply the re of the bse times the height. 2 Write n eqution for ech: To find 7 times 32, I double nd hlve. b To find 26 times 13, I multiply 20 times 13 nd dd it to 6 times 13. c To find 98 times 54, I multiply 100 times 54 nd subtrct 2 times 54. 3 Show your work for ech problem. Xvier counted 38 blls in one lyer of box. The box hs 17 lyers. How mny blls cn the box hold? b A box holds 448 blls. Ech lyer hs 28 blls. How mny lyers does the box hve? Bridges in Mthemtics Grde 5 Student Book 21

Unit 1 Module 4 Session 1 Multipliction & Division Bridges in Mthemtics Grde 5 Student Book 22

Unit 1 Module 4 Session 1 Mthemticl Thinking 1 Ktie sys she cn multiply 5 68 by multiplying 10 68 nd dividing the nswer in hlf. Do you gree or disgree? Explin your thinking. b Write n expression tht shows Ktie s thinking. Use prentheses. 2 Henry sys he cn multiply 99 57 by multiplying 100 57 nd then dding one more 57. Do you gree or disgree? Explin your thinking. b Write n expression tht shows Henry s thinking. Use prentheses. 3 Pris is pcking crte of flower pots. She puts 2 rows of 6 flowerpots in ech lyer of box. There re 2 lyers in the box. Write n expression tht shows how mny flowerpots re in the box. b Write n eqution to show how mny flowerpots re in the box. Bridges in Mthemtics Grde 5 Student Book 23

Unit 1 Module 4 Session 2 Division Story Problems pge 1 of 2 For ech problem on this pge nd the next, Write n eqution, including prentheses if needed, to mtch the sitution. Find the nswer. You cn use bse ten pieces to model nd solve the prt of the problem tht requires division. Lbel your nswer with the correct units. Explin wht you did with the reminder nd why. 1 Josh nd his three friends bked cookies lst Sturdy. When they were finished, they hd 65 cookies. Ech of the 4 friends te 2 cookies right wy nd divided the rest eqully to tke home. How mny cookies did ech of the friends get to tke home? 2 Sr nd 5 of her friends did chores ll Sturdy nd erned $75.00. Sr s dd ws so plesed with their work tht he gve ech of the 6 children $2.00 tip in ddition to the $75.00. They shred the work eqully, so they wnt to shre ll the money eqully. How much money will ech person get? 3 Mrs. O Donnell is tking 36 fifth grders nd 7 prent helpers on field trip. She wnts to give ech person, including herself, 2 grnol brs for sncks. If there re 5 grnol brs in box, how mny boxes will she need to buy? (continued on next pge) Bridges in Mthemtics Grde 5 Student Book 24

Unit 1 Module 4 Session 2 Division Story Problems pge 2 of 2 4 Eighty-nine kids showed up for the first soccer prctice. The coches orgnized them into groups of 4 for wrm-up exercises. How mny groups were there? 5 Jml nd three of his friends rked leves every weekend for month. By the end of the month, they erned $91.00. They pid $4.00 to Jml s little brother for helping out little on the lst dy. Then the four friends divided the rest of the money eqully. How much did ech friend get? 6 The drivers t Pizz Plce were loding up their 3 delivery vns for the evening. There were 65 pizzs. The boss told them to put n equl number of pizzs in ech vn nd sid they could split ny leftovers eqully. How much of leftover pizz did ech of the 3 drivers get? Bridges in Mthemtics Grde 5 Student Book 25

Unit 1 Module 4 Session 2 Wht Should You Do with the Reminder? 1 For ech problem below: Use numbers, words, or lbeled sketches to solve the problem Figure out the best wy to hndle the reminder for tht sitution Write n eqution to show ech problem nd the nswer Story Problem Four friends mde 55 cupckes nd shred them eqully. How mny cupckes did ech friend get? Your Work: b There re 55 kids in the After-School Club. Tomorrow they re going to the zoo. If ech cr cn crry 4 kids, how mny crs will they need to get to the zoo? Your Work: c Emm nd her 3 friends did chores for Emm s dd on Sturdy. They erned $55.00 nd split it evenly. How much money did ech of the 4 children get? Your Work: Bridges in Mthemtics Grde 5 Student Book 26

Unit 1 Module 4 Session 3 Rce Cr Problems 1 Rce crs cn drive bout 5 miles on 1 gllon of gsoline. If rce cr goes 265 miles in one rce, bout how mny gllons of gsoline will it use? Show ll your work. Note: You cn use the bse ten re nd liner pieces to help solve this problem. 2 There were 43 crs in the rce. They ll finished the 265 miles of the rce nd they ech used bout 1 gllon of gs to go 5 miles. About how mny gllons of gs did the crs use ltogether to finish the rce? Show ll your work. Bridges in Mthemtics Grde 5 Student Book 27

Unit 1 Module 4 Session 4 Quotients Win, Gme 2 Red Tem Blue Tem 1 2 140 10 = 300 20 = 3 4 100 20 = 150 15 = 5 6 100 10 = 260 10 = Red Score Bridges in Mthemtics Grde 5 Student Book 28 Blue Score

Unit 1 Module 4 Session 4 Work Plce Instructions 1D Quotients Win Ech pir of plyers needs: 2 copies of one of the 1D Quotients Win Record Sheets (there re 6 different sheets; mke sure you ech get copy of the sme one) 2 dice numbered 1 6 1 set of bse ten re pieces 1 set of bse ten liner pieces 1 red nd 1 blue colored pencil or fine-tip felt mrker 1 Ech plyer gets 1 die nd rolls it t the sme time. If they both get the sme number, they roll gin until they hve different numbers. 2 Ech plyer solves the problem tht hs the sme number s the number they rolled. Plyers solve their problems t the sme time. 3 Ech plyer mkes lbeled sketch of the problem on the record sheet nd fills in the nswer, using their colored pencil or mrker to sketch the dimensions nd regulr pencil for the rest of the work. Plyers cn build model with bse ten pieces first, but they don't hve to. Alish I rolled 2, so I hve to do problem 2 on the gme sheet. Tht s 130 10. First I ll ly out liner strip to show 10 nd then strt fitting in bse ten pieces until I get to 130. My rectngle turned out to be 13 long the other side, so tht s the nswer. Now I hve to mke sketch. 10 13 100 30 13 4 Plyers roll nd solve the problems until they hve ech solved 3. If they roll the number of problem tht hs lredy been solved, they roll gin until they get the number of problem tht hs not been solved yet. (Plyers must use the first number tht hs not been solved). When they re done, they check ech other's work. 5 At the end of the gme, plyers dd their quotients nd record their score t the bottom of the sheet. The plyer with the higher score wins. Gme Vritions A B Plyers tke turns insted of both going t once. They sketch nd solve their prtner's problems s well s their own on their record sheet. They work together to mke sure their nswers re correct. Plyers use Record Sheets 5 nd 6, which re much more chllenging. Bridges in Mthemtics Grde 5 Student Book 29

Unit 1 Module 4 Session 4 Multipliction & Division Problems 1 Fill in the missing numbers. 6 8 4 5 6 48 16 40 54 28 5 6 8 7 4 45 30 49 16 56 2 Write n eqution to nswer ech question below. Question Eqution Answer ex How mny qurters re in 75? 75 25 = 3 3 qurters How mny crtons of 12 eggs mke 36 eggs in ll? b There re 6 cns of sod in pck. How mny pcks mke 42 cns? c There re 24 cns of sod in cse. How mny cses mke 72 cns? d e There re 3 tennis blls in cn. How mny cns mke 27 blls? Jim rides his bike t 10 miles per hour. How mny hours will it tke him to ride 30 miles? Bridges in Mthemtics Grde 5 Student Book 30

Unit 1 Module 4 Session 5 Using Bsic Fcts to Solve Lrger Problems Knowing the bsic multipliction nd division fcts cn help you multiply lrger numbers too. Strt with the bsic fcts below nd then complete the relted fct fmily of lrger numbers. Then mke up your own fct fmily bsed on other relted numbers. ex 1 Bsic Fct Fmily Relted Fct Fmily Your Own Relted Fct Fmily 4 = 40 3 = 120 = 12 3 3 4 = 12 = = 4 12 3 3 = 120 40 = 3 = 120 40 3 120 40 40 12 3 = 4 = = = 80 6 = 480 = 30 1,200 1,200 30 40 40 30 1,200 1,200 30 40 6 8 = 48 = = = 480 80 = 6 = 2 48 6 = 8 = = = 40 9 = 360 = 9 4 = 36 = = = 360 40 = 9 = 3 36 9 = 4 = = = 30 7 = 210 = 7 3 = 21 = = = 210 30 = 7 = 21 7 = 3 = = Bridges in Mthemtics Grde 5 Student Book 31

Unit 2 Module 1 Session 1 Money & Frctions Note: You cn use the money vlue pieces to help solve these problems if you like. 1 Write ech mount s deciml. 2 qurters = b 3 dimes nd 5 pennies = 2 Write ech mount s frction of dollr. 3 qurters = b 7 dimes = 3 Use numbers, lbeled sketches, or words to show your work. Mil hs 1 2 of dollr. Clire hs 1 4 of dollr. How much money do the girls hve together? Record your nswer s frction nd s deciml. b Henry hs 1 1 4 dollrs. Angel hs 1 1 2 dollrs. How much money do the boys hve together? Record your nswer s frction nd s deciml. c CHALLENGE Iris hs 1 3 5 dollrs. Violet hs 2 5 10 dollrs. How much money do the girls hve together? Record your nswer s frction nd s deciml. Bridges in Mthemtics Grde 5 Student Book 32

Unit 2 Module 1 Session 2 Frctions & Mixed Numbers 1 Color in the strips to show the frctions nmed below. Ech strip represents 1 whole. ex 1 4 3 8 b 1 2 c 3 4 2 Color in the strips to show the improper frctions nmed below. The write the frction s mixed number. Ech strip represents 1 whole. ex 7 4 1 3 4 12 8 b c 3 2 9 8 3 Fill in the blnks to show the unit frction s frction of dollr nd s deciml (money) nottion. ex 1 10 = 10 100 = 0.10 1 2 = = b c 3 4 = = d 7 10 = = 1 4 = = Write in your mth journl using numbers, lbeled sketches, or words to explin your nswer to the two problems below. (Hint: Use money vlue pieces to help.) 4 Esther hd to solve 1 2 + 1 4. She wrote: $0.05 + $0.75 = $0.80, which is the sme s 100 80 of dollr. So 1 2 + 1 4 = 100. 80 Do you gree or disgree with her work? 5 Thnh hd to solve 1 10 + 1 5. He wrote: $0.10 + $0.20 = $0.30, which is the sme s 3 10 of dollr, so 1 10 + 1 5 = 3 10. Do you gree or disgree with his work? Bridges in Mthemtics Grde 5 Student Book 33

Unit 2 Module 1 Session 3 Frctions on Clock Fce 1 2 1 2 = 1 4 1 3 1 4 = 1 3 = 1 6 1 12 1 6 = 1 12 = Bridges in Mthemtics Grde 5 Student Book 34

Unit 2 Module 1 Session 3 Clock Fce Frctions 1 Color in the clock to show the frctions below. Ech clock represents 1 whole. 1 2 b 1 4 c 2 6 d 10 6 e 5 3 2 Use the pictures bove to help complete ech comprison below using <, >, or =. ex 1 2 12 5 > 6 4 1 1 2 b 5 6 5 12 c 10 6 1 1 2 d 6 2 6 4 e 3 6 2 3 3 Subtrct these frctions. (Hint: Think bout money or clocks to help.) 1 2 1 4 = b 3 4 1 10 = c 1 1 6 = d 2 1 1 4 = 4 A certin frction is greter thn 2. The denomintor is 8. Wht must be true bout the numertor? Explin your nswer.? 8 The numertor must be greter thn becuse: Bridges in Mthemtics Grde 5 Student Book 35

Unit 2 Module 1 Session 4 Clock Frctions Problem String Problem 1: Problem 2: + = + = Problem 3: Problem 4: + = + = Problem 5: Problem 6: + = + = Bridges in Mthemtics Grde 5 Student Book 36

Unit 2 Module 1 Session 4 Work Plce Instructions 2A Clock Frctions Ech pir of plyers needs: Two 2A Clock Frctions Record Sheets 1 spinner overly colored pencils in severl colors regulr pencils 1 Plyer 1 spins both spinners nd writes the two frctions s n ddition expression under the words Equtions for Ech Turn. 2 Then Plyer 1 shdes in both frctions on his first clock, using different color for ech frction. lbels ech frction records the sum of the two frctions to finish the eqution for tht turn. Three fourths is the sme s nine twelfths, so I m shding in nine twelfths red. One sixth is the sme s two twelfths, so I m shding in two twelfths green. These two shded prts dd up to eleven twelfths, so 3/4 + 1/6 = 11/12. 3 4 + 1 6 = 11 12 3 Both plyers check the work to mke sure tht Plyer 1 shded nd lbeled the frctions nd wrote the eqution correctly. 4 Plyer 2 tkes her turn nd both plyers check her work. 5 Plyers do not move on to the next clock until clock is completely filled. However, if clock is nerly filled nd plyer spins frction tht is too big for it, the plyer cn split the frction to complete the first clock nd put the rest of the frction in the next clock. 6 When clock is completely filled, plyers write n eqution tht shows the frctions in the clock on the line underneth the clock. 7 The first plyer to completely fill ll three clocks wins the gme. If plyer spins frction tht is too big for the third clock, she loses tht turn. Plyers must fill the lst clock with the exct frction needed. For exmple, if plyer s third clock hs 1/12 to fill in, the plyer hs to spin 1/12 to complete the clock. Gme Vritions A Plyers cn shorten the gme by filling only two clocks or lengthen the gme by drwing nother clock. B Plyers cn work together to complete one record sheet, discussing ech move nd representtion. Bridges in Mthemtics Grde 5 Student Book 37

Unit 2 Module 1 Session 4 Adding Frctions 1 Show the frctions on the strips. Then dd them nd report the sum. 3 4 First Second Add Them Sum 3 4 b c d 3 8 5 8 1 2 1 2 3 4 7 8 2 Model ech problem on clock to dd the frctions. Remember to lbel your work. 1 2 + 1 6 = b 2 3 + 1 6 = c 1 3 + 2 6 = d 2 3 + 5 6 = Bridges in Mthemtics Grde 5 Student Book 38

Unit 2 Module 1 Session 5 Equivlent Frctions on Clock This clock is broken! The hour hnd is stuck t the 12, but the minute hnd cn still move. 1 Mrcus looked t the clock shown bove nd sid, 1 4 of n hour hs pssed. Sierr sid, 12 3 of n hour hs pssed. Ali sid, 60 15 of n hour hs pssed. Their techer sid they were ll correct. Explin how this could be possible. 2 Lbel ech clock with t lest 3 equivlent frctions to show wht prt of n hour hs pssed. b c d e f g h Bridges in Mthemtics Grde 5 Student Book 39

Unit 2 Module 2 Session 1 Adding Frctions 1 Ech br below is divided into 12 equl pieces. Show ech frction on frction br. ex 1 3 2 3 1 3 b 4 c 4 1 d e 5 2 6 2 Rewrite ech pir of frctions so tht they hve the sme denomintor. Then use the frction br pictures to show their sum. Write n eqution to show both frctions nd their sum. Frctions to Add Rewrite with Common Denomintor Picture nd Eqution ex 2 3 + 1 2 2 3 + 1 2 = 4 6 + 3 6 4 6 + 3 6 = 7 6 or 1 1 6 2 3 + 3 4 2 3 + 3 4 = + b 1 3 + 5 6 1 3 + 5 6 = + c 7 12 + 3 4 7 12 + 3 4 = + Bridges in Mthemtics Grde 5 Student Book 40

Unit 2 Module 2 Session 2 Work Plce Instructions 2B Rcing Frctions Ech pir of plyers needs: 1 Rcing Frctions Gme Bord 1 Rcing Frctions Record Sheet 1 deck of Rcing Frctions Crds 8 red nd 8 blue gme mrkers 1 Ech plyer plces 1 gme mrker t 0 on ech of the eight frction number lines on the gme bord. 2 Ech plyer chooses frction crd. The plyer with the lrger frction goes first. 3 Plyer 1 tkes new frction crd nd then moves one or more gme mrkers the totl distnce shown on the crd. Student I got 4 5, so I could move 4 5 on the fifths trck. But I m relly close to 2 on the tenths trck, nd 4 5 is like 8 10 I cn use 2 10 to get to the 2. Then I still hve 3 5 left to move my mrker on the fifths trck! 4 The plyer writes the frction from the frction crd in the left-hnd column of her tble nd writes the frction or eqution tht describes how the gme pieces were moved in the right-hnd column. If the plyer selected 4 5 nd moved 4 5, she would write 4 5. If the plyer selected 4 5 nd moved one mrker 2 10 nd nother mrker 3 5, she would write 2 10 + 3 5 = 4 5. 5 Plyer 2 checks Plyer 1 s work. If Plyer 2 disgrees, he hs to convince Plyer 1 of his resoning nd Plyer 1 gets to try gin. 6 Then, Plyer 2 tkes turn nd Plyer 1 checks his work. 7 Plyers continue to tke turns, record moves, nd check ech other s work until ll of one plyer s gme mrkers re on the 2s. If there is no possible move, the plyer loses the turn. Gme Vrition A Plyers ply coopertively nd work together to help ech other finish the trck in certin time period. Bridges in Mthemtics Grde 5 Student Book 41

Unit 2 Module 2 Session 2 Frction Story Problems 1 Mesure the line below nd mke mrk long the line to show exctly where ech of these frctions belongs. Be sure to lbel ech mrk with the nme of the frction. 1 6, 1 4, 1 3, 1 2, 2 3, 3 4 0 1 b Explin how you figured out where to plce ech frction long the line. 2 Yesterdy Crson recycled 1 1 3 pounds of pper pckging. He lso recycled 3 4 of pound of plstic pckging. Combined, how mny pounds of pckging did Crson recycle yesterdy? Show ll your work. 3 Crmen rn 1 3 8 miles yesterdy. Her sister Lol rn 2 1 4 did Lol run thn Crmen? Show ll your work. miles. How much frther Bridges in Mthemtics Grde 5 Student Book 42

Unit 2 Module 2 Session 3 Double Number Line pge 1 of 2 1 For ech of the following: Drw line from ech eqution to the mtching double number line. Fill in the blnks on the lst three double number lines. Record the nswer to ech eqution. 2 9 + 1 5 = 0 11 3 14 21 11 21 1 7 2 3 3 8 + 2 6 = 0 9 9 8 24 2 6 17 24 1 5 2 3 1 7 = 0 7 7 5 12 35 12 35 2 9 1 5 + 1 7 = 0 10 10 45 1 5 19 45 2 Use double number line to solve these problems. On Mondy, Mr. Miles wlked 1 9 of the tril to wrm up nd then he rn 7 8 of the tril. Wht frction of the tril did Mr. Miles cover on Mondy? (continued on next pge) Bridges in Mthemtics Grde 5 Student Book 43

Unit 2 Module 2 Session 3 Double Number Line pge 2 of 2 b On Tuesdy, Mr. Miles wlked 2 9 of the tril to wrm up nd then he rn 4 6 of the tril. Wht frction of the tril did Mr. Miles cover on Tuesdy? c On Wednesdy, Mr. Miles wlked nd rn 9 10 of the tril. Then he wlked 1 8 of the tril bck nd stopped to rest. Wht frction of the course ws Mr. Miles from the beginning of the tril when he stopped? d On Thursdy, Mr. Miles wlked nd rn 19 20 of the tril. Then he wlked 1 3 of the tril bck before he stopped to rest. Wht frction of the tril ws Mr. Miles from the beginning of the tril when he stopped? Bridges in Mthemtics Grde 5 Student Book 44

Unit 2 Module 2 Session 3 Another Double Number Line 1 Solve the following. 1 4 of 24 b 3 4 of 24 2 Solve the following. 1 8 56 b 3 8 56 3 Mrk both the frction nd the distnce trveled on the number line below. 1 4 of 24 km b 3 4 24 km 0 km 24 km 4 Mrk the frction nd the distnce trveled on the number line below. 1 8 56 km b 3 8 of 56 km 0 km 56 km 5 Becky cnoed 7 8 she cnoe? of the wy down 56 kilometer river. How mny kilometers did Bridges in Mthemtics Grde 5 Student Book 45

Unit 2 Module 2 Session 4 Add or Subtrct Frctions 1 Solve the problems on this pge. If your nswer is n improper frction, find its equivlent mixed number. 2 3 + 2 3 = 4 3 = 1 1 3 4 3 is n improper frction becuse 4 is greter thn 3. 3 3 is equl to 1, so 4 3 is equl to 1 1 3. 1 8 10 4 10 = 3 4 2 4 = 6 10 + 4 10 = 1 2 + 3 4 = 3 6 1 2 = 2 4 + 2 2 10 = 2 3 2 6 = 1 1 4 + 2 6 = 3 3 4 + 2 1 8 = 2 Find two different wys to show tht 1 2 + 1 4 is not equl to 2 6. You cn use numbers, words, or lbeled sketches. Bridges in Mthemtics Grde 5 Student Book 46

Unit 2 Module 2 Session 5 Work Plce Instructions 2C Trget Prctice Ech pir of plyers needs: 1 spinner overly 2 Trget Prctice Record Sheets pencils 1 Plyers decide who will be Plyer 1 nd who will be Plyer 2. 2 Plyer 1 spins Spinner 1 twice nd Spinner 2 twice nd records ll four numbers spun on the Record Sheet. 3 Plyer 1 chooses two of the numbers spun to crete two unit frctions (frctions with 1 s the numertor) tht hve sum s close to 1 s possible, nd records the frctions creted on the Record Sheet. 4 Plyer 1 finds the sum of the frctions. 5 Then, Plyer 1 finds her score by figuring out how fr from one whole the sum is. Plyer 2 checks Plyer 1 s work. 6 Then it is Plyer 2 s turn. 7 After both plyers hve finished Round 1, they compre scores nd determine which is the smller frction. The plyer with the smller score wins the round nd circles his score. If the scores re the sme, tht round is tie. 8 For rounds 2 5, plyers spin ech spinner only one time to get two new numbers. They record the newly spun numbers nd the two unused numbers from the previous round on their Record Sheet. 9 After five rounds, plyers compre how mny rounds ech won to determine the winner of the gme. Gme Vritions A Plyers spin for four new numbers in ech round. B C Plyer work together to find the smllest score on one record sheet rther thn plying competitively. Plyers do not determine winner in ech round, insted they dd the five scores for ech round to determine the winner of the gme. Bridges in Mthemtics Grde 5 Student Book 47

Unit 2 Module 2 Session 5 Better Buys 1 Michel ws working on finding the better buy for grnol brs: 8 brs for $10 or 20 brs for $23. Fill in ech rtio tble to find equivlents. 8 brs 16 brs brs 32 brs 40 brs $10 $ $30 $ $50 20 brs brs $23 $46 b 20 brs 10 brs brs 1 br $23 $ $5.75 $1.15 8 brs 4 brs 1 br $10 $5 $1.25 2 Now Michel wnts to buy bgs of mixed nuts. He cn buy 12 bgs for 15 dollrs or 16 bgs for $19.20. Fill in the rtio tbles. 12 bgs bgs 3 bgs 1 bg $15 $7.50 $ $ 16 bgs 8 bgs 4 bgs 1 bg $19.20 $ $ $ b Explin how you cn use the informtion in the tbles to find the better buy of bgs of mixed nuts. Bridges in Mthemtics Grde 5 Student Book 48

Unit 2 Module 2 Session 6 Frction Estimte & Check Before you solve ech problem, look crefully t the frctions nd write wht you know bout the sum or difference. Then find the exct sum or difference. Show ll your work. If your nswer is greter thn 1, write it s mixed number, not n improper frction. Problem Wht You Know Before You Strt Show your work Exct Sum or Difference 1 8 3 + 9 12 The sum is more thn 3. 32 12 + 9 12 = 41 12 nd 41 12 = 3 5 12 3 5 12 2 1 2 5 12 3 3 10 + 4 5 4 3 4 1 5 5 12 6 8 12 6 12 8 + 3 4 Bridges in Mthemtics Grde 5 Student Book 49

Unit 2 Module 3 Session 1 Buying Grnol pge 1 of 2 Grnol costs $6 for 5 pounds. Use the rtio tbles to find the prices for different mounts of grnol: 1 4, 1 2, 3 4, 1, 2, 3, 8, 13, 15, 28, 31, 50, 60, nd 80 pounds. You cn find the prices in ny order. ex Price $6 $12 $1.20 $13.20 Pounds 5 10 1 11 11 $13.20 pounds cost. Price $6 Pounds 5 pounds cost. Price $6 Pounds 5 pounds cost. Price $6 Pounds 5 pounds cost. Price $6 Pounds 5 pounds cost. Price $6 Pounds 5 pounds cost. (continued on next pge) Bridges in Mthemtics Grde 5 Student Book 50

Unit 2 Module 3 Session 1 Buying Grnol pge 2 of 2 Price $6 Pounds 5 pounds cost. Price $6 Pounds 5 pounds cost. Price $6 Pounds 5 pounds cost. Price $6 Pounds 5 pounds cost. Price $6 Pounds 5 pounds cost. Price $6 Pounds 5 pounds cost. Price $6 Pounds 5 pounds cost. Bridges in Mthemtics Grde 5 Student Book 51

Unit 2 Module 3 Session 1 Buying Apples 1 Color in the geobords to show the frctions below. Ech geobord represents 1 whole. 1 2 b 1 4 c 3 4 d 1 8 e 2 8 f 5 8 Add the following frctions. If the sum is greter thn 1, write the nswer s both n improper frction nd mixed number. 2 Find equivlent frctions nd then dd or subtrct. ex 1 2 + 5 8 = 4 8 + 5 8 = 9 8 = 1 1 8 1 1 2 + 3 8 = + = = b 2 1 4 + 2 8 = + = = c 3 4 2 8 = = 3 Five pounds of pples cost $8. Use the rtio tble to find the cost for 9 pounds nd 11 pounds. You do not need to use ll of the tble cells. Price $8 Pounds 5 Cost of 9 pounds of pples: b Cost of 11 pounds of pples: Bridges in Mthemtics Grde 5 Student Book 52