SECOND EDITION STUDENT BOOK GRADE

Size: px
Start display at page:

Download "SECOND EDITION STUDENT BOOK GRADE"

Transcription

1 SECOND EDITION STUDENT BOOK GRADE 5

2 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 Tel 1 (800) 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 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 ISBN Bridges in Mthemtics Grde 5 Student Book

3 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? 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 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

4 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 Equivlent Mesures Different Mesures Meters & Meters Mesurements Rounding & Division Prctice Bse Ten Grid Pper Division Prctice Work Plce Instructions 3E Division Showdown Metric Conversions More Rounding & Estimtion Prctice Unit 4 Multiplying & Dividing Whole Numbers & Decimls Frction & Deciml Review Work Plce Instructions 4A The Product Gme, Version Product Problems Cllie s Cke Pops Multipliction Strtegy Box Puzzle Chllenges Work Plce Instructions 4B Multipliction Bttle Find the Product Cllie s Soccer Clets Multipliction Bttle More Plnning for Cllie With or Without Over & Under Mking Cupckes Double-Digit Multipliction Sketches Work Plce Instructions 4C Bet the Clcultor: Multipliction More About Qurters Double-Digit Multipliction Resonble Estimtes & Prtil Products Moving Towrd the Stndrd Algorithm Bottom to Top, Right to Left Understnding the Stndrd Algorithm Al s Prctice Sheet Fill in the Boxes Solving Problems with the Stndrd Algorithm Alex & the Algorithm Story Problems Leh s Problems Which Estimte Mkes the Most Sense? Work Plce Instructions 4D Estimte & Check by 3-Digit Multipliction Story Problem Pper Division on Bse Ten Grid Wter Conservtion Wter Conservtion Chllenge Division with Tbles & Sketches Work Plce Instructions 4E Lowest Reminder Wins Divisibility Rules Multipliction Problems & Mzes Bridges in Mthemtics Grde 5 Student Book

5 Unit 5 Multiplying & Dividing Frctions Mike s Mesurements Work Plce Instructions 5A Trget One Frctions Trget One Frctions A Frction of Whole Frctions of Wholes Thinking About Strtegy Ryn s Bsebll Crds More Geobord Perimeters More Geobord Perimeters, Chllenge Reviewing the Stndrd Algorithm for Multipliction Frction Multipliction Grids Simplifying Frctions Are of the Addition Key Multiplying Frctions with the Are Model Missing Frctions Brin s Boxes & Kevin's Pictures Find the Product Picturing Frction Multipliction Modeling Frction Multipliction Resoning About Multiplying with Frctions More Frction Multipliction Work Plce Instructions 5B Tic-Frc-Toe Tic-Frc-Toe Moves Grouping or Shring? Skills Review Skills Review Do-It-Yourself Story Problems Skills Review Skills Review More Do-It-Yourself Story Problems Skills Review Frction Estimte & Check Unit 6 Grphing, Geometry & Volume Frction & Deciml Story Problems Zero Ptterns Review Grphing the Cube Sequence Coordinte Dot-to-Dots Grphing Another Cube Sequence Short & Tll Towers Exploring New Sequence Tile Pools Tile Pools Chllenge More Coordinte Dot-to-Dots Anthony's Problem Grphing the Two Pyment Plns Mirnd s Number Ptterns Work Plce Instructions 6A Drgon s Tresure Rit's Robot Tringles Record Sheet More Geobord Tringles Thinking About Qudrilterls Perimeters & Trpezoids The Logic of Qudrilterls Chllenge Qud Construction Properties of Prllelogrms Bsebll Box Lbels Bseblls Pcked in Cube-Shped Boxes Pcking Mtt s Mrbles Grphing & Geometry Review Work Plce Instructions 6B Polygon Serch Finding Volume Volumes Record Sheet Tnk Volume Work Plce Instructions 6C Volume Bingo Volume Problems Pet Sncks More of Cleb s Flgs Aron s Arrys Thinking About Flgs Cleb s U.S. Themed Flgs Sophi s Work Design--Flg Chllenge Boxes & Bnners Simplifying Frctions Review Bridges in Mthemtics Grde 5 Student Book

6 Unit 7 Division & Decimls Rob s Review Arry Work Work Plce Instructions 7A Roll Five Roll Five & Rtio Tbles Fruit Pizz Thinking About Division Food Project Division with Frctions Story Problems Thinking About Money Multipliction Round & Check Frction Division on Clock Work Plce Instructions 7B Quotients Rce to One Hundred Dividing Frctions & Whole Numbers Dividing Mrbles Deling with Reminders Story Problems: Division with Reminders Division Prctice Exponents & Powers of Ten Ptterns in Multiplying by Powers of Ten Multiplying by Powers of Ten Prctice More Exponents & Powers of Ten Ptterns in Dividing by Powers of Ten Dividing by Powers of Ten Prctice Multiplying & Dividing by Powers of Ten Using the Are Model to Multiply Deciml Numbers Multiplying Two Deciml Numbers More Decks Decimls, Powers of Ten & Exponents Deciml Division with Money Compring & Multiplying Frctions & Decimls Using Models & Strtegies Common Division Mistkes Reviewing Deciml Addition & Subtrction Unit 8 Solr Design Temperture Conversions Absorbing & Reflecting Solr Energy Reding Line Grph Concentrting Solr Energy Solr Concentrtion Collecting Solr Energy Solr Collection Solr Boxes More Solr Boxes Chnging Surfce Are Erth Mterils Erth Mterils in Boxes Erth Mterils Questions Erth Mterils Experiment Window Orienttion Mking Windows Insultion Mterils Amount of Insultion Mterils Insulting Our House Buying Window Mterils Testing Our House Insultion Experiment Insultion Grph Questions Using Energy Solr Devices Solr PV Cells Solr Collector Experiment Choosing Our Mterils Another Solr House Determining House Mterils Testing Our Finl Houses Floor Pln Room Volume More Solr Fetures Bridges in Mthemtics Grde 5 Student Book

7 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 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 = = 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

8 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 = = 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

9 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 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 Bridges in Mthemtics Grde 5 Student Book 3

10 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 Bridges in Mthemtics Grde 5 Student Book 4

11 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) 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 Bridges in Mthemtics Grde 5 Student Book 5

12 Unit 1 Module 1 Session 5 Fct Connections 1 Fill in the fcts. Look for reltionships 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 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 = b 4 12 = c 8 8 = 5 CHALLENGE Complete the following equtions = (2 67) b = 2 ( 198) c 3,794 = 2 (4 3,794) Bridges in Mthemtics Grde 5 Student Book 6

13 Unit 1 Module 2 Session 1 Are They Equivlent? 1 Mrk ech of the following equtions true or flse nd tell how you know = 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 = 8 d 8 = 16 2 e 4 = 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 Is she correct? Prove your nswer. Bridges in Mthemtics Grde 5 Student Book 7

14 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 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

15 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

16 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 nd remove 2 groups of 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 = = Bridges in Mthemtics Grde 5 Student Book 10

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

18 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

19 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

20 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

21 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

22 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

23 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? = (100 34) (1 34) b = Bridges in Mthemtics Grde 5 Student Book 17

24 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 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

25 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

26 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 =. 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

27 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 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

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

29 Unit 1 Module 4 Session 1 Mthemticl Thinking 1 Ktie sys she cn multiply 5 68 by multiplying 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 by multiplying 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

30 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 $ Sr s dd ws so plesed with their work tht he gve ech of the 6 children $2.00 tip in ddition to the $ 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

31 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 $ 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

32 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

33 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

34 Unit 1 Module 4 Session 4 Quotients Win, Gme 2 Red Tem Blue Tem = = = = = = Red Score Bridges in Mthemtics Grde 5 Student Book 28 Blue Score

35 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 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 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 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

36 Unit 1 Module 4 Session 4 Multipliction & Division Problems 1 Fill in the missing numbers Write n eqution to nswer ech question below. Question Eqution Answer ex How mny qurters re in 75? = 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

37 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 = = 4 = = = 80 6 = 480 = 30 1,200 1, ,200 1, = 48 = = = = 6 = = 8 = = = 40 9 = 360 = 9 4 = 36 = = = = 9 = = 4 = = = 30 7 = 210 = 7 3 = 21 = = = = 7 = 21 7 = 3 = = Bridges in Mthemtics Grde 5 Student Book 31

38 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 dollrs. Angel hs dollrs. How much money do the boys hve together? Record your nswer s frction nd s deciml. c CHALLENGE Iris hs dollrs. Violet hs 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

39 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 b 1 2 c Color in the strips to show the improper frctions nmed below. The write the frction s mixed number. Ech strip represents 1 whole. ex b c Fill in the blnks to show the unit frction s frction of dollr nd s deciml (money) nottion. ex 1 10 = = = = 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 She wrote: $ $0.75 = $0.80, which is the sme s of dollr. So = Do you gree or disgree with her work? 5 Thnh hd to solve He wrote: $ $0.20 = $0.30, which is the sme s 3 10 of dollr, so = Do you gree or disgree with his work? Bridges in Mthemtics Grde 5 Student Book 33

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

41 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 Use the pictures bove to help complete ech comprison below using <, >, or =. ex > b c d e Subtrct these frctions. (Hint: Think bout money or clocks to help.) = b = c = d = 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

42 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

43 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/ = 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

44 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 Model ech problem on clock to dd the frctions. Remember to lbel your work = b = c = d = Bridges in Mthemtics Grde 5 Student Book 38

45 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, 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

46 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 b 4 c 4 1 d e 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 = = 7 6 or = + b = + c = + Bridges in Mthemtics Grde 5 Student Book 40

47 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 = 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

48 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, b Explin how you figured out where to plce ech frction long the line. 2 Yesterdy Crson recycled 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 miles yesterdy. Her sister Lol rn did Lol run thn Crmen? Show ll your work. miles. How much frther Bridges in Mthemtics Grde 5 Student Book 42

49 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 = = = = 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

50 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 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

51 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 b Mrk both the frction nd the distnce trveled on the number line below. 1 4 of 24 km b km 0 km 24 km 4 Mrk the frction nd the distnce trveled on the number line below 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

52 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 = 4 3 = is n improper frction becuse 4 is greter thn is equl to 1, so 4 3 is equl to = = = = = = = = = 2 Find two different wys to show tht is not equl to 2 6. You cn use numbers, words, or lbeled sketches. Bridges in Mthemtics Grde 5 Student Book 46

53 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

54 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 $ brs 4 brs 1 br $10 $5 $ Now Michel wnts to buy bgs of mixed nuts. He cn buy 12 bgs for 15 dollrs or 16 bgs for $ 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

55 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 The sum is more thn = nd = Bridges in Mthemtics Grde 5 Student Book 49

56 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 $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

57 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

58 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 = = 9 8 = = + = = b = + = = c = = 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

SECOND EDITION HOME CONNECTIONS GRADE

SECOND EDITION HOME CONNECTIONS GRADE SECOND EDITION HOME CONNECTIONS GRADE 5 Bridges in Mthemtics Second Edition Grde 5 Home Connections Volumes & 2 The Bridges in Mthemtics Grde 5 pckge consists of: Bridges in Mthemtics Grde 5 Techers Guide

More information

Student Book SERIES. Fractions. Name

Student Book SERIES. Fractions. Name D Student Book Nme Series D Contents Topic Introducing frctions (pp. ) modelling frctions frctions of collection compring nd ordering frctions frction ingo pply Dte completed / / / / / / / / Topic Types

More information

Student Book SERIES. Patterns and Algebra. Name

Student Book SERIES. Patterns and Algebra. Name E Student Book 3 + 7 5 + 5 Nme Contents Series E Topic Ptterns nd functions (pp. ) identifying nd creting ptterns skip counting completing nd descriing ptterns predicting repeting ptterns predicting growing

More information

SECOND EDITION HOME CONNECTIONS ANSWER KEY GRADE

SECOND EDITION HOME CONNECTIONS ANSWER KEY GRADE SECOND EDITION HOME CONNECTIONS ANSWER KEY GRADE 5 Bridges in Mthemtics Second Edition Grde 5 Home Connections Volumes & 2 The Bridges in Mthemtics Grde 5 pckge consists of: Bridges in Mthemtics Grde 5

More information

SECOND EDITION HOME CONNECTIONS GRADE

SECOND EDITION HOME CONNECTIONS GRADE SECOND EDITION HOME COECTIONS GRADE 4 Bridges in Mthemtics Second Edition Grde 4 Home Connections Volumes 1 & 2 The Bridges in Mthemtics Grde 4 pckge consists of: Bridges in Mthemtics Grde 4 Techers Guide

More information

GRADE SECOND EDITION HOME CONNECTIONS ANSWER KEY

GRADE SECOND EDITION HOME CONNECTIONS ANSWER KEY HOME CONNECTIONS SECOND EDITION ANSWER KEY GRADE 4 Bridges in Mthemtics Second Edition Grde 4 Home Connections Volumes 1 & 2 The Bridges in Mthemtics Grde 4 pckge consists of: Bridges in Mthemtics Grde

More information

Make Your Math Super Powered

Make Your Math Super Powered Mke Your Mth Super Powered: Use Gmes, Chllenges, nd Puzzles Where s the fun? Lern Mth Workshop model by prticipting in one nd explore fun nocost/low-cost gmes nd puzzles tht you cn esily bring into your

More information

Samantha s Strategies page 1 of 2

Samantha s Strategies page 1 of 2 Unit 1 Module 2 Session 3 Smnth s Strtegies pge 1 of 2 Smnth hs been working with vriety of multiplition strtegies. 1 Write n expression to desribe eh of the sttements Smnth mde. To solve 18 20, I find

More information

The Math Learning Center PO Box 12929, Salem, Oregon Math Learning Center

The Math Learning Center PO Box 12929, Salem, Oregon Math Learning Center Resource Overview Quntile Mesure: Skill or Concept: 300Q Model the concept of ddition for sums to 10. (QT N 36) Model the concept of sutrction using numers less thn or equl to 10. (QT N 37) Write ddition

More information

First Round Solutions Grades 4, 5, and 6

First Round Solutions Grades 4, 5, and 6 First Round Solutions Grdes 4, 5, nd 1) There re four bsic rectngles not mde up of smller ones There re three more rectngles mde up of two smller ones ech, two rectngles mde up of three smller ones ech,

More information

Series. Teacher. Numbers

Series. Teacher. Numbers Series B Techer Copyright 2009 3P Lerning. All rights reserved. First edition printed 2009 in Austrli. A ctlogue record for this book is vilble from 3P Lerning Ltd. ISBN 978-1-921860-17-1 Ownership of

More information

Addition Mission: Facts Practice

Addition Mission: Facts Practice Addition Mission: Fcts Prctice ++ Tble of Contents Addition Mission: Fcts Prctice Mth Counting Apple Mth Hippity Hop Crunchy Celery Addition Superstr Cherry Mth At the Librry Mth Sld -0 Sunny Summer Mth

More information

So Many Possibilities page 1 of 2

So Many Possibilities page 1 of 2 Otober Solving Problems Ativities & So Mny Possibilities pge of Use the blnk spe to solve eh problem. Show ll your work inluding numbers, words, or lbeled skethes. Write omplete sentene below your work

More information

1 tray of toffee 1 bar of toffee. 10 In the decimal number, 0 7, the 7 refers to 7 tenths or

1 tray of toffee 1 bar of toffee. 10 In the decimal number, 0 7, the 7 refers to 7 tenths or Chpter 3 Deciml Numers Do you know wht DECIMAL is? In chpter, we delt with units, s, 0 s nd 00 s. When you tke single unit nd divide it into (or 0 or 00) its, wht we then hve re deciml frctions of whole

More information

Polar Coordinates. July 30, 2014

Polar Coordinates. July 30, 2014 Polr Coordintes July 3, 4 Sometimes it is more helpful to look t point in the xy-plne not in terms of how fr it is horizontlly nd verticlly (this would men looking t the Crtesin, or rectngulr, coordintes

More information

Abacaba-Dabacaba! by Michael Naylor Western Washington University

Abacaba-Dabacaba! by Michael Naylor Western Washington University Abcb-Dbcb! by Michel Nylor Western Wshington University The Abcb structure shows up in n mzing vriety of plces. This rticle explores 10 surprising ides which ll shre this pttern, pth tht will tke us through

More information

GRADE SECOND EDITION STUDENT BOOK ANSWER KEY

GRADE SECOND EDITION STUDENT BOOK ANSWER KEY STUDENT BOOK SECOND EDITION ANSWER KEY GRADE 5 Bridges in Mathematics Second Edition Grade 5 Student Book Volumes & 2 The Bridges in Mathematics Grade 5 package consists of: Bridges in Mathematics Grade

More information

Theme: Don t get mad. Learn mod.

Theme: Don t get mad. Learn mod. FERURY When 1 is divided by 5, the reminder is. nother wy to sy this is opyright 015 The Ntionl ouncil of Techers of Mthemtics, Inc. www.nctm.org. ll rights reserved. This mteril my not be copied or distributed

More information

TRUMBULL PUBLIC SCHOOLS

TRUMBULL PUBLIC SCHOOLS PS TRUMBULL PUBLC SCHOOLS CURRCULUM DEPARTMENT 6254 Min St., Trumbull, CT 06611 (203) 452-4336 FAX (203) 452-4342 Lind S. Pslov, Ed.D. Director of Curriculum, nstruction, & Assessments e-mil: pslovl@trumbullps.org

More information

Geometric quantities for polar curves

Geometric quantities for polar curves Roerto s Notes on Integrl Clculus Chpter 5: Bsic pplictions of integrtion Section 10 Geometric quntities for polr curves Wht you need to know lredy: How to use integrls to compute res nd lengths of regions

More information

Math Circles Finite Automata Question Sheet 3 (Solutions)

Math Circles Finite Automata Question Sheet 3 (Solutions) Mth Circles Finite Automt Question Sheet 3 (Solutions) Nickols Rollick nrollick@uwterloo.c Novemer 2, 28 Note: These solutions my give you the nswers to ll the prolems, ut they usully won t tell you how

More information

MONOCHRONICLE STRAIGHT

MONOCHRONICLE STRAIGHT UPDATED 09-2010 HYDROCARBON Hydrocrbon is poncho-style cowl in bulky-weight yrn, worked in the round. It ws designed to be s prcticl s it is stylish, with shping tht covers the neck nd shoulders nd the

More information

SPECIAL EDITION. Spring 2012 Ezine. where crafty is contagious

SPECIAL EDITION. Spring 2012 Ezine.   where crafty is contagious Spring 2012 Ezine SPECIAL EDITION www.clubchiccircle.com where crfty is contgious shmrock sttionery It is so esy to mke these festive homemde crds! Mke homemde stmp from the end of n pencil erser. With

More information

Lecture 20. Intro to line integrals. Dan Nichols MATH 233, Spring 2018 University of Massachusetts.

Lecture 20. Intro to line integrals. Dan Nichols MATH 233, Spring 2018 University of Massachusetts. Lecture 2 Intro to line integrls Dn Nichols nichols@mth.umss.edu MATH 233, Spring 218 University of Msschusetts April 12, 218 (2) onservtive vector fields We wnt to determine if F P (x, y), Q(x, y) is

More information

Patterns and Relationships

Patterns and Relationships Series Techer Ptterns nd Reltionships opyright 009 3P Lerning. All rights reserved. First edition printed 009 in Austrli. A ctlogue record for this ook is ville from 3P Lerning Ltd. ISBN 978-1-91860-3-4

More information

Skills Practice Skills Practice for Lesson 4.1

Skills Practice Skills Practice for Lesson 4.1 Skills Prctice Skills Prctice for Lesson.1 Nme Dte Tiling Bthroom Wll Simplifying Squre Root Expressions Vocbulry Mtch ech definition to its corresponding term. 1. n expression tht involves root. rdicnd

More information

ECE 274 Digital Logic. Digital Design. Datapath Components Shifters, Comparators, Counters, Multipliers Digital Design

ECE 274 Digital Logic. Digital Design. Datapath Components Shifters, Comparators, Counters, Multipliers Digital Design ECE 27 Digitl Logic Shifters, Comprtors, Counters, Multipliers Digitl Design..7 Digitl Design Chpter : Slides to ccompny the textbook Digitl Design, First Edition, by Frnk Vhid, John Wiley nd Sons Publishers,

More information

10.4 AREAS AND LENGTHS IN POLAR COORDINATES

10.4 AREAS AND LENGTHS IN POLAR COORDINATES 65 CHAPTER PARAMETRIC EQUATINS AND PLAR CRDINATES.4 AREAS AND LENGTHS IN PLAR CRDINATES In this section we develop the formul for the re of region whose oundry is given y polr eqution. We need to use the

More information

9.4. ; 65. A family of curves has polar equations. ; 66. The astronomer Giovanni Cassini ( ) studied the family of curves with polar equations

9.4. ; 65. A family of curves has polar equations. ; 66. The astronomer Giovanni Cassini ( ) studied the family of curves with polar equations 54 CHAPTER 9 PARAMETRIC EQUATINS AND PLAR CRDINATES 49. r, 5. r sin 3, 5 54 Find the points on the given curve where the tngent line is horizontl or verticl. 5. r 3 cos 5. r e 53. r cos 54. r sin 55. Show

More information

Unit 1: Chapter 4 Roots & Powers

Unit 1: Chapter 4 Roots & Powers Unit 1: Chpter 4 Roots & Powers Big Ides Any number tht cn be written s the frction mm, nn 0, where m nd n re integers, is nn rtionl. Eponents cn be used to represent roots nd reciprocls of rtionl numbers.

More information

Seven Sisters. Visit for video tutorials

Seven Sisters. Visit   for video tutorials Seven Sisters This imge is from www.quiltstudy.org. Plese visit this website for more informtion on Seven Sisters quilt ptterns. Visit www.blocloc.com for video tutorils 1 The Seven Sisters design cn be

More information

Example. Check that the Jacobian of the transformation to spherical coordinates is

Example. Check that the Jacobian of the transformation to spherical coordinates is lss, given on Feb 3, 2, for Mth 3, Winter 2 Recll tht the fctor which ppers in chnge of vrible formul when integrting is the Jcobin, which is the determinnt of mtrix of first order prtil derivtives. Exmple.

More information

METHOD OF LOCATION USING SIGNALS OF UNKNOWN ORIGIN. Inventor: Brian L. Baskin

METHOD OF LOCATION USING SIGNALS OF UNKNOWN ORIGIN. Inventor: Brian L. Baskin METHOD OF LOCATION USING SIGNALS OF UNKNOWN ORIGIN Inventor: Brin L. Bskin 1 ABSTRACT The present invention encompsses method of loction comprising: using plurlity of signl trnsceivers to receive one or

More information

CHAPTER 2 LITERATURE STUDY

CHAPTER 2 LITERATURE STUDY CHAPTER LITERATURE STUDY. Introduction Multipliction involves two bsic opertions: the genertion of the prtil products nd their ccumultion. Therefore, there re two possible wys to speed up the multipliction:

More information

Patterns and Algebra

Patterns and Algebra Student Book Series D Mthletis Instnt Workooks Copyright Series D Contents Topi Ptterns nd funtions identifying nd reting ptterns skip ounting ompleting nd desriing ptterns numer ptterns in tles growing

More information

c The scaffold pole EL is 8 m long. How far does it extend beyond the line JK?

c The scaffold pole EL is 8 m long. How far does it extend beyond the line JK? 3 7. 7.2 Trigonometry in three dimensions Questions re trgeted t the grdes indicted The digrm shows the ck of truck used to crry scffold poles. L K G m J F C 0.8 m H E 3 m D 6.5 m Use Pythgors Theorem

More information

Kirchhoff s Rules. Kirchhoff s Laws. Kirchhoff s Rules. Kirchhoff s Laws. Practice. Understanding SPH4UW. Kirchhoff s Voltage Rule (KVR):

Kirchhoff s Rules. Kirchhoff s Laws. Kirchhoff s Rules. Kirchhoff s Laws. Practice. Understanding SPH4UW. Kirchhoff s Voltage Rule (KVR): SPH4UW Kirchhoff s ules Kirchhoff s oltge ule (K): Sum of voltge drops round loop is zero. Kirchhoff s Lws Kirchhoff s Current ule (KC): Current going in equls current coming out. Kirchhoff s ules etween

More information

Synchronous Generator Line Synchronization

Synchronous Generator Line Synchronization Synchronous Genertor Line Synchroniztion 1 Synchronous Genertor Line Synchroniztion Introduction One issue in power genertion is synchronous genertor strting. Typiclly, synchronous genertor is connected

More information

Comparing Fractions page 1 of 2 1 Color in the grid to show the fractions below. Each grid represents 1 whole. a 1 2 b 1. d 16

Comparing Fractions page 1 of 2 1 Color in the grid to show the fractions below. Each grid represents 1 whole. a 1 2 b 1. d 16 Unit 2 Moule Session 2 Compring Frtions pge of 2 Color in the gri to show the frtions below. Eh gri represents whole. 2 b 4 0 0 e 4 2 Use the pitures bove to help omplete eh omprison below using ,

More information

Section 16.3 Double Integrals over General Regions

Section 16.3 Double Integrals over General Regions Section 6.3 Double Integrls over Generl egions Not ever region is rectngle In the lst two sections we considered the problem of integrting function of two vribles over rectngle. This sitution however is

More information

Spotted at APA. Top Points this week. Spring f ro. Year 7. Year 8. Year 9. Year 10. Year 11. Student Newsletter ~

Spotted at APA. Top Points this week. Spring f ro. Year 7. Year 8. Year 9. Year 10. Year 11. Student Newsletter ~ Spring 2017 Top Points this week Yer 7 ly l x Mo Ale Yer 8 ict is Le w ed Be n Yer 9 sh er Ele Du ej on e Yer 10 Yer 11 ri em Me Another very busy week in the cdemy hs just gone by s we hd our APA World

More information

Misty. Sudnow Dot Songs

Misty. Sudnow Dot Songs Sudnow Dot Songs isty T The Dot Song is nottionl system tht depicts voiced chords in wy where the non-music reder cn find these firly redily. But the Dot Song is not intended be red, not s sight reder

More information

Exercise 1-1. The Sine Wave EXERCISE OBJECTIVE DISCUSSION OUTLINE. Relationship between a rotating phasor and a sine wave DISCUSSION

Exercise 1-1. The Sine Wave EXERCISE OBJECTIVE DISCUSSION OUTLINE. Relationship between a rotating phasor and a sine wave DISCUSSION Exercise 1-1 The Sine Wve EXERCISE OBJECTIVE When you hve completed this exercise, you will be fmilir with the notion of sine wve nd how it cn be expressed s phsor rotting round the center of circle. You

More information

Algebra Practice. Dr. Barbara Sandall, Ed.D., and Travis Olson, M.S.

Algebra Practice. Dr. Barbara Sandall, Ed.D., and Travis Olson, M.S. By Dr. Brr Sndll, Ed.D., Dr. Melfried Olson, Ed.D., nd Trvis Olson, M.S. COPYRIGHT 2006 Mrk Twin Medi, Inc. ISBN 978-1-58037-754-6 Printing No. 404042-EB Mrk Twin Medi, Inc., Pulishers Distriuted y Crson-Dellos

More information

ECE 274 Digital Logic Fall 2009 Digital Design

ECE 274 Digital Logic Fall 2009 Digital Design igitl Logic ll igitl esign MW -:PM, IL Romn Lysecky, rlysecky@ece.rizon.edu http://www.ece.rizon.edu/~ece hpter : Introduction Slides to ccompny the textbook igitl esign, irst dition, by rnk Vhid, John

More information

Challenge! 1 Warm-up. 2 Conversation. Language box. a Discuss the pictures with a partner.

Challenge! 1 Warm-up. 2 Conversation. Language box. a Discuss the pictures with a partner. Focus Grmmr Vocbulry Strtegy tlking bout wishes nd possibilities second conditionl I wish + simple pst verbs nd definitions moving to new country showing surprise 1 Wrm-up Discuss the pictures with prtner.

More information

CS 135: Computer Architecture I. Boolean Algebra. Basic Logic Gates

CS 135: Computer Architecture I. Boolean Algebra. Basic Logic Gates Bsic Logic Gtes : Computer Architecture I Boolen Algebr Instructor: Prof. Bhgi Nrhri Dept. of Computer Science Course URL: www.ses.gwu.edu/~bhgiweb/cs35/ Digitl Logic Circuits We sw how we cn build the

More information

Have u Herd? Herd is the Word. join. toolkit. COOL WAYS to TALK ABOUT BOOKS WITH YOUR

Have u Herd? Herd is the Word. join. toolkit. COOL WAYS to TALK ABOUT BOOKS WITH YOUR Hve u Herd? Herd is the Word join Th to K nks Wel ir from Libr lingto comin ry L n b g brilli up with for The nt nme the Word o Herd f! toolkit COOL WAYS to TALK ABOUT BOOKS WITH YOUR your friends for

More information

Spiral Tilings with C-curves

Spiral Tilings with C-curves Spirl Tilings with -curves Using ombintorics to Augment Trdition hris K. Plmer 19 North Albny Avenue hicgo, Illinois, 0 chris@shdowfolds.com www.shdowfolds.com Abstrct Spirl tilings used by rtisns through

More information

Algorithms for Memory Hierarchies Lecture 14

Algorithms for Memory Hierarchies Lecture 14 Algorithms for emory Hierrchies Lecture 4 Lecturer: Nodri Sitchinv Scribe: ichel Hmnn Prllelism nd Cche Obliviousness The combintion of prllelism nd cche obliviousness is n ongoing topic of reserch, in

More information

Application Note. Differential Amplifier

Application Note. Differential Amplifier Appliction Note AN367 Differentil Amplifier Author: Dve n Ess Associted Project: Yes Associted Prt Fmily: CY8C9x66, CY8C7x43, CY8C4x3A PSoC Designer ersion: 4. SP3 Abstrct For mny sensing pplictions, desirble

More information

Domination and Independence on Square Chessboard

Domination and Independence on Square Chessboard Engineering nd Technology Journl Vol. 5, Prt, No. 1, 017 A.A. Omrn Deprtment of Mthemtics, College of Eduction for Pure Science, University of bylon, bylon, Irq pure.hmed.omrn@uobby lon.edu.iq Domintion

More information

FP2 POLAR COORDINATES: PAST QUESTIONS

FP2 POLAR COORDINATES: PAST QUESTIONS FP POLAR COORDINATES: PAST QUESTIONS. The curve C hs polr eqution r = cosθ, () Sketch the curve C. () (b) Find the polr coordintes of the points where tngents to C re prllel to the initil line. (6) (c)

More information

The Discussion of this exercise covers the following points:

The Discussion of this exercise covers the following points: Exercise 4 Bttery Chrging Methods EXERCISE OBJECTIVE When you hve completed this exercise, you will be fmilir with the different chrging methods nd chrge-control techniques commonly used when chrging Ni-MI

More information

EQ: What are the similarities and differences between matrices and real numbers?

EQ: What are the similarities and differences between matrices and real numbers? Unit 4 Lesson 1 Essentil Question Stndrds Objectives Vocbulry Mtrices Mtrix Opertions Wht re the similrities nd differences between mtrices nd rel numbers? M.ALGII.2.4 Unit 4: Lesson 1 Describe how you

More information

Topic 20: Huffman Coding

Topic 20: Huffman Coding Topic 0: Huffmn Coding The uthor should gze t Noh, nd... lern, s they did in the Ark, to crowd gret del of mtter into very smll compss. Sydney Smith, dinburgh Review Agend ncoding Compression Huffmn Coding

More information

ECE 274 Digital Logic

ECE 274 Digital Logic ECE - Digitl Logic (Textbook - Required) ECE Digitl Logic Instructor: Romn Lysecky, rlysecky@ece.rizon.edu Office Hours: TBA, ECE F Lecture: MWF :-: PM, ILC Course Website: http://www.ece.rizon.edu/~ece/

More information

Triangles and parallelograms of equal area in an ellipse

Triangles and parallelograms of equal area in an ellipse 1 Tringles nd prllelogrms of equl re in n ellipse Roert Buonpstore nd Thoms J Osler Mthemtics Deprtment RownUniversity Glssoro, NJ 0808 USA uonp0@studentsrownedu osler@rownedu Introduction In the pper

More information

Birka B22: threaded in variation

Birka B22: threaded in variation Tblet Weving: 4-Hole Ptterns Stringcrfter The chrt, fining your wy roun the pttern, n suggestions for viking style bris for rnks in the Drchenwl Acemy of Defence You will nee: 22 crs 1 repet 88 Thres:

More information

THE SONGWRITING CLUB SONGS

THE SONGWRITING CLUB SONGS THE SOGWRITIG LUB SOGS LYRIS AD UKE HORDS BOOK OE It s time to sing with your friends nd fmily! Tips for plying re included re on the lst pge. You cn listen to the recordings (nd the kroke trcks) nd find

More information

SOLVING TRIANGLES USING THE SINE AND COSINE RULES

SOLVING TRIANGLES USING THE SINE AND COSINE RULES Mthemtics Revision Guides - Solving Generl Tringles - Sine nd Cosine Rules Pge 1 of 17 M.K. HOME TUITION Mthemtics Revision Guides Level: GCSE Higher Tier SOLVING TRIANGLES USING THE SINE AND COSINE RULES

More information

INTRODUCTION TO TRIGONOMETRY AND ITS APPLICATIONS

INTRODUCTION TO TRIGONOMETRY AND ITS APPLICATIONS CHAPTER 8 INTRODUCTION TO TRIGONOMETRY AND ITS APPLICATIONS (A) Min Concepts nd Results Trigonometric Rtios of the ngle A in tringle ABC right ngled t B re defined s: sine of A = sin A = side opposite

More information

LECTURE 9: QUADRATIC RESIDUES AND THE LAW OF QUADRATIC RECIPROCITY

LECTURE 9: QUADRATIC RESIDUES AND THE LAW OF QUADRATIC RECIPROCITY LECTURE 9: QUADRATIC RESIDUES AND THE LAW OF QUADRATIC RECIPROCITY 1. Bsic roerties of qudrtic residues We now investigte residues with secil roerties of lgebric tye. Definition 1.1. (i) When (, m) 1 nd

More information

Polar coordinates 5C. 1 a. a 4. π = 0 (0) is a circle centre, 0. and radius. The area of the semicircle is π =. π a

Polar coordinates 5C. 1 a. a 4. π = 0 (0) is a circle centre, 0. and radius. The area of the semicircle is π =. π a Polr coordintes 5C r cos Are cos d (cos + ) sin + () + 8 cos cos r cos is circle centre, nd rdius. The re of the semicircle is. 8 Person Eduction Ltd 8. Copying permitted for purchsing institution only.

More information

Yellowknife km Vancouver km NEL

Yellowknife km Vancouver km NEL ic tio n Yellowknife Pr e- Pu bl 1566 km 67.3 Vncouver 112 1870 km hpter 3 tio n cute Tringle Trigonometry ic LERNING GOLS You will be ble to develop your sptil sense by Pr e- Pu bl? Using the sine lw

More information

Translate and Classify Conic Sections

Translate and Classify Conic Sections TEKS 9.6 A.5.A, A.5.B, A.5.D, A.5.E Trnslte nd Clssif Conic Sections Before You grphed nd wrote equtions of conic sections. Now You will trnslte conic sections. Wh? So ou cn model motion, s in E. 49. Ke

More information

Synchronous Machine Parameter Measurement

Synchronous Machine Parameter Measurement Synchronous Mchine Prmeter Mesurement 1 Synchronous Mchine Prmeter Mesurement Introduction Wound field synchronous mchines re mostly used for power genertion but lso re well suited for motor pplictions

More information

How to Build Wealth Like Warren Buffett.

How to Build Wealth Like Warren Buffett. Your FREE gift for ordering How to Build Welth Like Wrren Buffett The video ABC-TV clled lively, informtive, nd lot of fun. You cn t help but get swept up by the enthusism of this rewrding film. Don t

More information

Defining the Rational Numbers

Defining the Rational Numbers MATH10 College Mthemtis - Slide Set 2 1. Rtionl Numers 1. Define the rtionl numers. 2. Redue rtionl numers.. Convert etween mixed numers nd improper frtions. 4. Express rtionl numers s deimls.. Express

More information

EE Controls Lab #2: Implementing State-Transition Logic on a PLC

EE Controls Lab #2: Implementing State-Transition Logic on a PLC Objective: EE 44 - Controls Lb #2: Implementing Stte-rnsition Logic on PLC ssuming tht speed is not of essence, PLC's cn be used to implement stte trnsition logic. he dvntge of using PLC over using hrdwre

More information

CS2204 DIGITAL LOGIC & STATE MACHINE DESIGN SPRING 2005

CS2204 DIGITAL LOGIC & STATE MACHINE DESIGN SPRING 2005 CS2204 DIGITAL LOGIC & STATE MACHINE DESIGN SPRING 2005 EXPERIMENT 1 FUNDAMENTALS 1. GOALS : Lern how to develop cr lrm digitl circuit during which the following re introduced : CS2204 l fundmentls, nd

More information

Synchronous Machine Parameter Measurement

Synchronous Machine Parameter Measurement Synchronous Mchine Prmeter Mesurement 1 Synchronous Mchine Prmeter Mesurement Introduction Wound field synchronous mchines re mostly used for power genertion but lso re well suited for motor pplictions

More information

Section 17.2: Line Integrals. 1 Objectives. 2 Assignments. 3 Maple Commands. 1. Compute line integrals in IR 2 and IR Read Section 17.

Section 17.2: Line Integrals. 1 Objectives. 2 Assignments. 3 Maple Commands. 1. Compute line integrals in IR 2 and IR Read Section 17. Section 7.: Line Integrls Objectives. ompute line integrls in IR nd IR 3. Assignments. Red Section 7.. Problems:,5,9,,3,7,,4 3. hllenge: 6,3,37 4. Red Section 7.3 3 Mple ommnds Mple cn ctully evlute line

More information

MATH 118 PROBLEM SET 6

MATH 118 PROBLEM SET 6 MATH 118 PROBLEM SET 6 WASEEM LUTFI, GABRIEL MATSON, AND AMY PIRCHER Section 1 #16: Show tht if is qudrtic residue modulo m, nd b 1 (mod m, then b is lso qudrtic residue Then rove tht the roduct of the

More information

Module 9. DC Machines. Version 2 EE IIT, Kharagpur

Module 9. DC Machines. Version 2 EE IIT, Kharagpur Module 9 DC Mchines Version EE IIT, Khrgpur esson 40 osses, Efficiency nd Testing of D.C. Mchines Version EE IIT, Khrgpur Contents 40 osses, efficiency nd testing of D.C. mchines (esson-40) 4 40.1 Gols

More information

MEASURE THE CHARACTERISTIC CURVES RELEVANT TO AN NPN TRANSISTOR

MEASURE THE CHARACTERISTIC CURVES RELEVANT TO AN NPN TRANSISTOR Electricity Electronics Bipolr Trnsistors MEASURE THE HARATERISTI URVES RELEVANT TO AN NPN TRANSISTOR Mesure the input chrcteristic, i.e. the bse current IB s function of the bse emitter voltge UBE. Mesure

More information

SAMPLE. End of term: TEST A. Year 4. Name Class Date. Complete the missing numbers in the sequences below.

SAMPLE. End of term: TEST A. Year 4. Name Class Date. Complete the missing numbers in the sequences below. End of term: TEST A You will need penil nd ruler. Yer Nme Clss Dte 2 Complete the missing numers in the sequenes elow. 50 25 00 75 8 30 3 28 2 9 Put irle round two of the shpes elow whih hve 3 shded. 3

More information

Experiment 3: Non-Ideal Operational Amplifiers

Experiment 3: Non-Ideal Operational Amplifiers Experiment 3: Non-Idel Opertionl Amplifiers Fll 2009 Equivlent Circuits The bsic ssumptions for n idel opertionl mplifier re n infinite differentil gin ( d ), n infinite input resistnce (R i ), zero output

More information

Lecture 16. Double integrals. Dan Nichols MATH 233, Spring 2018 University of Massachusetts.

Lecture 16. Double integrals. Dan Nichols MATH 233, Spring 2018 University of Massachusetts. Leture 16 Double integrls Dn Nihols nihols@mth.umss.edu MATH 233, Spring 218 University of Msshusetts Mrh 27, 218 (2) iemnn sums for funtions of one vrible Let f(x) on [, b]. We n estimte the re under

More information

A Development of Earthing-Resistance-Estimation Instrument

A Development of Earthing-Resistance-Estimation Instrument A Development of Erthing-Resistnce-Estimtion Instrument HITOSHI KIJIMA Abstrct: - Whenever erth construction work is done, the implnted number nd depth of electrodes hve to be estimted in order to obtin

More information

CS2204 DIGITAL LOGIC & STATE MACHINE DESIGN fall 2008

CS2204 DIGITAL LOGIC & STATE MACHINE DESIGN fall 2008 CS224 DIGITAL LOGIC & STATE MACHINE DESIGN fll 28 STAND ALONE XILINX PROJECT 2-TO- MULTIPLEXER. Gols : Lern how to develop stnd lone 2-to- multiplexer () Xilinx project during which the following re introduced

More information

Engineer-to-Engineer Note

Engineer-to-Engineer Note Engineer-to-Engineer Note EE-297 Technicl notes on using Anlog Devices DSPs, processors nd development tools Visit our Web resources http://www.nlog.com/ee-notes nd http://www.nlog.com/processors or e-mil

More information

University of North Carolina-Charlotte Department of Electrical and Computer Engineering ECGR 4143/5195 Electrical Machinery Fall 2009

University of North Carolina-Charlotte Department of Electrical and Computer Engineering ECGR 4143/5195 Electrical Machinery Fall 2009 Problem 1: Using DC Mchine University o North Crolin-Chrlotte Deprtment o Electricl nd Computer Engineering ECGR 4143/5195 Electricl Mchinery Fll 2009 Problem Set 4 Due: Thursdy October 8 Suggested Reding:

More information

& Y Connected resistors, Light emitting diode.

& Y Connected resistors, Light emitting diode. & Y Connected resistors, Light emitting diode. Experiment # 02 Ojectives: To get some hndson experience with the physicl instruments. To investigte the equivlent resistors, nd Y connected resistors, nd

More information

Cardinal Fiber Co. Fine hand dyed yarns

Cardinal Fiber Co. Fine hand dyed yarns Crdinl Fiber Co. Fine hnd dyed yrns Crdinl Fiber Compny Trunk Show SATURDAY MAY 5 1:00 TO 3:00 PM Frncofille nits hs new nme. ocl hnd dyer, B. Devn Steiner, is now crfting her beutiful yrns under the nme

More information

Arduino for Model Railroaders

Arduino for Model Railroaders Steve Mssikker Arduino for Model Rilroders Ornge Book Protocol 2 Full Description November 28 Tble of contents Dontors Documenttion Kit V.4-8 Pge 2 I wnt to tke the time to sincerely thnk you for your

More information

Experiment 3: Non-Ideal Operational Amplifiers

Experiment 3: Non-Ideal Operational Amplifiers Experiment 3: Non-Idel Opertionl Amplifiers 9/11/06 Equivlent Circuits The bsic ssumptions for n idel opertionl mplifier re n infinite differentil gin ( d ), n infinite input resistnce (R i ), zero output

More information

Crime Scene Documentation. Crime Scene Documentation. Taking the C.S. What should my notes include. Note Taking 9/26/2013

Crime Scene Documentation. Crime Scene Documentation. Taking the C.S. What should my notes include. Note Taking 9/26/2013 Crime Scene Documenttion Crime Scene Documenttion Most importnt step in C.S. processing Purpose: permnently record the condition of C.S. & physicl evidence Time consuming Documenter must be orgnized nd

More information

Understanding Basic Analog Ideal Op Amps

Understanding Basic Analog Ideal Op Amps Appliction Report SLAA068A - April 2000 Understnding Bsic Anlog Idel Op Amps Ron Mncini Mixed Signl Products ABSTRACT This ppliction report develops the equtions for the idel opertionl mplifier (op mp).

More information

MAXIMUM FLOWS IN FUZZY NETWORKS WITH FUNNEL-SHAPED NODES

MAXIMUM FLOWS IN FUZZY NETWORKS WITH FUNNEL-SHAPED NODES MAXIMUM FLOWS IN FUZZY NETWORKS WITH FUNNEL-SHAPED NODES Romn V. Tyshchuk Informtion Systems Deprtment, AMI corportion, Donetsk, Ukrine E-mil: rt_science@hotmil.com 1 INTRODUCTION During the considertion

More information

Probability and Statistics P(A) Mathletics Instant Workbooks. Copyright

Probability and Statistics P(A) Mathletics Instant Workbooks. Copyright Proility nd Sttistis Student Book - Series K- P(A) Mthletis Instnt Workooks Copyright Student Book - Series K Contents Topis Topi - Review of simple proility Topi - Tree digrms Topi - Proility trees Topi

More information

DRAWING TABLE SYSTEM

DRAWING TABLE SYSTEM DRWING TBLE SYSTEM DT31, DT61S, & CDTC71 MODEL VIEWS MY NOT REPRESENT EXCT MODEL PURCHSED : : CRETED NME THIS DRWING IS THE SOLE PROPERTY OF DIVERSIFIED WOOD CRFTS. IT MY NOT BE LTERED OR CHNGED WITHOUT

More information

Shuli s Math Problem Solving Column

Shuli s Math Problem Solving Column Shuli s Mth Problem Solvig Colum Volume, Issue Jue, 9 Edited d Authored by Shuli Sog Colordo Sprigs, Colordo shuli_sog@yhoocom Cotets Mth Trick: Metl Clcultio: b cd Mth Competitio Skill: Divisibility by

More information

Digital Design. Chapter 1: Introduction

Digital Design. Chapter 1: Introduction Digitl Design Chpter : Introduction Slides to ccompny the textbook Digitl Design, with RTL Design, VHDL, nd Verilog, 2nd Edition, by, John Wiley nd Sons Publishers, 2. http://www.ddvhid.com Copyright 2

More information

Convolutional Networks. Lecture slides for Chapter 9 of Deep Learning Ian Goodfellow

Convolutional Networks. Lecture slides for Chapter 9 of Deep Learning Ian Goodfellow Convolutionl Networks Lecture slides for Chpter 9 of Deep Lerning In Goodfellow 2016-09-12 Convolutionl Networks Scle up neurl networks to process very lrge imges / video sequences Sprse connections Prmeter

More information

From Off-The-Shelf to Market-Ready New Age Enclosures is your Single Source Solution. Let us quote modifiying our Stock Enclosures to meet your

From Off-The-Shelf to Market-Ready New Age Enclosures is your Single Source Solution. Let us quote modifiying our Stock Enclosures to meet your From Off-The-Shelf to Market-Ready New ge Enclosures is your Single Source Solution. Let us quote modifiying our Stock Enclosures to meet your end-use. visit newageenclosures.com/services or call 855-4N-ENCL

More information

Macroscopic and Microscopic Springs Procedure

Macroscopic and Microscopic Springs Procedure Mrosopi nd Mirosopi Springs Proedure OBJECTIVE Purpose In this l you will: investigte the spring-like properties of stright wire, disover the strethiness of mteril, independent of the size nd shpe of n

More information

(1) Primary Trigonometric Ratios (SOH CAH TOA): Given a right triangle OPQ with acute angle, we have the following trig ratios: ADJ

(1) Primary Trigonometric Ratios (SOH CAH TOA): Given a right triangle OPQ with acute angle, we have the following trig ratios: ADJ Tringles nd Trigonometry Prepred y: S diyy Hendrikson Nme: Dte: Suppose we were sked to solve the following tringles: Notie tht eh tringle hs missing informtion, whih inludes side lengths nd ngles. When

More information

(CATALYST GROUP) B"sic Electric"l Engineering

(CATALYST GROUP) Bsic Electricl Engineering (CATALYST GROUP) B"sic Electric"l Engineering 1. Kirchhoff s current l"w st"tes th"t (") net current flow "t the junction is positive (b) Hebr"ic sum of the currents meeting "t the junction is zero (c)

More information

Options. Exposed Ends (EXP) Flush Ends (FL) Flush Unexposed Ends (FUE) Cabinet Systems Winter

Options. Exposed Ends (EXP) Flush Ends (FL) Flush Unexposed Ends (FUE) Cabinet Systems Winter Exposed Ends (EXP) Mtching specie veneer on 1/2" thick cbinet sides. Avilble in both Advntge nd Essence lines. Specify: L (Left), R (Right) or B (Both). 1/4" revel from edge of front frme to surfce of

More information