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 Techers Guide Units 8 Bridges in Mthemtics Grde 5 Assessment Guide Bridges in Mthemtics Grde 5 Techer Msters Bridges in Mthemtics Grde 5 Student Book Volumes & 2 Bridges in Mthemtics Grde 5 Home Connections Volumes & 2 Bridges in Mthemtics Grde 5 Techer Msters Bridges in Mthemtics Grde 5 Student Book Bridges in Mthemtics Grde 5 Home Connections 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 2929, Slem, Oregon 97309. Tel (800) 575-830 www.mthlerningcenter.org 207 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 Home Connections, refer to number 2B4HC5 (pckge of 5 sets, Volumes & 2). QBB5903 ( & 2) Updted 206-05-6. Number Corner Grde 5 Techers Guide Volumes 3 Number Corner Grde 5 Techer Msters Number Corner Grde 5 Student Book Number Corner Grde 5 Techer Msters Number Corner Grde 5 Student Book 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--60262-426-9 Bridges in Mthemtics Grde 5 Home Connections

Bridges Grde 5 Home Connections Volumes & 2 Unit Expressions, Equtions & Volume Wht s the Problem?... Multipliction Connections...3 Better Boxes...5 Smnth s Strtegies...7 Finding Fctors...9 Piper s Ping-Pong Tem... Student Strtegies...3 More Expressions & Equtions...5 Expressions, Equtions & Stories...7 Agree or Disgree?...9 Unit 2 Adding & Subtrcting Frctions Compring Frctions... 2 More Adding Frctions... 23 Cfeteri Problems... 25 Adding & Subtrcting Frctions... 27 Frction Action... 29 Using Rtio Tble...3 In the Librry... 33 Frction Addition & Subtrction Story Problems... 35 Find the Greter Frction... 37 Working with Frctions... 39 Unit 3 Plce Vlue & Decimls Finding Equivlent Expressions...4 Cndy Sles Grph & More... 43 Modeling Decimls... 45 Deciml & Frction Grids... 47 Red, Write & Compre Decimls... 49 More Deciml Prctice... 5 Deciml Prctice... 53 Very Smll & Very Lrge Numbers... 55 Division Gmes... 57 Unit 3 Review... 65 Unit 4 Multiplying & Dividing Whole Numbers & Decimls Number Review... 67 Thinking About Strtegy... 69 Multipliction Strtegies... 7 Dnte s Decision... 73 Using Qurters... 75 Multipliction Models & More... 77 Mri s Multipliction... 79 Skills Review... 8 Number Reltionships... 83 Unit 4 Review... 85 Bridges in Mthemtics Grde 5 Home Connections

Unit 5 Multiplying & Dividing Frctions Multipliction & Division Review... 89 More Frctions of Wholes... 9 Gmes, Crds & More... 93 The Tngerine Problem... 95 Frctions & Division... 97 Compring, Simplifying & Adding Frctions Review... 99 Frction Multipliction Models... 0 Shring & Grouping Multiplying & Dividing... 03 Operting with Frctions & Whole Numbers 05 Unit 5 Review... 07 Unit 6 Grphing, Geometry & Volume Plotting Points on Grph... More About the Short Towers Sequence...3 The Lemonde Stnd...5 Types of Tringles...9 Clssifying Qudrilterls... 2 Mesurement & Multipliction Review... 23 Cmping Trip... 25 Another Cmping Trip... 27 Abby s Arrys... 29 Unit 6 Review... 3 Unit 7 Division & Decimls More Arry Work... 33 More Roll Five & Rtio Tbles... 35 More Division with Frctions... 37 You Choose... 39 Relted Division Problems... 4 More Division Prctice... 43 Division Review... 45 Reviewing Numbers Smll & Lrge... 47 Olympic Swimmers... 49 Olympic Trck Str... 5 Unit 8 Solr Design Looking for Solr Energy in Our Neighborhood... 53 Solr Reflection & Absorption Hunt... 55 Volume of Boxes... 57 Volume of Erth Mterils... 59 Windows on House... 6 Buying Mterils... 63 Energy in Our Homes... 65 Drwing House to Scle... 67 Designing Solr House... 69 Design Their House... 7 Bridges in Mthemtics Grde 5 Home Connections

Unit Module Session 2 Wht s the Problem? pge of 2 ex To find 3 times ny number, Mri doubles the number, then dds the number gin. Write n expression with prentheses to show how Mri would solve 3 6. (2 6) + 6 b Wht is 3 6? c Wht is nother wy to think bout 3 6? You could do 3 5, which is relly esy, nd then dd 3 more, like this (3 5) + 3 To find 4 times ny number, Susn uses the Double-Double strtegy (multiply by 2, then by 2 gin). Susn wrote (2 9) 2 to record how she would solve 4 9. Wht is 4 9? b Wht is nother wy to solve 4 9? 2 To find 5 times ny number, Kylee first multiplies by 0 nd then finds hlf the product. Write n expression with prentheses to show how Kylee would solve 7 5. b Wht is 7 5? c Wht is nother wy to solve 7 5? 3 When given ny number times 9, Jsper multiplies the number by 0 nd then removes one group of the number. Write n expression with prentheses to show how Jsper would solve 3 9. b Wht is 3 9? 8 36 (7 0) 2 (my vry slightly) 35 (3 0) 3 (my vry slightly) 27 Work will vry. Exmple: (4 4) + (4 5) = 6 + 20 = 36 Work will vry. Exmple: (5 5) + (2 5) = 25 + 0 = 35 c Wht is nother wy to think bout 3 9? Work will vry. Exmple: (3 5) + (3 4) = 5 + 2 = 27 Bridges in Mthemtics Grde 5 Home Connections (continued on next pge)

Unit Module Session 2 Wht s the Problem? pge 2 of 2 4 Brden loves multiplying by 8 becuse he cn double-double-double. Write n expression with prentheses to show how Brden would solve 8 7. b Wht is 8 7? c Wht is nother wy to think bout 8 7? 5 Jonh ws sked to dd 4 nd 7 then multiply the sum by 9. Which expression shows Jonh s problem? (The sum is the nswer to n ddition problem.) (4 + 7) 9 b (7 4) 9 c 4 + (7 9) 6 Ptrick needed to multiply 4 nd 6 then subtrct 2 from the product. Write n expression with prentheses to show the problem. (The product is the nswer to multipliction problem.) 7 Violet divided 8 by 9 then multiplied the quotient by 3. Write n expression with prentheses to show the problem. (The quotient is the nswer to division problem.) 8 Solve. ((7 2) 2) 2 56 54 (3 8) b (28 7) 4 30 6 Work will vry. Exmple: (4 7) 2 Exmple: (4 6) 2 Note: prentheses re not required due to order of opertions. Students my omit them. Exmple: (8 9) 3 Note: prentheses re not required due to order of opertions. Students my omit them. 9 CHALLENGE Rfel ws given the problem 44 9. Write n expression to show how you would solve the problem. Work will vry. Exmple: (44 0) (44 ) = 440 44 = 396 Bridges in Mthemtics Grde 5 Home Connections 2

Unit Module Session 4 Multipliction Connections pge of 2 ex To multiply number by 5, Mriss first multiplies by 0 nd then finds hlf the product. ex Write n expression with prentheses to show how Mriss would solve 24 5. (24 0) 2 ex Wht is 24 5? 20 To multiply number by 2, Crter likes to multiply the number by 0 nd then multiply it by 2 nd dd the products. Here is picture of his thinking. 6 0 2 2 Write n expression with prentheses to show how Crter would solve 2 6. Exmple: (6 0) + (6 2) b Wht is 2 6? 92 2 To multiply number by 99, Sofi likes to multiply by 00 nd then subtrct group of the fctor. Here is picture of her thinking. 00 8 8 99 Write n expression with prentheses to show how Sofi would solve 8 99. Exmple: (8 00) (8 ) b Wht is 8 99? 792 8 (continued on next pge) Bridges in Mthemtics Grde 5 Home Connections 3

Unit Module Session 4 Multipliction Connections pge 2 of 2 3 Fill in the dimensions of this box: Note: Students my record the dimensions in ny order. 3 3 9 4 Solve the following problems. 2 3 4 3 8 3 0 28 28 5 28 5 26 52 04 280 40 420 3 4 52 5 Find the products. 80 80 80 (2 5) 8 = b (2 8) 5 = c (5 8) 2 = 6 Which of the problems in item 5 is the esiest for you to solve? In other words, in which order would you prefer to multiply the three fctors? Why? Responses will vry. 7 Find the products. 420 420 420 (6 7) 0 = b (6 0) 7 = c (7 0) 6 = 8 Which of the problems in item 7 is the esiest for you to solve? In other words, in which order would you prefer to multiply the three fctors? Why? Responses will vry. Bridges in Mthemtics Grde 5 Home Connections 4

Unit Module 2 Session Better Boxes pge of 2 Brd found some dditionl boxes in his storeroom. He is wondering if these boxes will work for pckging some of his hnd-stitched bseblls. For ech of the following problems, ssume tht bll fits into spce. Use numbers, lbeled sketches, or words to find the nswers. Show your work. How mny bseblls would fit in box tht hs the dimensions (3 5) 2? 30 2 How mny bseblls would fit in box tht hs the dimensions (2 4) 5? 40 3 How mny bseblls would fit in box tht hs the dimensions 4 (3 6)? 72 4 How mny bseblls would fit in this box? 24 5 How mny bseblls would fit in this box? 00 (continued on next pge) Bridges in Mthemtics Grde 5 Home Connections 5

Unit Module 2 Session Better Boxes pge 2 of 2 6 How mny bseblls would fit in this box? 96 7 Brd is hoping to pckge exctly 48 bseblls together. He sees the side of box in his storeroom tht is 2 3. Wht is he hoping the other dimension is? 8 8 Brd is hoping to pckge exctly 64 bseblls together. He sees the side of box in his storeroom tht is 4 2. Wht is he hoping the other dimension is? 8 9 CHALLENGE Hrris sid tht 5 9 is equivlent to 45 3 becuse you cn multiply one dimension by 3 nd divide the other dimension by 3. His prtner sid tht only works when you double one number nd hlve the other. Who is right? Explin. Hrris is correct. Explntions will vry. Bridges in Mthemtics Grde 5 Home Connections 6

Unit Module 2 Session 3 Smnth s Strtegies pge of 2 Smnth hs been working with vriety of multipliction strtegies. Expressions my vry. Write n expression to describe ech of the sttements Smnth mde. To solve 8 20, I find double 8 nd then multiply by 0. 8 2 0 b To solve 6 8, I double nd hlve. Exmples: (6 2) (8 2) or 8 36 or ((6 2) 2) 2 ((8 2) 2) 2 = 2 44 c To solve 3 8, I find 3 8, multiply by 0, nd then dd group of 8. (3 8 0) + 8 2 Evlute the three expressions bove (in other words, solve the problems). 360 b c 288 248 3 Fill in the blnks. (5 3) = 60 b 4 ( 9) = 72 c 7 ( 2 ) = 42 3 2 4 3 d ( 5) 5 = 75 3 e (3 3) = 27 (continued on next pge) Bridges in Mthemtics Grde 5 Home Connections 7

Unit Module 2 Session 3 Smnth s Strtegies pge 2 of 2 4 True or Flse? F T T T T 9 9 = (0 0) b 7 2 = (20 7) + ( 7) c 6 20 = 0 (6 2) d 8 3 = 2 52 e 6 8 = (6 20) (6 2) 5 Willim needs box to hold his golf bll collection. He found box tht cn fit 8 lyers with 4 blls in ech lyer. How mny golf blls cn this box hold? Show your work. 2 Work will vry. 6 Willim found different box in his grge. The lbel outside sid it would hold 20 golf blls. If 24 blls fit in ech lyer, how mny lyers tll is the box? Show your work. 5 Work will vry. 7 CHALLENGE Willim hs totl of 292 golf blls in his collection. Write n eqution to show how mny golf blls re left if Willim fills the two boxes described in problems 5 nd 6 bove. Equtions my vry slightly. Exmple: 292 (2 + 20) = 60 b Wht re the dimensions of two different boxes tht Willim could use to store the rest of his collection? Show your work. Options to contin the 60 remining golf blls include, but re not limited to: 6 2 5 3 4 5 2 3 0 Bridges in Mthemtics Grde 5 Home Connections 8

Unit Module 2 Session 5 Finding Fctors pge of 2 Find ll the fctors of ech of the numbers below. ex 5:, 3, 5, 5 2:,, 3, 7 2 b 28:,, 2, 4, 7, 4 28 c 42:,, 2, 3, 6, 7, 4, 2 42 2 3 4 5 6 0 2 5 20 30 60 d 60:,,,,,,,,,,, 2 Find t lest three multiples for ech number below. ex 5: 30, 45, 60 42 63 84 50 75 00 c 70 05 40 84 26 68 2:,, b 25:,, 35:,, d 42:,, 3 List ll the fctors of 36., 36, 2, 8, 3, 2, 4, 9, 6 Work will vry. The first three multiples (other thn the number itself) of ech number re shown here. (in order:, 2, 3, 4, 6, 9, 2, 8, 36) b How do you know you hve listed them ll? Explntions will vry. Exmple: If you multiply to mke the number strting t times the number nd work your wy up, you cn tell when you hve ll of the fctors becuse the equtions repet themselves bckwrds (6 9, then 9 6). 4 Milo is tlking to his sister Lis bout fctors. He sid he thinks tht ny even number lwys hs more fctors thn ny odd number. Lis sid she doesn't gree with him. Explin who you gree with nd why. Agree with Lis. Explntions will vry. Exmple: If you look t the fctors for 4 (even) nd 45 (odd), you cn see tht 45 hs more fctors thn 4. (continued on next pge) Bridges in Mthemtics Grde 5 Home Connections 9

Unit Module 2 Session 5 Finding Fctors pge 2 of 2 ex Wht fctors do 2 nd 24 hve in common?, 2, 3, 4, 6, 2 5 Wht fctors do 8 nd 2 hve in common?, 2, 4 6 Wht fctors do 6 nd 4 hve in common?, 2 ex Wht re two multiples tht 5 nd 6 hve in common? 30, 60 7 Wht re two multiples tht 4 nd 8 hve in common? Work will vry. Exmples: 6, 24, 32, 40 8 Wht re two multiples tht 5 nd 7 hve in common? Work will vry. Exmples: 35, 70, 05, 40 9 CHALLENGE Hun is redesigning his bedroom, which is the shpe of rectngle. Hun knows the re of his bedroom is 80 squre feet. Wht re ll the possible whole number dimensions of Hun s bedroom? by 80 2 by 90 3 by 60 4 by 45 5 by 36 6 by 30 9 by 20 0 by 8 2 by 5 b Which dimensions re the most likely dimensions for Hun s bedroom? Why? Opinions will vry. Students might reson tht the bedroom must be wide enough on t lest one side to include bed nd room to wlk round it. Bridges in Mthemtics Grde 5 Home Connections 0

Unit Module 3 Session Piper s Ping-Pong Tem pge of 2 Piper is the cptin of her school s ping-pong tem. Help Piper keep trck of the tem s equipment. Show your work using numbers, lbeled sketches, or words. Piper brought this box of ping-pong blls to prctice on Tuesdy. How mny ping-pong blls does the box hold if one ping-pong bll fits in unit unit unit spce? 540 (5 2 9) b How much crdbord does it tke to mke the box? 2 Piper needs to buy 320 new ping-pong blls for the tem. Ping-pong blls come in sets of 6. 426 sq. units (2 5 2) + (2 9 2) + (2 5 9) How mny sets of ping-pong blls should Piper buy? 20 b If one set of 6 ping-pong blls costs $8, how much will 320 ping-pong blls cost? $60 (continued on next pge) Bridges in Mthemtics Grde 5 Home Connections

Unit Module 3 Session Piper s Ping-Pong Tem pge 2 of 2 3 Piper sw lrge box of ping-pong blls with 48 blls in ech lyer. If the box hs 5 lyers, how mny blls cn the box hold? 240 b If the box hs 5 lyers, how mny blls cn the box hold? 4 Is the eqution true or flse? 27 5 = (20 5) (7 5) b 45 8 = (40 0) + (40 8) + (5 0) + (5 8) c 720 99 3 = (00 3) ( 3) T d 64 5 = 32 30 F T T 5 Write n expression for ech item below. ex To find 2 times 7, I multiply 0 times 7 nd 2 times 7 nd dd the two products together. (0 7) + (2 7) To find 79 times 24, I multiply 80 times 24 nd tke off one group of 24. 80 24 24 Students my include prentheses for clrity. b To find 2 times 3, I double 3 nd hlve 2 nd then multiply. (3 2) (2 2) c CHALLENGE To find,88 divided by 2, I think bout,200 divided by 2 tht s 00 groups of 2.,88 hs fewer group of 2.,200 2 Students my include prentheses for clrity. Bridges in Mthemtics Grde 5 Home Connections 2

Unit Module 3 Session 3 Student Strtegies pge of 2 Julin loves multiplying by 8 becuse she cn double-double-double. Write n expression to show how Julin would solve 8 23. 23 2 2 2 Students my include prentheses for clrity. 84 b Wht is 8 23? c Write n expression tht shows different wy to solve 8 23. Work will vry. Exmple: (8 20) + (8 3) 2 Kevin ws sked to dd 6 nd 9 then multiply by 7. Which expression shows Kevin s problem? 6 + 9 7 b (6 + 9) 7 c 6 + (9 7) ex Elizbeth needed to multiply 7 nd 8 nd then subtrct 3. Write n expression to show the problem. Then, solve the problem nd write n eqution. Expression (7 8) 3 b Eqution (7 8) 3 = 43 3 Kden divided 96 by 2 nd then multiplied by 6. Write n expression to show the problem. Then, solve the problem nd write n eqution. Expression: 96 2 6 Students my include prentheses for clrity. b Eqution: 96 2 6 = 48 Students my include prentheses for clrity. Bridges in Mthemtics Grde 5 Home Connections 3

Unit Module 3 Session 3 Student Strtegies pge 2 of 2 Evlute the following expressions. = 8 = 72 4 8 (9 7) 5 (54 6) 8 How mny cubes re in the following rectngulr prisms? For ech problem, write n expression nd evlute it to find the number of cubes. 5 4 8 60 6 Expression: Number of cubes: 3 7 6 26 7 Expression: Number of cubes: 8 CHALLENGE Chloe is sorting items t thrift store. She finds box of tiny blocks tht hs,344 written on the outside. She cn see tht ech lyer in the box hs 64 blocks. How mny lyers of blocks re there? 2 lyers b Wht is nother wy Chloe could rrnge the,344 blocks to fit in different box? Work will vry. Possibilities include, but re not limited to, these rrngements: 6 84 8 68 42 32 Bridges in Mthemtics Grde 5 Home Connections 4

Unit Module 4 Session More Expressions & Equtions pge of 2 Write numericl expression tht includes grouping symbols. To find 73 9, I find 73 times 0 nd remove group of 73. b To find the volume of box tht hs n 8 by 25 bse nd 2 lyers, I multiply the re of the bse times the height. 2 Write nd solve n eqution to represent ech sitution. To find 23 times 8, I double nd hlve. 23 8 = (23 2) (8 2) = 46 4 = (46 2) (4 2) = 92 2 = 84 b To find 24 times 7, I multiply 20 times 7 nd dd it to 4 times 7. (20 7) + (4 7) = 340 + 68 = 408 3 True or Flse? 2 7 = 6 34 b 99 75 = (00 75) c 73 0 73 Students my include prentheses for clrity. 8 25 2 Students my include prentheses for clrity. T F To find the volume of box, I cn multiply the length times the width. F 4 Evlute ech expression (solve ech problem). (7 8) 9 = 504 b 2 (5 5) + 3 (4 4) c (00 67) ( 67) d (98 47) + (2 47) = 98 = 6,633 = 4,700 (continued on next pge) Bridges in Mthemtics Grde 5 Home Connections 5

Unit Module 4 Session More Expressions & Equtions pge 2 of 2 5 How mny cubes re in the following rectngulr prisms? Write nd solve equtions to show. Eqution for number of cubes: 7 3 4 = 84 cubes b Eqution for number of cubes: 4 5 6 = 20 cubes 6 5 4 6 A box holds 25 blls. Ech lyer hs 25 blls. How mny lyers does the box hve? Show your work. 5 lyers. Work will vry. 7 CHALLENGE A box holds 425 blls. Ech lyer hs 7 blls. How mny lyers does the box hve? Show your work. 25 lyers. Work will vry. Bridges in Mthemtics Grde 5 Home Connections 6

Unit Module 4 Session 3 Expressions, Equtions & Stories pge of 2 Students my include dditionl prentheses for clrity. Write n expression with prentheses for ech sttement below. I multiplied 7 times 8 nd then I dded 9. b I multiplied 3 times 2 nd then multiplied the product of 3 times 2 by 5. (3 2) 5 c I subtrcted 4 from 30 nd then I multiplied the difference by 6. (30 4) 6 2 Emir loves multiplying by 99 becuse he cn use n over strtegy. Write n expression to show how Emir would solve 99 76. (00 76) 76 7,524 b Wht is 99 76? c Show different wy to solve 99 76. Work will vry. Exmple: 3 Eric likes to multiply by 25 becuse she cn use the double-hlf strtegy. Write n expression to show how Eric would solve 25 28. (25 2) (28 2) b Wht is 25 28? c Show different wy to solve 25 28. 4 Evlute ech expression. (25 0) 0 = 700 b 4 (4 4) + 3 (3 3) = c (00 89) ( 89) = (7 8) + 9 6 5 99 76 594 + 6930 7,524 Work will vry. Exmple: 25 4 7 = 00 7 = 700 2,500 9 8,8 (continued on next pge) Bridges in Mthemtics Grde 5 Home Connections 7

Unit Module 4 Session 3 Expressions, Equtions & Stories pge 2 of 2 5 For ech problem below: Use numbers, words, or lbeled sketches to solve the problem. Show ll your work. Figure out the best wy to hndle the reminder, if there is one, for tht sitution. Write n eqution to show ech problem nd the nswer, lbeled with the correct units. Thirty-eight fifth grders t Vernon Elementry re going on the field trip to the rt museum. They re riding in vns tht ech hold 9 students. How mny vns will they need for everyone to get to the rt museum? 5 vns Work nd equtions will vry. Eqution b When Alex nd Mrcus went to the store with their mom, she sid they could split the chnge evenly. The totl cost of their groceries ws $57.32. She gve the cshier three $20 bills. How much money did Alex nd Mrcus ech get? $.34 38 9= 4 R2 (($20 3) $57.32) 2 = $.34 Eqution c CHALLENGE On Fridy fternoon, My relizes tht she hs put off her reding for too long nd tht she needs to finish her book by Mondy. The book is 265 pges long. She is on pge 27. How mny pges will she need to red ech night to finish the book before school on Mondy morning? 46 pges (265 27) 3 = 46 Eqution Bridges in Mthemtics Grde 5 Home Connections 8

Unit Module 4 Session 5 Agree or Disgree? pge of 2 Choose 5 of the 6 problems on this pge nd the next. For ech one you choose, write whether you gree or disgree. Then explin your thinking using numbers, words, nd/ or lbeled sketches. Explntions nd work will vry. Do you gree or disgree? Explin your thinking. The 5th grders set up 20 rows of chirs with 25 chirs in ech row for the ssembly. Mrs. Lord sked if they d set up enough chirs for ll 552 students. Kmil sid he could skip-count to find out how mny chirs there were in ll, nd then they d know if they hd enough. Agree (Kmil is correct). 2 The trck t the high school is 400 meters. After she rn 6 times round the trck, Isuko sid she d gone more thn 2 kilometers. Agree (Isuko is correct). 3 Mr. Mdison needs 75 grnol brs for the 5th grde field trip. The brs come in boxes of 0. He ll need to buy 7 boxes to hve enough. Disgree (he would only hve 70 brs from 7 boxes, so he'd be 5 brs short). (continued on next pge) Bridges in Mthemtics Grde 5 Home Connections 9

Unit Module 4 Session 5 Agree or Disgree? pge 2 of 2 Do you gree or disgree? Explin your thinking. 4 To multiply 247 4, you cn do these smller problems nd dd them together: 200 4 4 4 7 4 Disgree (200 4, 40 4, nd 7 4 would work). 5 There re 46 kids in the After-School Club. Tody they re going to the pool t the Community Center. If ech minivn cn tke 6 kids, they ll need 8 minivns for ll the kids. Agree. 6 CHALLENGE Brd wnts to pckge his bseblls in sets of 00. Bethny sys the box tht will tke the lest mount of crdbord for 00 bseblls is one with bse of 2 5 nd height of 0. Disgree. For exmple, 5 5 4 box hs smller surfce re (30 sq. units) thn 2 5 0 box (60 sq. units). Bridges in Mthemtics Grde 5 Home Connections 20

Unit 2 Module Session 2 Compring Frctions pge of 2 Color in the grid to show the frctions below. Ech grid represents whole. 2 b 4 c 3 0 Students my color in ny configurtion of the correct number of squres. Exmples shown. d 6 0 e 6 4 2 Use the pictures bove to help complete ech comprison below using <, >, or =. ex 2 > 0 3 = < 6 4 2 b 6 0 3 4 c > 6 0 2 d < > 6 0 6 4 e 3 0 4 3 Add these frctions. (Hint: Think bout money to help.) 2 + 4 = b 2 + 3 4 = c d 3 2 + 0 = 0 + 4 = 3/4 2 /4 60/00 or 6/0 55/00 or /20 (continued on next pge) Bridges in Mthemtics Grde 5 Home Connections 2

Unit 2 Module Session 2 Compring Frctions pge 2 of 2 4 Frncisco nd his mother bought some fruit yesterdy. They bought 2 2 pounds of peches, 7 0 of pound of rspberries, nd 4 pounds of pricots. How mny pounds of fruit did they buy in ll? Show ll your work. 4 45/00 pounds. Work will vry. 5 CHALLENGE Write three frction ddition problems in which the frctions hve different denomintors nd the sum is. ex 2 + 2 4 = b c Problems will vry. 6 CHALLENGE Fill in the missing numertors nd denomintors to mke ech comprison true. Work will vry. 5 3 5 2 > 4 2 b 4 = 2 c 6 32 < 8 Bridges in Mthemtics Grde 5 Home Connections 22

Unit 2 Module Session 4 More Adding Frctions pge of 2 Students my shde in the strips nd clocks in vrying configurtions. Show the frctions on the strips or clocks. Then dd them nd report the sum. First Second Add Them Sum 2 b 3 4 c 5 8 d 3 4 3 8 3 8 2 7 8 7/8 /8 /8 5/8 e 4 2 3 /2 f 3 4 2 3 5/2 g 5 6 3 4 7/2 h 2 5 6 2/6 (or /3 or 4/2) Bridges in Mthemtics Grde 5 Home Connections 23

Unit 2 Module Session 4 More Adding Frctions pge 2 of 2 Show your work for ech problem using numbers, sketches, or words. Work will vry. 2 Abby nd Luren re prepring for dnce performnce. On Mondy, they prcticed for 2 3 of n hour. On Tuesdy, they prcticed for 5 6 of n hour. How long did they prctice on Mondy nd Tuesdy together? /2 hours (or 90 minutes or hour, 30 minutes) 3 On Wednesdy, Abby nd Luren could not prctice together, so they prcticed seprtely. Abby prcticed for 2 of n hour nd Luren prcticed for 2 3 of n hour. How long did they prctice on Wednesdy? 7/2 hours (or 95 minutes or hour, 35 minutes) 4 CHALLENGE If you re dding two frctions tht re both greter thn 2, wht must be true bout the sum? Give three exmples to support your thinking. Explntions will vry. The sum must be: greter thn 5 CHALLENGE If you re dding two frctions tht re both less thn 2, wht must be true bout the sum? Give three exmples to support your thinking. Explntions will vry. The sum must be: less thn Bridges in Mthemtics Grde 5 Home Connections 24

Unit 2 Module 2 Session Cfeteri Problems pge of 2 The cfeteri t King Elementry sked the students to vote on their fvorite min dishes. The circle grphs below show the results. Use the informtion to nswer the questions below. Work will vry. Fourth Grde Fvorites Fifth Grde Fvorites Key 8 4 8 2 6 6 3 3 Cheese Pizz Turkey Burgers Chicken Nuggets Super Sld Wht frction of the fourth grders did not vote for super sld? Show your work. 7/8 b Wht frction of the fifth grde voted for turkey burgers or chicken nuggets? Show your work. /2 c 92 fourth grders voted. How mny of them voted for turkey burgers? Show your work. 48 d 74 fifth grders voted. How mny of them voted for chicken nuggets? 29 (continued on next pge) Bridges in Mthemtics Grde 5 Home Connections 25

Unit 2 Module 2 Session Cfeteri Problems pge 2 of 2 2 Wht is: 2 of 60? b 3 60? c 2 of 00? d 5 00? 30 20 50 20 3 While witing for his grndm to rrive, Ptrick spent 2 of n hour on the phone with friend nd 4 of n hour listening to the rdio. How long did Ptrick spend witing for his grndm? Write your nswer both in minutes nd s frction of n hour. 3/4 hour 45 minutes 4 Beth wlked 3 of mile from her house to her friend s house, 4 of mile to the post office, nd then nother 2 of mile from the post office bck home. How fr did Beth wlk? /2 miles 5 CHALLENGE Rodney nd Josih ech bought pckge of the sme kind of cookies t the store. Rodney te 2 pckge of cookies on Mondy nd 3 of the sme pckge on Tuesdy. Josih te 5 2 of his pckge on Mondy nd 2 of the pckge on Tuesdy. Who te more? How much more? Josih te /2 of pckge more thn Rodney. Bridges in Mthemtics Grde 5 Home Connections 26

Unit 2 Module 2 Session 3 Adding & Subtrcting Frctions pge of 2 Solve the problems on this pge. If your nswer is n improper frction, find its equivlent mixed number. 3 4 + 2 = 3 4 + 2 4 = 5 4 = 4 5 4 is n improper frction becuse 5 is greter thn 4. 4 4 is equl to, so 5 4 is equl to 4. 4 3 4 = c 4 /0 2 + 2 3 = 2 5 0 4 0 = b 7 5/6 0 4 = /4 f 4 30 60 + 4 = 5 3/4 d 2 3 + 6 = e 5 2 Find two different wys to show tht 3 + 4 is not equl to 2 7. You cn use numbers, words, nd lbeled sketches. Work will vry. Exmples: /3 + /4 = 4/2 + 3/2 = 7/2, nd 7/2 2/7. 7/2 is more thn /2 nd 2/7 is less thn /2, so they cn't be equl. Bridges in Mthemtics Grde 5 Home Connections 27

Unit 2 Module 2 Session 3 Adding & Subtrcting Frctions pge 2 of 2 3 Dn must do homework for 2 n hour nd clen his room for of n hour before 3 he cn ply. Wht frction of n hour must Dn do homework nd clen before he cn ply? 5/6 hour 4 Dnielle found nickel on the plyground t school. She lso found $0.20 on the sidewlk. How much money did she find? $0.25 (25 ) b Wht frction of dollr did Dnielle find? /4 dollr 5 CHALLENGE Mrih hs n fter-school bbysitting job. This is record of the number of hours she worked lst week. Dy of the Week Bby-sitting Hours Mondy 2 2 Tuesdy 3 2 Wednesdy 2 4 Thursdy 3 2 3 Mrih gets pid $6 per hour. How much money did she ern bbysitting lst week? Show your work. $7.50. Work will vry. Bridges in Mthemtics Grde 5 Home Connections 28

Unit 2 Module 2 Session 5 Frction Action pge of 2 Students my color in ny configurtion of the correct number of circles. Color some of the circles in ech set to show the frctions below. 2 b 4 c 3 4 d 6 e 2 6 f 5 6 g 3 h 3 3 i 0 3 2 Add the following frctions. If the sum is greter thn, write the nswer s both n improper frction nd mixed number. ex 2 + 3 4 = 5 4 = 0 4 3 + 2 8 b 4 + 5 6 c = /2 3 + 3 4 = 2/2 = 9/2 = 3/4 6 + 3 d 3 = 2/8 = 3/2 = /2 (continued on next pge) Bridges in Mthemtics Grde 5 Home Connections 29

Unit 2 Module 2 Session 5 Frction Action pge 2 of 2 3 Mrsh wlked 2 miles to school yesterdy morning. After school, she wlked 3 4 of mile to her unt's house. How mny miles did she wlk in ll yesterdy? Estimte the nswer. Estimtes will vry. b Find the exct nswer. Show ll your work. 2 /4 miles Work will vry. 4 Frncisco nd his mom got some fruit t the fruit stnd yesterdy. They bought 2 2 pounds of peches, 7 8 of pound of rspberries, nd 4 pounds of pricots. How mny pounds of fruit did they buy in ll? Estimte the nswer. Estimtes will vry. b Find the exct nswer. Show ll your work. 4 5/8 pounds Work will vry. 5 CHALLENGE Cmil hd lrge collection of bsketbll crds. She gve hlf of them to her friend Erin nd sixth of them to her brother. She still hs 50 crds left. How mny crds did she strt with? Show ll your work. 450 crds Work will vry. Bridges in Mthemtics Grde 5 Home Connections 30

Unit 2 Module 3 Session Using Rtio Tble pge of 2 Use rtio tble to multiply the numbers. ex 23 26 2 4 0 20 26 23 46 92 230 460 598 35 44 2 4 40 44 35 70 40,400,540 b 39 20 2 20 39 78 780 c 8 65 2 20 8 65 30,300,70 d 4 8 Work will vry. Exmple shown. 2 4 8 36 72 e 75 5 00 50 25 75 5,500 750 375,25 (continued on next pge) Bridges in Mthemtics Grde 5 Home Connections 3

Unit 2 Module 3 Session Using Rtio Tble pge 2 of 2 2 True or Flse? 98 34 = (00 34) (2 34) T b 46 28 = 23 56 T 3 Veronic hs to multiply 398 8. She sys she cn multiply 400 8 nd then tke wy one group of 8. Do you gree with Veronic? Explin. No, disgree. Explntions will vry. b Write n expression tht shows Veronic s thinking. (400 8) 8 c Wht is 398 8? Show your work. 7,64 Work will vry. Exmple: 400 8 (2 8) 4 CHALLENGE The qurium hs 98 fish tnks with 5 fish in ech. They lso hve 297 tnks with 2 crustcens in ech. Does the qurium hve more fish or more crustcens? How mny more? Mke n estimte nd explin your resoning. Then determine the ctul nswer. Estimte nd resoning: Estimtes nd resoning will vry. b Actul nswer: (Show your work.) The qurium hs 594 more crustcens thn fish. Work will vry. c Is your nswer resonble? (Think bout your estimte.) Answers will vry. Bridges in Mthemtics Grde 5 Home Connections 32

Unit 2 Module 3 Session 3 In the Librry pge of 2 The librrin t our school sked the fourth nd fifth grders to vote on their fvorite kind of book. The circle grphs below show the results. Use the informtion to nswer the questions below. Fourth Grde Fvorites Fifth Grde Fvorites Key 8 Fiction 4 2 3 4 Fntsy Nonfiction Work nd explntions will vry. Wht frction of the fourth grders sid they liked nonfiction books best? How do you know? /4 b If there re 96 fourth grders, how mny like fntsy books best? Show your work. 24 c Wht frction of the fifth grders sid they like fntsy books best? How do you know? /8 d If there re 2 fifth grders, how mny like nonfiction books best? Show your work. 4 e Wht frction of the fifth grders sid they liked fiction books best? How do you know? 3/4 Explntions will vry. (continued on next pge) Bridges in Mthemtics Grde 5 Home Connections 33

Unit 2 Module 3 Session 3 In the Librry pge 2 of 2 2 Mdeline wlked 2 miles to her Aunt Jenny s house yesterdy morning. After visiting with Aunt Jenny, Mdeline wlked 3 4 of mile to the prk, where her mother picked her up. How mny miles in ll did she wlk yesterdy? Show ll your work. 2 /4 miles Work will vry. Equivlent nd improper frctions re cceptble. 3 Sr nd her mother bought some vegetbles t the frmer s mrket yesterdy. They bought 2 3 4 pounds of cbbge, 2 pound of onions, nd 3 8 pounds of crrots. How mny pounds of vegetbles did they buy in ll? Show ll your work. 4 5/8 pounds Work will vry. Equivlent nd improper frctions re cceptble. 4 CHALLENGE Mdison went to the mll with her big sister lst weekend. Their mom dropped them off t :00 nd sid, I ll pick you up t 2:30. The girls spent 5 6 of n hour t the toy store, 2 3 of n hour t the pet store, nd 2 n hour t the food court. When they got bck to the bench to meet their mom, she ws lredy there. She sid, Where hve you been? I ve been witing of n hour for you! How long hd their mom been witing for them? /2 hour Bridges in Mthemtics Grde 5 Home Connections 34

Unit 2 Module 3 Session 5 Frction Addition & Subtrction Story Problems pge of 2 Find the sum or the difference for ech pir of numbers. Show ll your work. 5 4 + 4 5 = 7 /70 b 9 4 7 = 3/63 Work will vry. Equivlent nd improper frctions re cceptble. 4/5 /5 c 7 5 + 3 9 = d 2 3 3 5 = 2 George nd his dd mde some snck mix for their cmping trip. To mke it, they used 2 cups of mini pretzels, 3 4 cup of penuts, nd 2 3 cup of chocolte chips. How mny cups of snck mix did they hve when they were finished? Show ll your work. 3 5/2 cups. Work will vry. Equivlent nd improper frctions re cceptble. (continued on next pge) Bridges in Mthemtics Grde 5 Home Connections 35

Unit 2 Module 3 Session 5 Frction Addition & Subtrction Story Problems pge 2 of 2 3 Lis drnk 7 6 of bottle of wter during the soccer gme. Julinne drnk 2 3 of the wter in bottle tht ws the sme size s Lis s. Who drnk more wter nd by exctly how much? Show ll of your work. Julinne drnk /48 of bottle more thn Lis. Work will vry. 4 CHALLENGE Austin went to the science museum. He ws there for 2 hours. He spent 3 5 of his time doing experiments. Then, he spent 3 of his time t the wter sttion. Finlly, he spent the rest of his time looking t skeletons. How long did Austin spend looking t skeletons? Show ll your work, nd express your nswer s number of minutes nd s frction of n hour. 8 minutes = 8/60, 4/30, or 2/5 of n hour. Work will vry. Bridges in Mthemtics Grde 5 Home Connections 36

Unit 2 Module 4 Session Find the Greter Frction pge of 2 Find the lest common multiple for ech pir of numbers. Show ll your work. ex 3 nd 5 3: 3, 6, 9, 2, 5, 8 5: 5, 0, 5, 20 The LCM is 5. 4 nd 6 b 3 nd 7 2 c 5 nd 8 d 6 nd 9 40 2 8 2 Use the lest common multiple to find equivlent frctions for ech frction pir. Then, use the symbol < or > to show the bigger frction. ex 3 4 nd 4 5 6 8 nd 2 3 4 4, 8, 2, 6 5/8 = 5/24 nd 2/3 = 6/24 6 6, 2, 8, 24 5/24 < 6/24 so 5/8 < 2/3 3 4 = 3 3 4 3 = 9 2 4 6 = 4 2 6 2 = 8 2 9 2 > 8 2 so 3 4 > 4 6 b 6 nd 2 9 c 7 2 nd 5 8 /6 = 3/8 nd 2/9 = 4/8 7/2 = 4/24 nd 5/8 = 5/24 3/8 < 4/8 so /6 < 2/9 4/24 < 5/24 so 7/2 < 5/8 (continued on next pge) Bridges in Mthemtics Grde 5 Home Connections 37

Unit 2 Module 4 Session Find the Greter Frction pge 2 of 2 Solve the story problems below. Show your work using numbers, sketches, or words. Work will vry. 3 Mtthew red 2 3 of book. Crig red 4 5 of the sme book. Who red more? How much more? Crig red 2/5 more of the book. 4 Crlos hd two extr sndwiches. They were exctly the sme size. He gve 7 9 of the first sndwich to his friend Ben nd 4 6 of the second sndwich to his friend Corey. Whose piece is bigger, Corey s or Ben s? Ben's. (It is /9 of sndwich lrger.) b CHALLENGE If Crlos te the remining pieces of the two sndwiches, did he get more or less thn Corey? Did he get more or less thn Ben? He got less thn both Corey nd Ben. (Ben got 7/9 = 4/8 nd Corey got 4/6 = 2/8, so Crlos got 0/8 = 5/9 of sndwich.) Bridges in Mthemtics Grde 5 Home Connections 38

Unit 2 Module 4 Session 3 Working with Frctions pge of 2 Which is greter, 2 3 or 4 5? Exctly how much difference is there between these two frctions? If you wnt to compre, dd, or subtrct two frctions, rewrite them so they both hve the sme denomintor. To do this: Find the lest common multiple of the denomintors of the frctions. multiples of 3 3, 6, 9, 2, 5 multiples of 5 5, 0, 5 The lest common multiple of 3 nd 5 is 5. Multiply the numertor nd denomintor of ech frction by the sme number so the denomintors re equl. 2 5 = 0 3 5 5 4 3 = 2 5 3 5 4 5 is greter thn 2 3 by exctly 2 5. Find the lest common multiple (LCM) of ech pir of numbers. Work my vry, nd students do not need to show work. ex 4 nd 0 5 nd 6 b 2 nd 7 4, 8, 2, 6, 20 0, 20 20 is the LCM of 4 nd 0 5, 0, 5, 20, 25, 30 6, 2, 8, 24, 30 30 is the LCM of 5 nd 6. 2, 4, 6, 8, 0, 2, 4 7, 4 4 is the LCM of 2 nd 7. 2 Add or subtrct the frctions by rewriting them so they hve common denomintors. Hint: Use the informtion from problem to help. ex 3 4 0 7 = 3 5 4 5 = 20 5 7 2 0 2 = 20 4 5 20 20 4 = 20 4 5 + 5 6 = b 24/30 + 25/30 = 49/30 = 9/30 4 7 2 = 8/4 7/4 = /4 3 Find the gretest common fctor for ech pir of numbers below. Use extr pper if you need more spce. 6, 2, 4, 8, 6 5, 3, 5, 5 28, 2, 4, 7, 4, 28 36, 2, 3, 4, 6, 9, 2, 8, 36 GCF 4 GCF 3 (continued on next pge) Bridges in Mthemtics Grde 5 Home Connections 39

Unit 2 Module 4 Session 3 Working with Frctions pge 2 of 2 4 Find the simplest form of ech frction below. c e 4/7 6 28 b /7 2 4 d 5/2 5 36 f 4 48 28 6 56 42 /2 3/4 /3 5 Add or subtrct. Show your work. Hint: Use the informtion in problem 4 bove to help. b c 6 28 + 2 4 = 5 36 + 48 4 = 28 6 + 25 00 = 4/7 + /7 = 5/7 5/2 + /2 = 6/2 = /2 3/4 + /4 = 2 6 Alici sys tht the gretest common fctor of 8 nd 2 is 24. Do you gree or disgree? Explin. Disgree (Alici is incorrect). Explntions will vry. 24 is not fctor of 8 or 2 it's multiple of them, nd it is the lest common multiple (LCM). 7 Felix sys tht 33 is in simplest form. Do you gree or disgree? Explin. Disgree (Felix is incorrect: /33 = /3). Explntions will vry. 8 CHALLENGE List three exmples of times when people need to dd or subtrct frctions in their dily lives. Exmples will vry. Bridges in Mthemtics Grde 5 Home Connections 40

Unit 3 Module Session 2 Finding Equivlent Expressions pge of 2 Mtch ech frction expression on the top with n equivlent deciml expression on the bottom. Frction Expressions 4 0 + 00 20 60 00 0 4 00 + 3 0 4 0 + 00 75 5 00 0 4 00 + 00 2 Deciml Expressions 0.04 + 0.3.4 + 0.75 0.4 + 0.2 0.4 + 0.20 0.60 0. 0.5 0. 2 Evlute ech expression. Represent your nswer s both frction nd deciml. 0.60 0.25 = 0.35 b 0.70 0.55 = 0.5 c 0.2 + 0.05 = 0.25 35/00 = 7/20 5/00 = 3/20 25/00 = /4 d 40 00 0 = 30/00 = 0.3 e = 00/00 = 4 0 + 00 60 f 9 0 + 00 30 = 20/00 = /5 3 Students t Jonh s school cn wlk or run lps t recess. At the end of ech month, the clss tht hs covered the most distnce is recognized by the prent group. Jonh nd Hyley wlked 4 3 lps round the trck yesterdy nd 3 2 lps tody. How mny lps did they wlk together in the lst two dys? Show your work. 7 5/6 lps Work will vry. b Jonh rn 3 4 lps on Mondy, 2 3 0 lps on Tuesdy, nd 6 5 lps on Wednesdy. How much frther did he run on Wednesdy thn on the other two dys combined? Show your work. He rn 2 3/20 lps more on Wednesdy thn on Mondy nd Tuesdy combined. Work will vry. (continued on next pge) Bridges in Mthemtics Grde 5 Home Connections 4

Unit 3 Module Session 2 Finding Equivlent Expressions pge 2 of 2 4 Jonh nd Hyley mde brownies to bring s clss tret. Some were plin nd some hd sprinkles. The clss te 3 4 of one pn nd 6 of nother pn of the plin brownies. They te 5 6 of one pn nd 0 of nother pn of brownies with sprinkles. If the brownie pns were the sme size, did the clss et more plin brownies or more brownies with sprinkles? They te /2 pn of plin nd 4/5 pn of sprinkles. They te more brownies with sprinkles becuse 4/5 > /2. b How much more? Show your work. /60 pn more. Work will vry. Exmple: 4/5 /2 = 56/60 55/60 = /60 5 CHALLENGE A coch took his tem out for pizz fter their lst gme. There were 4 plyers, so they hd to sit in smller groups t different tbles. Six plyers st t one tble nd got 4 smll pizzs to shre eqully. The other 8 plyers st t different tble nd got 6 smll pizzs to shre eqully. Afterwrds, one of the plyers sid it wsn t fir becuse some kids got more pizz thn others. Do you gree? Use numbers, words, or lbeled sketches to explin your nswer. Agree (ssuming tht students consider unequl mounts of pizz to be unfir) some plyers got more pizz thn others. Work nd explntions will vry. Exmple: At the tble with 6 plyers, ech plyer got 4/6 (2/3) of pizz. At the tble with 8 plyers, ech plyer got 6/8 (3/4) of pizz. 3/4 > 2/3, so the plyers in the group of 6 got more pizz thn the plyers in the group of 8. Bridges in Mthemtics Grde 5 Home Connections 42

Unit 3 Module Session 4 Cndy Sles Grph & More pge of 2 The orgnizers of concession stnd were thinking bout mking chnges to the types of cndy they sold. They mde br grph to show the profits erned t the first two gmes of the seson for ech type of cndy. Use the grph to nswer the questions below. Show your work. Look t the informtion for bubble gum. Wht ws the profit for bubble gum during Gme? $.75 b Wht ws the profit for bubble gum during Gme 2? $0.00 $9.00 $8.00 Money for Concessions Legend Gme Gme 2 c $3.50 How much more profit ws mde on bubble gum during Gme 2 thn Gme? $.75 $7.00 $6.00 $5.00 2 How much more profit ws mde on hrd cndy during Gme 2 thn Gme? $4.00 $3.75 3 How much more profit ws mde on sour strings during Gme 2 thn Gme? $5.50 4 How much greter ws the profit from sles of ll three cndies during Gme 2 thn during Gme? $.00 $3.00 $2.00 $.00 Bubble Gum Hrd Cndy Sour Strings (continued on next pge) Bridges in Mthemtics Grde 5 Home Connections 43

Unit 3 Module Session 4 Cndy Sles Grph & More pge 2 of 2 5 Evlute (solve) the following: (2 5) 2 b 0 (24 4) c (50 0) + (5 5) = 20 = 60 = 40 6 Trin sid $.05 + $2.25 = $3.75 becuse dollr nd 2 qurters plus 2 dollrs nd qurter equls 3 dollrs nd 3 qurters. Do you gree with her sttement? Explin. No, disgree (Trin is incorrect). Explntions will vry. Exmple: $.05 + $2.25 = $3.30. $.05 is equl to dollr nd nickel, not dollr nd two qurters. 7 Evlute (solve) the following:.37 + 8.26 = 9.63 b 5.0 + 5.0 = 0. 8 CHALLENGE A box holds 540 blls. Ech lyer hs 8 blls. How mny lyers does the box hve? 30 lyers Bridges in Mthemtics Grde 5 Home Connections 44

Unit 3 Module 2 Session Modeling Decimls pge of 2 The bse ten models below cn be used to represent deciml numbers. whole tenth hundredth thousndth Write the number tht ech model represents. ex Model Deciml Number.025.004 b 2.34 c.07 (continued on next pge) Bridges in Mthemtics Grde 5 Home Connections 45

Unit 3 Module 2 Session Modeling Decimls pge 2 of 2 2 For ech question, fill in the missing deciml or frction equivlent(s), or shde the grid to mtch the missing numbers. b Deciml: 0.3 Frction Equivlent(s): 3/0 = 30/00 Deciml: 0.25 Frction Equivlent(s): 25/00 = /4 c Configurtions of shding my vry. d Configurtions of shding my vry. Deciml: 0.2 Deciml: Frction Equivlent(s): 2/0 = 20/00 0.6 Frction Equivlent(s): 60 00 3 CHALLENGE Julin wlked 6 0 of mile to his friend s house nd then nother 35 00 of mile to the store. He wlked 4 of mile bck home. Julin s sister sid he wlked 5 miles. Do you gree? Why or why not? Yes, gree (Julin's sister is correct). Explntions will vry. (continued on next pge) Bridges in Mthemtics Grde 5 Home Connections 46

Unit 3 Module 2 Session 3 Deciml & Frction Grids pge of 2 For ech question, fill in the missing deciml or frction equivlent(s), or shde the grid to mtch the numbers given. 2 0.5 Deciml: Frction Equivlent(s): 5/0 = 50/00 = /2 3 4 Configurtions of shding my vry. 0.4 Deciml: Frction Equivlent(s): 4/0 = 40/00 Configurtions of shding my vry. Deciml: 0.5 Deciml: Frction Equivlent(s): 5/0 = /2 0.7 Frction Equivlent(s): 70 00 5 Use one of these symbols (<, >, or =) to compre ech pir of deciml numbers. = < < 6.0 6.00 b 5.54 5.54 c 3.04 3.4 > < d 32.30 32.03 e 0.00 0.00 (continued on next pge) Bridges in Mthemtics Grde 5 Home Connections 47

Unit 3 Module 2 Session 3 Deciml & Frction Grids pge 2 of 2 6 Round ech deciml to the nerest one, tenth, nd hundredth. (Hint: Look t the digit to the right of the plce to which you re rounding. If it s less thn 5, round down. If it s 5 or more, round up.) Number To the Nerest To the Nerest Tenth To the Nerest Hundredth ex 4.862 5.0 4.9 4.86 0.048 0 0.0 0.05 b 4.964 5 5.0 4.96 c 7.065 7 7. 7.07 d 94.24 94 94. 94.2 7 Complete the tble below to show ech frction s deciml, nd ech deciml s frction. Frction 3 4 Deciml b 0.20 c 3 00 d 0.72 e /5 (2/0 = 20/00) 72/00 (36/50 = 8/25) 6 0 0.75 0.03 0.6 8 CHALLENGE Riley collected rin for severl weeks in rin guge. He collected.48 inches the first week, hlf tht much the second week, nd one inch the third week. How much more rin will Riley need to collect before he hs 5 inches?.78 inches Bridges in Mthemtics Grde 5 Home Connections 48

Unit 3 Module 2 Session 5 Red, Write & Compre Decimls pge of 2 Complete the chrt. Bse-Ten Numerl Expnded Form 25.893 (2 0) + (5 ) + (8 0) + (9 00) + (3 000) 7.043 4.570 3.63 6.49 0.37 0.863 2 Complete the chrt. Bse-Ten Numerl (7 ) + (0 /0) + (4 /00) + (3 /000) (4 ) + (5 /0) + (7 /00) + (0 /000) (3 ) + (6 0) + ( 00) + (3 (6 ) + (4 0) + (9 00) ( 0) + (8 0) + (6 00) + (3 Number Nme 000) (0 ) + (3 /0) + ( /00) + (7 /000) 000).893 one nd eight hundred ninety-three thousndths 0.600 six tenths or six hundred thousndths.503.03 one nd five hundred three thousndths one nd thirteen thousndths 2.002 two nd two thousndths 0.037 thirty-seven thousndths 0.040 forty thousndths 3 List the decimls from problem 2 in order from lest to gretest. Include the exmple. 0.037 0.040 0.600.03.503.893 2.002 < < < < < < Bridges in Mthemtics Grde 5 Home Connections 49

Unit 3 Module 2 Session 5 Red, Write & Compre Decimls pge 2 of 2 4 Fill in the bubble to show which of the two deciml numbers is greter. Use numbers, words, or lbeled sketches to explin your nswer. How do you know the number you ve selected is greter? NN.200 Explntions will vry. NN.002 5 Write four deciml numbers tht re less thn.004. Work will vry. Any numbers less thn.004 re cceptble, including those less thn.,,, 6 Write four deciml numbers tht hve n even number in the tenths plce, n odd number in the hundredths plce, nd prime number in the thousndths plce. Work will vry. Exmples: 0.237, 0.893, 0.475, 0.652 (numerls before the deciml point don't mtter).,,, 7 CHALLENGE Rob bbysits the kids next door every dy fter school for.5 hours. He erns $3.50 n hour. How much money will he ern in 6 weeks if school is in session 5 dys week the whole time? Show your work. $57.50 Work will vry. Bridges in Mthemtics Grde 5 Home Connections 50

Unit 3 Module 2 Session 7 More Deciml Prctice pge of 2 Round ech deciml number to the nerest whole number. 9.7 b 6.45 c 25.3 0 6 25 2 Round ech deciml number to the nerest tenth..65 b 0.3 c 8.07.7 0.3 8. 3 CHALLENGE Round ech deciml number to the nerest hundredth. 0.35 b 0.289 c 3.06 0.35 0.29 3.02 4 Solve. 8.53 8.98 7.89 + 2.48 4.76 + 2.2.0 4.22 30.0 5 Solve. Show your work. 7.45 20.75 83.75 9.98 2.53 = 7.68 + 3.07 = 00.03 6.28 = (continued on next pge) Bridges in Mthemtics Grde 5 Home Connections 5

Unit 3 Module 2 Session 7 More Deciml Prctice pge 2 of 2 Story Problems Show your work using numbers, lbeled sketches, or words. Work will vry. 6 Rchel hs $0.00. She wnts to buy book tht costs $6.79. Will she hve enough money left over to buy pen for $3.50? Explin. No, she will only get $3.2 in chnge. 7 Diego hs 3 dollr bills, 3 qurters, dime, nd 7 pennies. Sm hs 2 dollr bills, 5 qurters, 6 dimes, nd 9 pennies. Who hs more money? How much more? Sm hs $0.02 more thn Diego. b How much money do the boys hve in ll? $7.86 Review: Show your work using numbers, lbeled sketches, or words. 8 Tony hs box tht mesures 2 cm by 7 cm by 9 cm. Wht is the volume of the box?,596 cm 3 9 Eric is keeping trck of rinwter. On Mondy, it rined 3 4 cm. On Tuesdy it rined 2 8 cm. How much more did it rin on Tuesdy thn on Mondy? 3/8 cm Bridges in Mthemtics Grde 5 Home Connections 52

Unit 3 Module 3 Session 2 Deciml Prctice pge of 2 Fill in the blnks to convert the units in ech problem below. The following informtion my help you: gigbyte (GB) is equl to,000 megbytes (MB). megbyte (MB) is equl to,000 kilobytes (KB). kilobyte (KB) is equl to,000 bytes. 9,000 9 KB = bytes 43,000 b 43 KB = bytes c 9,600 9.6 KB = bytes 8,000 d 8 MB = KB e f 4,000 4 MB = KB 7,300 7.3 MB = KB 7,000 g 7 GB = MB 56,000 h 56 GB = MB i j 2,400 2.4 GB = MB 6,000,000 6 MB = bytes 2 Round ech deciml number to the nerest whole number. 5.3 b 6.8 c 2.25 5 7 2 (continued on next pge) Bridges in Mthemtics Grde 5 Home Connections 53

Unit 3 Module 3 Session 2 Deciml Prctice pge 2 of 2 3 Round ech number to the nerest tenth. 8.85 b 2.09 c 00.5 8.9 2. 00.2 4 Round ech number to the nerest hundredth. 24.275 b 36.308 c 3.495 24.28 36.3 3.50 5 Add or subtrct the decimls. 2.03 5.0 25.67 00.00 + 4.78 3.98 + 4.32 96.75 6.8.03 39.99 3.25 6 Isbell is building tree fort. The bse of the fort is 78 inches wide by 92 inches long. Wht is the re of the bse in squre inches? Show your work. 7,76 sq. inches Work will vry. b CHALLENGE Wht is the re of the bse in squre feet? Show your work. 49.83 sq. ft. Work will vry. Bridges in Mthemtics Grde 5 Home Connections 54