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 4 Techers Guide Units 1 8 Bridges in Mthemtics Grde 4 Assessment Guide Bridges in Mthemtics Grde 4 Techer Msters Bridges in Mthemtics Grde 4 Student Book Volumes 1 & 2 Bridges in Mthemtics Grde 4 Home Connections Volumes 1 & 2 Bridges in Mthemtics Grde 4 Techer Msters Bridges in Mthemtics Grde 4 Student Book Bridges in Mthemtics Grde 4 Home Connections Bridges in Mthemtics Grde 4 Components & Mnipultives Bridges Eductor Site Work Plce Gmes & Activities Digitl resources noted in itlics. The Mth Lerning Center, PO Box 12929, Slem, Oregon 97309. Tel 1 (800) 575-8130 www.mthlerningcenter.org 2017 by The Mth Lerning Center All rights reserved. Bridges nd Number Corner re registered trdemrks of The Mth Lerning Center. Prepred for publiction using Mc OS X nd Adobe Cretive Suite. Printed in the United Sttes of Americ. To reorder Home Connections, refer to number 2B4HC5 (pckge of 5 sets, Volumes 1 & 2). QBB4903 (1 & 2) Updted 2017-06-19. Number Corner Grde 4 Techers Guide Volumes 1 3 Number Corner Grde 4 Techer Msters Number Corner Grde 4 Student Book Number Corner Grde 4 Techer Msters Number Corner Grde 4 Student Book Number Corner Grde 4 Components & Mnipultives Word Resource Crds The Mth Lerning Center grnts permission to reproduce nd shre print copies or to shre electronic copies of the mterils in this publiction for use in the clssroom for which the publiction ws purchsed. Licensed users my shre print or electronic copies of the mterils with other district stff nd techers nd with students nd their fmilies in support of implementtion in the clssroom for which the mterils were purchsed. All other uses nd distribution of the mterils re expressly prohibited, nd you my not mke print or electronic copies of the mterils vilble for public ccess. For usge questions, plese contct The Mth Lerning Center. Bridges in Mthemtics is stndrds-bsed K 5 curriculum tht provides unique blend of concept development nd skills prctice in the context of problem solving. It incorportes Number Corner, collection of dily skill-building ctivities for students. The Mth Lerning Center is nonprofit orgniztion serving the eduction community. Our mission is to inspire nd enble individuls to discover nd develop their mthemticl confidence nd bility. We offer innovtive nd stndrds-bsed professionl development, curriculum, mterils, nd resources to support lerning nd teching. To find out more, visit us t www.mthlerningcenter.org. ISBN 978-1-60262-425-2 Bridges in Mthemtics Grde 4 Home Connections

Bridges Grde 4 Home Connections Volumes 1 & 2 Unit 1 Multiplictive Thinking Number Line Puzzles...1 Models for Multipliction...3 Modeling Multipliction & Division...5 Fctors & Te Lights...7 Multipliction Fct Strtegies...9 Multiplying by 8 & 9...11 Multiples, Flowers & Crds...13 Arrys & Fctors...15 Mesuring Lengths...17 Mss & Volume Story Problems...19 Unit 2 Multi-Digit Multipliction & Erly Division Mesuring in Centimeters... 21 More Multiplying by Ten... 25 Which Opertion?... 27 Coins & Arrys...31 Multipliction Strtegies... 33 Multiplying by Multiples of Ten... 35 Design Floor Pttern... 37 Multiplying & Dividing...41 Multipliction & Division Puzzles... 43 Moolh on My Mind... 45 Unit 3 Frctions & Decimls Skills Review 2... 49 Frction & Division Story Problems... 51 Thinking About Frctions... 53 Brownie Dessert... 55 Plnning Grden... 57 Frctions & More Frctions... 59 More Compring Decimls & Frctions...61 Decimls, Frctions & Story Problems... 63 Equl, Not Equl... 65 Frnkie s Frctions & Decimls... 67 Unit 4 Addition, Subtrction & Mesurement Number Riddles & Stories... 69 Big Numbers... 71 Addition Algorithm & More... 73 Think Before You Add... 75 Number Crds... 77 Thinking About Subtrction... 79 Which Mesurement Is Best?... 81 Running the Rce... 83 Unit 4 Review 1... 85 Unit 4 Review 2... 87 Bridges in Mthemtics Grde 4 Home Connections

Unit 5 Geometry & Mesurement Reviewing Are & Perimeter... 89 Angles & Rectngles... 91 Protrctor Prctice... 93 Drwing Two-Dimensionl Figures... 95 Symmetry... 99 Clssifying & Drwing Qudrilterls... 101 Are & Perimeter Review... 103 Are, Perimeter & Multipliction... 105 Clock Angles & Shpe Sketches... 107 Unit 5 Review...109 Unit 6 Multipliction & Division, Dt & Frctions Are & Perimeter Story Problems...111 Frction Stories...113 Conrd s Room...115 Plom s Picture...117 Frnkie s Firground...119 Perimeter & Are... 121 Rope Climb Results & Skills Review... 123 Bkery Bundles... 125 Dnny s Dt... 127 Unit 6 Review... 129 Unit 7 Reviewing & Extending Frctions, Decimls & Multi-Digit Multipliction Conversion Tbles... 131 Multipliction Review & Frction Comprisons... 133 Sketch & Compre Frctions... 135 Frction Action... 137 Decimls on Number Lines & Grids... 139 Stndrd Algorithms... 141 Choose Your Strtegy... 143 Vribles & Expressions... 145 Unit 7 Review... 147 Unit 8 Plyground Design Another Grssy Field... 149 Ten-Foot Seesw... 151 Circle Explortions... 153 Most Importnt Items... 155 Pricing Plyground Equipment... 157 Mesurement & Deciml Review... 159 Drwing the Plyground... 161 Plyground Mp... 163 Designing Plyground Equipment... 165 Bridges in Mthemtics Grde 4 Home Connections

Unit 1 Module 1 Session 2 Number Line Puzzles pge 1 of 2 Note to Fmilies Students cn use number lines to review the multipliction fcts they lerned in third grde. Number lines cn help students use fcts they know to help them figure fcts they don t remember. Tlk together bout reltionships between fcts tht you see in the two number lines below, such s numbers tht double. 1 Fill in the blnks in the number lines. 2 4 3 4 4 4 8 4 9 4 8 12 16 32 36 10 40 4 b 2 8 8 4 8 16 3 32 64 8 8 8 10 8 24 72 9 80 2 Complete the fcts. 8 8 8 8 8 7 7 2 4 8 10 9 10 9 16 32 64 80 72 70 63 3 Roger s little brother, Sul, wnts to know if 5 7 = 7 5. If you were Roger, how would you explin to Sul whether the eqution is true? Work will vry, it is true tht 5 7 = 7 5. (continued on next pge) Bridges in Mthemtics Grde 4 Home Connections 1

Unit 1 Module 1 Session 2 Number Line Puzzles pge 2 of 2 4 Ech of the 29 students in Mr. Brown s fourth grde brought 2 notebooks to clss the first dy of school. How mny notebooks ws tht in ll? Show your thinking with numbers, sketches, or words. Then write n eqution tht represents your work. 29 students 2 notebooks per student = 58 notebooks Eqution 58 notebooks Answer, lbeled with correct units 5 Ech of the students in Mr. Smith s clss lso brought in 3 pocket folders. Mr. Smith wrote multipliction eqution to compre the number of students to the number of pocket folders they brought in. Fill in the bubble to show wht this eqution mens. 87 = 3 29 NN 87 is 3 more thn 29 N 87 is 3 times s mny s 29 NN 29 is 3 times s mny s 87 6 CHALLENGE If 5 students ech brought in 8 boxes with 10 pencils per box, nd 10 students ech brought in 8 boxes with 5 pencils per box, how mny totl pencils did the students bring in? Show your thinking with numbers, sketches, or words. (5 8 10) + (10 8 5) = 800 Eqution 800 pencils Answer, lbeled with correct units Bridges in Mthemtics Grde 4 Home Connections 2

Unit 1 Module 1 Session 4 Models for Multipliction pge 1 of 2 Write story sitution to go with ech multipliction model. ex 1 2 3 4 Multipliction Model 2 3 = 6 0 7 14 21 28 35 42 7 6 = 42 4 4 = 16 4 6 = 24 Number of 1 2 4 8 Number of 6 12 24 Story Keith s dog, Spot, te 2 cns of dog food every dy for 3 dys in row. Spot te 6 cns of dog food in 3 dys. Work will vry. Exmple: A grsshopper jumps 7 times, nd ech jump is 6 feet, for totl of 42 feet. Work will vry. Exmple: There were 4 kids. Ech kid te 4 brownies. They te 16 brownies in ll. Work will vry. Exmple: A number grid is 4 feet wide nd 6 feet long. Its totl re is 24 sq. ft. Work will vry. Exmple: One nt hs 6 legs. For ny number of nts, multiply by 6 to find the totl number of legs. (continued on next pge) Bridges in Mthemtics Grde 4 Home Connections 3

Unit 1 Module 1 Session 4 Models for Multipliction pge 2 of 2 5 6 Multipliction Model 5 6 = 30 $8 $8 $8 $8 $8 $8 $8 $8 $8 8 9 = 72 Story Work will vry. Exmple: Five rows with 6 tiles per row cover floor. The floor is covered by 30 tiles. Work will vry. Exmple: Mrs. Smith hs 9 grndchildren. She gve ech grndchild $8. She gve them $72 in ll. 7 There re 4 rows of cryons in this box. Ech row hs the sme number of cryons. How mny cryons re in the box? Show your thinking. 64 Cryons 8 Techers collected $5 from ech of the 130 fourth grde students t the beginning of the yer for field trips. The first field trip cost $120. The second field trip cost $250. How much cn they spend on the lst field trip if they need to hve $25 left over to wsh the bus? Show your thinking using words, numbers, or pictures. $255 Bridges in Mthemtics Grde 4 Home Connections 4

Unit 1 Module 1 Session 6 Modeling Multipliction & Division pge 1 of 2 For problems 1 nd 2, complete the sketches nd write the equtions. 4 3 1 2 5 6 5 = = 3 3 Copy one eqution from bove nd write story problem to go with it. ex I bought 5 pcks of pencils. Ech pck hd 4 pencils in it. How mny pencils did I get? (5 4 = 20) Work will vry. 4 20 18 6 Complete the number line nd rtio tble. 4 5 2 5 3 5 4 5 5 5 6 5 1 2 3 4 5 6 7 8 15 25 10 20 30 3 6 9 12 15 18 21 24 (continued on next pge) Bridges in Mthemtics Grde 4 Home Connections 5

Unit 1 Module 1 Session 6 Modeling Multipliction & Division pge 2 of 2 6 Mr. Still s clss hs music for 50 minutes nd then independent reding for 20 minutes. Music strts t 8:30. Wht time does Mr. Still s clss finish independent reding? 9:40 7 Ms. Ford s clss strts rt t 9:30 nd finishes t 10:15. They spend twice s much time in mth clss. If they strt mth t 1:10, wht time do they finish mth? 2:40 Bridges in Mthemtics Grde 4 Home Connections 6

Unit 1 Module 2 Session 2 Fctors & Te Lights pge 1 of 2 1 Imgine using 48 tiles to build ech rectngle below. Write in the missing dimensions on the rectngle sketches. 1 48 48 2 24 48 6 3 12 8 48 16 48 4 48 2 The fctors of 48 re: 48 1 nd 2 nd 4 nd 8 nd 16 nd 3 Is 48 prime number or composite number? Composite b How do you know? Work will vry. Exmple: It hs mny fctors. 24 12 6 3 4 Study your list of fctors for 48. Wht ptterns do you observe? Work will vry. Exmple: If you double one fctor, you hlve the other to mke fctor pirs. You cn hve one odd nd one even fctor or two even fctors. You cnnot hve two odd fctors in fctor pir. (continued on next pge) Bridges in Mthemtics Grde 4 Home Connections 7

Unit 1 Module 2 Session 2 Fctors & Te Lights pge 2 of 2 5 Write the missing prts on this number line: 3 7 8 3 3 9 10 3 3 11 3 12 24 21 27 30 33 36 6 Te light cndles re being pckged 6 to box. Fill in the tble: Number of Boxes 4 5 6 7 8 9 10 Totl Number of 24 30 36 42 48 54 60 Cndles For the problems below, use numbers, words, or lbeled sketches to explin your nswers. 7 Jne hs 7 te light cndles. Aish hs 5 times more cndles thn Jne. How mny cndles does Aish hve? 35 cndles 8 Theo hs 50 te light cndles. Mdeline hs hlf s mny cndles s Theo. How mny cndles does Mdeline hve? 25 cndles Bridges in Mthemtics Grde 4 Home Connections 8

Unit 1 Module 2 Session 4 Multipliction Fct Strtegies pge 1 of 2 Doubles Plus One Set Fcts When one of the fctors is 3, you cn think bout the Doubles fct, nd then dd one more set of the number being doubled. For exmple, 6 3 is 6 doubled (12) plus one more set of 6. 3 6 = (2 6) + 6 12 + 6 = 18 7 3 = (7 2) = 14 14 + 7 = 21 You cn use this strtegy with lrger numbers, too: 3 25 = (2 25) + 25 50 + 25 = 75 150 3 = (2 150) + 150 300 + 150 = 450 1 Shde in the res nd complete the equtions. 3 5 = 3 8 = 2 If you hd 2 boxes of 8 cryons nd your techer gve you nother box of 8 cryons, how mny cryons would you hve? 24 cryons 15 24 3 Cody bought 2 bgs of 5 pples. He lredy hd 1 bg of 5 pples t home. How mny pples does Cody hve in ll? 15 pples 4 Write story problem for Doubles Plus One Set ( 3) fct. Work will vry. (continued on next pge) Bridges in Mthemtics Grde 4 Home Connections 9

Unit 1 Module 2 Session 4 Multipliction Fct Strtegies pge 2 of 2 Tens Fcts 5 Circle the groups of 10 in the rrys below, nd solve the equtions. 7 10 = 10 9 = When you understnd plce vlue, multiplying lrger numbers by 10 cn be esy, too. 10 25 = 250 670 10 = 6700 Hlf-Tens Fcts 70 When one of the fctors is 5, you cn multiply the other fctor by 10 nd then divide the nswer in hlf. 90 6 Fill in the blnks below. 30 30 5 6 = 6 10 = 60 Hlf of 60 is Hlf-Tens Fcts n 10 5 1 10 5 2 20 10 3 30 15 4 40 20 5 50 25 6 60 30 7 Mx hd 6 dimes in his pocket. How much money did he hve? 60 8 Jose hd 7 nickels in his pocket. How much money did he hve? 35 9 If Suzie bought 9 bskets with 5 lrge peches in ech bsket, how mny peches did she buy? 45 peches Bridges in Mthemtics Grde 4 Home Connections 10

Unit 1 Module 2 Session 6 Multiplying by 8 & 9 pge 1 of 2 1 Circle ll the Double-Double-Doubles fcts ( 8) in blue. Then solve them nd use regulr pencil to write ech product. 2 Circle ll the Tens Minus One Set fcts ( 9) in red. Then solve them nd use regulr pencil to write ech product. 6 9 7 7 5 9 4 8 9 8 54 36 56 63 40 3 4 9 8 9 9 8 6 8 9 3 Pick one fct from bove nd write it here:. Work will vry. b Color in the rry for tht fct on the grid below. c 27 32 54 Lbel the rry to show how you found the product, nd use equtions or words to explin your work. 64 81 Work will vry. (continued on next pge) Bridges in Mthemtics Grde 4 Home Connections 11

Unit 1 Module 2 Session 6 Multiplying by 8 & 9 pge 2 of 2 4 Shde in nd lbel the rrys of two more Double-Double-Double fcts in the grids below. Write n eqution for ech fct. Work will vry. 5 Shde in nd lbel the rrys of two more Tens Minus One Set fcts in the grids below. Write n eqution for ech fct. Work will vry. Bridges in Mthemtics Grde 4 Home Connections 12

Unit 1 Module 3 Session 2 Multiples, Flowers & Crds pge 1 of 2 1 When you count by number, you re nming the multiples of tht number. For exmple, if you skip-count by 5s, you re nming the multiples of 5: 5, 10, 15, 20, 25, nd so on. In ech sequence below, fill in the missing multiples. ex 5, 10, 15,, 25, 30, 3, 6,, 9 12, 15, 18,, 21 24 b 6,, 12 18,, 24 30 c 9, 18,, 27 36, 45,, 54 63 2 Circle ll the multiples of the number in ech box. ex 5 16 20 15 42 36 45 18 2 5 6 7 8 14 21 10 b 4 8 6 14 16 20 28 19 c 7 22 33 21 14 16 42 35 d 8 28 32 48 16 60 72 19 e 3 21 35 18 36 44 12 29 3 Fill in the missing numbers. 9 3 4 2 7 9 9 4 6 8 81 20 35 27 16 12 56 3 8 24 7 2 14 6 5 30 9 4 36 3 4 12 6 6 6 6 6 2 4 8 16 32 12 24 48 96 192 (continued on next pge) Bridges in Mthemtics Grde 4 Home Connections 13

Unit 1 Module 3 Session 2 Multiples, Flowers & Crds pge 2 of 2 4 Four friends were mking crds to sell t the holidy sle. Ech friend mde 9 crds. They put ll their crds together nd then bundled them in groups of 6 crds to sell. How mny bundles of 6 crds did they mke? Show ll your work. 6 bundles 5 CHALLENGE Zck mesured rectngulr grden t the prk. The longer sides ech mesured 15 feet nd were 3 times longer thn the shorter sides. If Zck wlked ll the wy round the grden, how fr did he wlk? 40 feet Bridges in Mthemtics Grde 4 Home Connections 14

Unit 1 Module 3 Session 4 Arrys & Fctors pge 1 of 2 1 Drw nd lbel rectngulr rry to show two fctors for ech number. Do not use 1 s fctor. Then write the fct fmily tht goes with ech rry tht you drw. ex 8 16 b 18 Work will vry. Work will vry. 4 Exmple: Exmple: 2 2 8 3 6 2 4 = 4 2 = 8 4 2 = 8 2 8 8 4 = 2 8 16 3 6 18 = = = = = 8 2 16 6 3 18 = 16 8 2 18 6 3 16 = 2 8 18 3 6 = 2 List ll the fctors of ech number below. ex 12 1, 2, 3, 4, 6, 12 16 1, 2, 4, 8, 16 b 17 c 24 1, 17 1, 2, 3, 4, 6, 8, 12, 24 d 9 e 36 1, 3, 9 1, 2, 3, 4, 6, 9, 12, 18, 36 3 Circle the prime number(s) in problem 2. 17 Drw squre round the squre number(s) in problem 2. 9, 16, 36 (continued on next pge) Bridges in Mthemtics Grde 4 Home Connections 15

Unit 1 Module 3 Session 4 Arrys & Fctors pge 2 of 2 4 Is the number 25 prime or composite? How do you know? Composite. Work will vry, Exmple: it hs 3 fctors. 1, 5, 25. 5 Judy hs collection of 30 stmps. She cn divide the stmps into 2 equl groups of 15 stmps. Wht re two other wys she could divide the stmps into equl groups? Work will vry, Exmple: 3 groups of 10 (or 10 groups of 3) 5 groups of 6 (or 6 groups of 5) 15 groups of 2 6 CHALLENGE Judy s brother Sm hs collection of 96 comic books. Wht re the ten wys Sm could divide his comic books into equl groups? 2 groups of 48 (48 groups of 2) 3 groups of 32 (32 groups of 3) 4 groups of 24 (24 groups of 4) 6 groups of 16 (16 groups of 6) 8 groups of 12 (12 groups of 8) Bridges in Mthemtics Grde 4 Home Connections 16

Unit 1 Module 4 Session 1 Mesuring Lengths pge 1 of 2 1 Would you use centimeters or meters to mesure the length of your bedroom? b your big toe? c cr? d mouse? e meters meters centimeters centimeters meters the gym? 2 Fill in the tble below to convert between centimeters nd meters. The first 2 rows re done for you. centimeters (cm) meters (m) 100 cm 1 m 200 cm 2 m 300 cm 3 m 800 cm 8 m 2500 cm 25 m 3100 cm 31 m 3 For ech of the following story problems, show your work using numbers, lbeled sketches, or words. Write n eqution, including the nswer lbeled with the correct units, to represent your work. Chloe is bby who is 24 inches tll. Her fther is 3 times s tll s she is. How mny inches tll is Chloe s fther? 72 inches 24 inches 3 = 72 inches (continued on next pge) Bridges in Mthemtics Grde 4 Home Connections 17

Unit 1 Module 4 Session 1 Mesuring Lengths pge 2 of 2 b Chloe s dog, Wilson, is 27 inches long. Chloe s hmmock is 4 times s long s Wilson. How mny inches long is the hmmock? 108 inches 27 inches 4 = 108 inches 4 CHALLENGE A smll tble is 2 feet by 3 feet. A lrge tble is twice s long nd twice s wide s the smll tble. Wht is the re of the lrge tble in squre feet? 24 sq. ft. Bridges in Mthemtics Grde 4 Home Connections 18

Unit 1 Module 4 Session 3 Mss & Volume Story Problems pge 1 of 2 For ech problem, show your thinking with numbers, sketches, or words. Then write n eqution tht represents your work. 1 DJ nd Tyler re wtering plnts. DJ uses 18 liters of wter. Tyler uses 5 times s much wter. How much wter does Tyler use? 18 liters 5 = 90 liters Eqution 90 liters Answer, lbeled with correct units 2 Chris nd Jocelyn re building ptio out of bricks. Chris uses 23 kilogrms of bricks. Jocelyn uses 6 times s mny kilogrms. How mny kilogrms of bricks does Jocelyn use? 23 kg 6 = 138 kg Eqution 138 kg Answer, lbeled with correct units 3 The mss of one bouncy bll is 14 grms. Trcy hs 8 bouncy blls. Wht is the mss of ll 8 bouncy blls? 14 g/bll 8 blls = 112 g Eqution 112 grms Answer, lbeled with correct units 4 True or Flse? A liter is 1,000 times s much s milliliter. b A grm is 300 times smller thn kilogrm. c There re 99 centimeters in meter. 5 Fill in the bubble to show which unit you would use to mesure the mount of wter in very lrge pitcher. NN milliliter NN kilogrm N liter NN F T F centimeter (continued on next pge) Bridges in Mthemtics Grde 4 Home Connections 19

Unit 1 Module 4 Session 3 Mss & Volume Story Problems pge 2 of 2 6 Fill in the bubble to show which unit you would use to mesure the mss of mouse. NN centimeter N grm NN liter NN kilogrm 7 CHALLENGE Ann hs 15 stickers. Ros hs 3 times s mny stickers s Ann. Dwn hs 3 times s mny stickers s Ros. Sr hs 17 fewer stickers thn Dwn. How mny stickers does Ros hve? Show your work. 45 stickers b How mny stickers does Dwn hve? Show your work. 135 stickers c How mny stickers does Sr hve? Show your work. 118 stickers Bridges in Mthemtics Grde 4 Home Connections 20

Unit 2 Module 1 Session 2 Mesuring in Centimeters pge 1 of 3 Note to Fmilies This Home Connection sks students to mesure common items t home in centimeters. If you hve ruler or tpe mesure t home mrked in centimeters, hve your child use it. If not, you cn cut out the strips below nd tpe or glue them together to crete mesuring tpe. Mesuring in Centimeters 1 Find ruler or tpe mesure tht is mrked in centimeters. You cn lso cut out the strips below nd tpe or glue them together to mke your own mesuring tpe. 2 By yourself or with fmily member or two, mesure the items listed on the worksheet nd record your results. 1 2 3 4 5 6 7 8 9 10 glue or tpe 11 12 13 14 15 16 17 18 19 21 22 23 24 25 26 27 28 29 31 32 33 34 35 36 37 38 39 41 42 43 44 45 46 47 48 49 20 30 40 50 glue or tpe glue or tpe glue or tpe glue or tpe 51 52 53 54 55 56 57 58 59 60 (continued on next pge) Bridges in Mthemtics Grde 4 Home Connections 21

Bridges in Mthemtics Grde 4 Home Connections 22

Unit 2 Module 1 Session 2 Mesuring in Centimeters pge 2 of 3 Plese mesure the following objects in centimeters nd record the results. 1 width of your bed 2 width of door Object To Be Mesured Mesurement in Centimeters Work will vry, exmple: 102 cm Work will vry, exmple: 104 cm 3 height from the floor to the set of your fvorite chir 4 length of telephone or cell phone Work will vry, exmple: 46 cm Work will vry, exmple: 15 cm 5 dimensions of your fvorite book (length nd width) Lorett nd Pls Work will vry, exmple: 14 cm 21 cm 6 width of your refrigertor Work will vry, exmple: 102 cm 7 dimensions of towel (length nd width) 8 length of your toothbrush Work will vry, exmple: 75 cm Work will vry, exmple: 19 cm (continued on next pge) Bridges in Mthemtics Grde 4 Home Connections 23

Unit 2 Module 1 Session 2 Mesuring in Centimeters pge 3 of 3 Locte objects t home tht re bout 6 cm nd 80 cm long or tll. Record the nme of the object below. Approximte Length 1 bout 6 cm long or tll 2 bout 80 cm long or tll Object You Found Work will vry, exmple: door key Work will vry, exmple: bedside tble 3 Jsmine is mking cookies for the fourth grde clss. The recipe clls for 8 ounces of chocolte chips. She needs to triple the recipe to hve enough for everyone, nd she is going to dd 2 more ounces of chocolte chips to the tripled btch to mke the cookies extr delicious. How mny ounces of chocolte chips does she need? Use numbers, lbeled sketches, or words to solve the problem. Show your work. 26 ounces b Fill in the bubble beside the eqution tht best represents this problem. (The letter c stnds for ounces of chocolte chips.) NN 8 + 3 + 2 = c N (8 3) + 2 = c N N (8 3) 2 = c 4 Jsmine cn fit 12 cookies on cookie sheet. She needs 6 times tht mny cookies for the whole fourth grde. Jsmine lso wnts to hve 2 cookies for ech of the 4 techers. How mny cookies does Jsmine need to mke? Show your work. 80 cookies 5 CHALLENGE When 2 pieces of rope re plced end-to-end, they mesure 40 meters in length. When the 2 pieces re lid side-by-side, one is 10 meters longer thn the other. How long is ech piece of rope? Show your work. 15m nd 25m. Work will vry. Exmple: if you tke off the extr 10m, the totl is 30 m, so ech lengh is the sme: 15m. Tht mens the shorter one is 15 cm nd the longer one is 25m. 15 m 10 m 30 m totl, 15 m ech. Bridges in Mthemtics Grde 4 Home Connections 24

Unit 2 Module 1 Session 4 More Multiplying by Ten pge 1 of 2 1 For ech rectngle below, lbel the dimensions, find the re, nd write n eqution to describe the rry. Lbeled Arry Are Multipliction Eqution ex 10 6 60 sq. units 6units 10 units = 60 sq. units 10 8 80 sq. units 8 units 10 units = 80 sq. units b 10 7 70 sq. units 7 units 10 units = 70 sq. units c 10 3 10 130 sq. units 10 units 13 units = 130 sq. units (continued on next pge) Bridges in Mthemtics Grde 4 Home Connections 25

Unit 2 Module 1 Session 4 More Multiplying by Ten pge 2 of 2 2 Write multipliction eqution or story problem in ech empty box to complete the tble. Story Problems Multipliction Eqution ex Srh hs 5 dimes. How much money does she hve? 5 10 = 50 b c Jmes hs 12 dimes in his pocket. How much money does he hve? Lrry hd 16 dimes in his collection of old coins. How much money does he hve? Work will vry. Exmple: Alex hs 30 dimes. How much money does he hve? 12 10 = 120 or $1.20 16 10 = 160 or $1.60 10 30 = $3.00 d Work will vry. Exmple: Eloise found 21 dimes while clening the house. How much money did she find? 21 10 = $2.10 3 CHALLENGE Dn hs only nickels in her hnd, nd Ajh hs exctly the sme number of dimes nd no other coins. Together they hve totl of 90. How mny coins is ech person holding? Show your work below. 6 coins ech. Work will vry, exmple: # of coins nickels dimes 9 45 90 4 20 40 5 25 50 6 30 60 Bridges in Mthemtics Grde 4 Home Connections 26

Unit 2 Module 2 Session 1 Which Opertion? pge 1 of 3 1 Josie ws plnning prty. She drew sketch of how she wnted to set up the chirs nd tbles. Which eqution best represents the number of chirs she sketched? NN 4 + 6 = 10 N 6 4 = 24 NN 42 4 = 20 NN 6 6 = 36 Key: 1 Chir: 1 Tble: 2 There were 24 kids t Josie s prty (including her), nd ech of them te 3 pieces of pizz. Which expression shows how mny pieces of pizz they te in ll? NN 3 + 24 NN 24 3 NN 24 3 N 24 3 3 At the end of the prty, the kids broke open the piñt. When they scrmbled for the cndy, Gbe got 5 pieces. Mri got 3 times s mny pieces s Gbe. Which of the numbers described below shows how mny pieces of cndy Mri got? NN The sum of 5 nd 3 NN The difference between 5 nd 3 N The product of 5 nd 3 NN The quotient of 5 nd 3 4 Josie hs 5 gllons of fruit punch. This tble shows how mny cups there re in different numbers of gllons. Gllons Cups 1 16 2 32 3 48 Wht is one wy to figure out how mny cups of punch tht is? NN Add 16 to 5 N Multiply 5 by 16 NN Divide 16 by 5 NN Subtrct 5 from 16 (continued on next pge) Bridges in Mthemtics Grde 4 Home Connections 27

Unit 2 Module 2 Session 1 Which Opertion? pge 2 of 3 5 Drw line to mtch ech story problem below to the eqution tht best shows how to solve the problem. Then complete ech eqution. You cn use the Bse Ten Grid Pper on the next pge if you like. Josie s mom bought 4 pckges of mini-cndy brs to put in the piñt. There were 28 in ech pckge. How mny mini-cndy brs were there 28 + 4 = 32 in ll? b Josie got 28 npkins out of the pckge but then relized tht she could put 4 of them wy. How mny did she set out on the tbles? 24 28 4 = c d Josie s brother blew up 28 blloons for the prty nd hd enough to put 4 t ech tble. How mny tbles were there? Josie hd $28 in her svings ccount. Josie erned $10 helping with chores. Josie spent $6 right wy, but she put the other $4 in her ccount. How much money did she hve in her svings ccount then? 112 28 4 = 7 28 4 = 6 Write story problem for ech of the two equtions below, nd then solve your own problems. Use the Bse Ten Grid Pper on the next pge if you like. Equtions Story Problems Solution 16 8 = Work will vry. 128 b 16 8 = Work will vry. 2 7 CHALLENGE Josie s mom bought 9 pizzs for the prty. How will she need to cut them in order to hve enough pieces for the prty? (See Problem 2 for more informtion.) Use numbers, sketches, or words to show your work on nother sheet of pper. She will need to cut them into thirds to hve more thn 24 pieces. Bridges in Mthemtics Grde 4 Home Connections 28 (continued on next pge)

Unit 2 Module 2 Session 1 Which Opertion? pge 3 of 3 Bse Ten Grid Pper Bridges in Mthemtics Grde 4 Home Connections 29

Unit 2 Module 2 Session 3 Coins & Arrys pge 1 of 2 1 Write multipliction eqution to show how much ech group of coins is worth. Coin Group of Coins Multipliction Eqution ex 5 nickels 5 5 = 25 b c d e f g h 10 nickels 15 nickels 10 dimes 20 dimes 30 dimes 8 qurters 12 qurters 17 qurters 10 5 = 50 15 5 = 75 10 10 = 100 or $1.00 20 10 = 200 or $2.00 30 10 = 300 or $3.00 8 25 = 200 or $2.00 12 25 = 300 or $3.00 17 25 = 425 or $4.25 2 Lbel ech rry frme below. Then fill it in with lbeled rectngles. Write n eqution to show how you got the totl, nd then write multipliction eqution to mtch the rry. (Cut out the bse ten re pieces if you wnt to build the rrys.) Lbeled Arry Frme & Rectngles 10 4 Addition Eqution Multipliction Eqution ex 4 4 x 10 4 x 4 40+16=56 4 14=56 10 9 3 3 10 3 9 30 + 27 = 57 3 19 = 57 (continued on next pge) Bridges in Mthemtics Grde 4 Home Connections 31

Unit 2 Module 2 Session 3 Coins & Arrys pge 2 of 2 Lbeled Arry Frme & Rectngles Addition Eqution Multipliction Eqution 10 3 b 5 5 10 5 3 50 + 15 = 65 5 13 = 65 10 6 c 6 6 10 6 6 60 + 36 = 96 6 16 = 96 3 CHALLENGE Rin sid, How mny different wys re there to mke 30 using pennies, nickels, dimes, or qurters? Wht is this problem sking you to do? Work will vry. Exmple: Find ll the wys to mke 30 with pennies, nickels, dimes, or qurters. b Check the strtegy you pln to use (check one): Work wil vry. guess nd check mke tble or n orgnized list drw digrm other c Show your work below. 18 d There re different wys to mke 30 using pennies, nickels, dimes, or qurters. Bridges in Mthemtics Grde 4 Home Connections 32

Unit 2 Module 2 Session 5 Multipliction Strtegies pge 1 of 2 1 Solve these problems in your hed. Fill in the blnks. 10 3 30 20 3 30 3 40 3 60 90 120 50 3 60 3 70 3 150 180 210 80 90 100 1,000 10,000 100,000 3 3 3 3 3 3 240 270 300 3,000 30,000 300,000 1,000,000 3 3,000,000 2 Explin ny strtegies you used to mke it esier to figure out the nswers to the problems bove. Work will vry. 3 Solve these problems in your hed. Fill in the blnks. 10 20 30 40 50 60 70 4 5 7 2 5 4 5 40 100 210 80 250 240 350 80 90 100 1,000 60 70 80 4 5 8 9 8 2 5 320 450 800 9,000 480 140 400 400 300 500 600 200 700 800 4 6 5 9 8 4 5 1,600 1,800 2,500 5,400 1,600 2,800 4,000 (continued on next pge) Bridges in Mthemtics Grde 4 Home Connections 33

Unit 2 Module 2 Session 5 Multipliction Strtegies pge 2 of 2 4 Look t the rectngle below. If the re is 240 squre centimeters nd one side is 12 centimeters, wht is the length of the other side? Show your work. Write the nswer on the line provided below. Be sure to lbel it with the correct units. x 12 cm 240 sq. cm The length of the side lbeled x is 5 Soni mesured the cover of the librry book she ws reding. The length ws 10 inches nd the width ws 5 inches. Which eqution below represents how to find the re of her book s cover? Fill in the bubble to show. NN 10 5 = NN 10 5 = N 10 5 = NN 6 Fill in the rtio tble for 31. 20 cm 1 2 20 3 30 10 5 50 31 62 620 93 930 310 155 1550 10 + 5 = 7 CHALLENGE 900 400 800 600 700 800 800 9 12 9 12 11 8 12 8,100 4,800 7,200 7,200 7,700 6,400 9,600 Bridges in Mthemtics Grde 4 Home Connections 34

Unit 2 Module 3 Session 2 Multiplying by Multiples of Ten pge 1 of 2 1 Solve ech problem below: 2 16 = 32 b 20 16 = 320 c 4 21 = 84 d 40 21 = 840 e 8 15 = 120 f 80 15 = 1,200 2 Fill in the blnks 6 20 = 6 2 10 b 30 8 = 3 10 8 c 5 100 = 5 10 10 d 40 7 = 4 10 7 4 Fill in the Multiple Wheel below. 36 240 360 8 90 2 9 20 4 60 3 6 30 24 120 80 12 (continued on next pge) Bridges in Mthemtics Grde 4 Home Connections 35

Unit 2 Module 3 Session 2 Multiplying by Multiples of Ten pge 2 of 2 5 Kyr is putting up stremers for prty. She uses 75 feet of stremers to decorte one wll. Two more wlls lso ech use 75 feet of stremers. Kyr cuts 75 feet of stremers for the lst wll, but this wll hs lrge poster on it, nd she only needs to use 68 feet of stremers. How mny feet of stremers did Kyr use in ll? 293 feet 6 CHALLENGE Luis nd Kyr re getting redy for the prty. Luis mkes 6 sheets of cookies. Ech sheet hs 13 cookies on it. He lso mkes 4 trys of brownies. Ech try hs 16 brownies on it. How mny cookies nd brownies did Luis mke in ll? 142 brownies nd cookies Bridges in Mthemtics Grde 4 Home Connections 36

Unit 2 Module 3 Session 4 Design Floor Pttern pge 1 of 3 Note to Fmilies This Home Connection combines mth nd design. Students use their cretivity to design pttern nd then prctice computtion to determine how much it would cost to mke tht pttern in tiles. 1 Choose one of the two Floor Plns: Floor Pln 1 below or Floor Pln 2 on the bck of this pge. (If you relly enjoy this project, you cn do both.) 2 Drw one of the following 3 tile designs in ech squre on your floor pln. Do not use the sme design for every squre. Tile A Tile B Tile C 3 Answer questions 1 6 on the worksheet. Floor Pln 1 (continued on next pge) Bridges in Mthemtics Grde 4 Home Connections 37

Unit 2 Module 3 Session 4 Design Floor Pttern pge 2 of 3 Floor Pln 2 (continued on next pge) Bridges in Mthemtics Grde 4 Home Connections 38

Unit 2 Module 3 Session 4 Design Floor Pttern pge 3 of 3 Clculting the Costs of Your Floor Pttern(s) Here is the cost of ech tile. Tile A: 25 cents Tile B: 50 cents Tile C: 1 dollr Use your floor pln(s) nd the informtion bove to nswer the questions below (Remember, you only hve to do one of the floor plns, not both.) Question Floor Pln 1 Floor Pln 2 1 How mny tiles did you need for the floor pln you chose? 2 How mny of ech tile did you use in your design of the floor pln? 3 How much money did ll the A tiles cost? 4 How much money did ll the B tiles cost? 5 How much money did ll the C tiles cost? 6 How much money did the entire floor pttern cost? b c 20 tiles 80 tiles Work will vry. Work will vry. Work will vry. Work will vry. Work will vry. Work will vry. Work will vry. b c Work will vry. Work will vry. Work will vry. Work will vry. Work will vry. Work will vry. Work will vry. Bridges in Mthemtics Grde 4 Home Connections 39

Unit 2 Module 4 Session 1 Multiplying & Dividing pge 1 of 2 1 Fill in the missing numbers. 8 4 6 5 7 7 6 8 6 6 32 30 49 48 36 8 9 5 7 8 7 7 5 6 9 56 63 25 42 72 2 Complete the multipliction tbles below. ex 5 2 9 3 8 6 7 4 2 10 4 18 6 16 12 14 8 5 2 9 3 8 6 7 4 10 50 20 90 30 80 60 70 40 b c 5 2 9 3 8 6 7 4 5 25 10 45 15 40 30 35 20 5 2 9 3 8 6 7 4 9 45 18 81 27 72 54 63 36 3 Use wht you know bout multiplying by 10 to help solve these problems. 12 12 12 18 18 18 10 5 9 10 5 10 120 60 108 180 90 180 (continued on next pge) Bridges in Mthemtics Grde 4 Home Connections 41

Unit 2 Module 4 Session 1 Multiplying & Dividing pge 2 of 2 4 Mrs. Lrsen ws mking gift bgs for the 6 students in her reding group. She ws putting little ersers in the bgs. She hd bg of 20 ersers. How mny ersers did ech student get? Show ll your work. Ech student got 3 ersers, nd 2 were left over. Work will vry. 5 The techer wnted his clss to work in groups of 4. After he divided them into groups, there were 6 groups of 4 nd 1 group of 3. How mny students were in the clss? Show ll your work. 27 students Work will vry. b If the techer wnted ll the groups to be exctly the sme size, how mny students should be in ech group? How mny smll groups would there be? Show ll your work. 9 groups of 3 students ech or 3 groups of 9 students ech Work will vry. Bridges in Mthemtics Grde 4 Home Connections 42

Unit 2 Module 4 Session 4 Multipliction & Division Puzzles pge 1 of 2 1 Fill in the missing numbers. 7 3 9 8 5 6 6 9 3 8 42 18 81 24 40 5 9 4 6 9 2 5 8 6 3 10 45 32 36 27 2 Use multipliction nd division to find the secret pth through ech mze. The strting nd ending points re mrked for you. You cn only move one spce up, down, over, or digonlly ech time. Write four equtions to explin the pth through the mze. ex b strt 3 4 12 strt 81 6 36 strt end 1 3 2 36 6 2 9 4 6 end 3 4 = 12 12 2 = 6 6 6 = 36 36 9 = 4 6 9 4 7 42 9 end 81 9 = 9 9 4 = 36 36 6 = 6 6 7 = 42 6 2 9 3 18 2 1 2 = 2 2 9 = 18 18 3 = 6 6 3 = 2 3 Complete the division tble below. 60 24 12 18 54 540 180 120 6 10 4 2 3 9 90 30 20 (continued on next pge) Bridges in Mthemtics Grde 4 Home Connections 43

Unit 2 Module 4 Session 4 Multipliction & Division Puzzles pge 2 of 2 4 Ryn bought 4 dozen eggs. His recipe for cookies clls for 3 eggs in ech btch. How mny btches of cookies cn he mke with the eggs he bought? 16 btches 5 CHALLENGE Write story problem to mtch the eqution 36 5 = 7 R1. Work will vry. Bridges in Mthemtics Grde 4 Home Connections 44

Unit 2 Module 4 Session 5 Moolh on My Mind pge 1 of 3 Note to Fmilies For this Home Connection, you ll ply gme clled Moolh on My Mind with your child. We hve plyed the gme in school, nd your child cn help you lern to ply. You cn lso follow the directions below. The gme is designed to provide prctice multiplying lrge numbers using coin vlues, which re esier for mny students to work with right now. You ll need two pencils nd pperclip to ply Moolh on My Mind. Use your pencil nd the pperclip s spinner. Instructions for Moolh on My Mind 1 Tke turns spinning one of the number spinners with prtner. The plyer with the highest number goes first. 2 Spin both number spinners nd the coin spinner. 3 Write n expression in the first column to show the results of your spins. You ll dd the two numbers nd multiply by the vlue of the coin. 4 Multiply to find out how much money you collected nd write tht mount in the second column. Write it gin in the lst column so you cn keep running totl of your money. 5 Tke turns with your prtner. Help ech other mke sure tht you re dding your money ccurtely. In other words, be sure ech other s running totls re correct. Rvi 2 5 25 $1.75 (5 + 4) 10 $.90 $1.75 $2.65 6 When both plyers hve tken 10 turns, the gme is over nd the plyer with the most money wins. 7 Ply nother round if you like, using the optionl record sheets. Moolh on My Mind Spinner 6 5 1 2 4 3 6 1 2 + 5 4 3 (continued on next pge) Bridges in Mthemtics Grde 4 Home Connections 45

Unit 2 Module 4 Session 5 Moolh on My Mind pge 2 of 3 Moolh on My Mind Record Sheet Multipliction Expression sum of the 2 numbers times the coin vlue ( + ) Student Amount of Money You Got This Turn Totl So Fr Multipliction Expression sum of the 2 numbers times the coin vlue ( + ) Fmily Member Amount of Money You Got This Turn Totl So Fr (continued on next pge) Bridges in Mthemtics Grde 4 Home Connections 46

Unit 2 Module 4 Session 5 Moolh on My Mind pge 3 of 3 Moolh on My Mind Record Sheet (optionl second gme) Multipliction Expression sum of the 2 numbers times the coin vlue ( + ) Student Amount of Money You Got This Turn Totl So Fr Multipliction Expression sum of the 2 numbers times the coin vlue ( + ) Fmily Member Amount of Money You Got This Turn Totl So Fr Bridges in Mthemtics Grde 4 Home Connections 47

Unit 3 Module 1 Session 2 Skills Review 2 pge 1 of 2 1 Did you know tht there re 14 Life Sver cndies in roll of Life Svers? Fill in the blnks on the rtio tble to show how mny Life Svers there re in different numbers of rolls. Number of Rolls Number of Lifesvers 1 roll 14 Life Svers 3 rolls 42 Life Svers 4 rolls 56 Life Svers 8 rolls 112 Life Svers 10 rolls 140 Life Svers 2 When people ply gme of pool, they often use 15 numbered blls nd 1 cue bll for totl of 16 blls. Fill in the blnks on the rtio tble to show how mny blls there re in different numbers of sets. Number of Sets Number of Blls 1 set 16 blls 2 sets 32 blls 4 sets 64 blls 5 sets 80 blls 10 sets 160 blls LIFESAVERS 3 List ll the fctor pirs for the number 36. 1, 36 2, 18 3, 12 4, 9 6, 6 4 List ll the fctor pirs for the number 42. 1, 42 2, 21 3, 14 6, 7 (continued on next pge) Bridges in Mthemtics Grde 4 Home Connections 49

Unit 3 Module 1 Session 2 Skills Review 2 pge 2 of 2 5 Bryce hs rug tht is 14 decimeters by 16 decimeters. Drw sketch of Bryce s rug. Then find the re of his rug. Show your work nd lbel the nswer with the correct units. 16 dm 224 dm 2 14 dm 6 Kim s bedroom is 13 feet long nd 11 feet wide. Drw sketch of Kim s bedroom floor. Then find the re of Kim s bedroom. Show your work nd lbel the nswer with the correct units. 13 ft 143 sq. ft. 11 ft 7 CHALLENGE Ell nd Jde both rn mrthon. Ell finished in 4 hours, 6 minutes, nd 13 seconds. Jde finished in 4 hours, 3 minutes, nd 18 seconds. Who ws fster? By how mny seconds? Show your work nd lbel the nswer with the correct units. Jde ws fster by 175 seconds. Bridges in Mthemtics Grde 4 Home Connections 50

Unit 3 Module 1 Session 4 Frction & Division Story Problems pge 1 of 2 On Tuesdy, Dvid nd three friends shred lrge pizz for n fter-school tret. Ech of the four boys te the sme mount of pizz. On Thursdy, Dvid shred 2 lrge pizzs with 7 friends from his soccer tem. Ech of the 8 tem members got equl mounts. 1 Use the circles below to drw lbeled models showing how much pizz Dvid got to et on both dys. Tuesdy s Pizz Shres b Thursdy s Pizz Shres 1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4 2 Wht frction of lrge pizz did Dvid et on Tuesdy? 3 Wht frction of lrge pizz did Dvid et on Thursdy? 4 Did Dvid et more pizz on Tuesdy or on Thursdy? He te the sme mount both dys. 5 Write t lest three mthemticl observtions tht you cn mke from your sketches for this sitution. Work will vry. Exmple: when you divide 1 pizz into 4 equl prts, ech is 1/4. When you divide 2 pizzs into 8 equl prts, ech is 1/4 lso. There re 4 fourths in 1 nd 8 fourths in 2. 1/4 1/4 (continued on next pge) Bridges in Mthemtics Grde 4 Home Connections 51

Unit 3 Module 1 Session 4 Frction & Division Story Problems pge 2 of 2 6 Write story problem to mtch ech of the equtions below: ex 13 4 = 3 R1 The gym techer hs 13 plyground blls for the 4 fourth grde clssrooms to shre. How mny blls will ech clssroom get? 13 4 = 3 1 4 work will vry b 13 4 = $3.25 work will vry c 16 4 = 4 work will vry 7 CHALLENGE LToy hd lrge collection of bsketbll crds. She decided to give hlf of them to her friend, Erin, nd fourth of them to her brother. She still hs 75 crds left. How mny crds did she strt with? 300 crds Bridges in Mthemtics Grde 4 Home Connections 52

Unit 3 Module 1 Session 6 Thinking About Frctions pge 1 of 2 1 Rico s dd brought home two pizzs tht were exctly the sme size. The pepperoni pizz ws cut into 6 equl pieces. The cheese pizz ws cut into 12 equl pieces. Rico s little brother, Luis, te 2 pieces of pepperoni pizz. His big sister, Crlot, te 4 pieces of the cheese pizz. Luis strted crying becuse he thought Crlot got more pizz thn he did. Crlot sid they got exctly the sme mount. Who ws right, Luis or Crlot? b Use lbeled sketches, numbers, nd words to explin your nswer. Pepperoni Crlot Cheese 2 Vincent sys tht 1 4 is bigger thn 1 3 becuse 4 is more thn 3. Work will vry. Exmple: 2/6 of pizz is equl to 4/12 of pizz tht is the sme size. Do you gree with Vincent? Work will vry. He is not correct. b Use lbeled sketches, numbers, nd words to explin your nswer. Work will vry. Exmple: 1/3 > 1/4 1/3 1/4 (continued on next pge) Bridges in Mthemtics Grde 4 Home Connections 53

Unit 3 Module 1 Session 6 Thinking About Frctions pge 2 of 2 3 Tli sys tht 1 3 nd 2 6 re equivlent frctions. Do you gree with Tli? Work will vry. She is correct. b Use lbeled sketches, numbers, nd words to explin your nswer. (You cn use the egg crton digrms to help if you like.) 1/3 2/6 Work will vry. Exmple: You cn see tht 1/3 = 2/6. They re both equl to 4 out of 12 eggs. c 4/12 Nme nother frction tht is equivlent to 1 3. 4 CHALLENGE In 12-egg crton, 1 6 equls 2 eggs. Use the grids below to help you imgine nd drw crtons where: 1 6 is 3 eggs. b 5 6 is 25 eggs. c How did you decide on the sizes of the crtons for nd b? Work will vry. Bridges in Mthemtics Grde 4 Home Connections 54

Unit 3 Module 2 Session 2 Brownie Dessert pge 1 of 2 A fourth grde clss erned brownie dessert prty for hving the highest ttendnce in one grding period. Smll pns of brownies were cut into 9 pieces, nd lrge pns were cut into 16 pieces. 1 Tori te 2 brownies from smll pn. Wht frction of the brownies in tht pn did she et? Drw sketch to show your thinking. Work will vry. Exmple: 2/9 2 Holly te 1 more brownie thn Tori from the sme smll pn. Write two equivlent frctions tht describe how much Holly te. 3/9 nd 1/3 3 Henry s tble group sets 5 students. Ech student te 2 brownies from lrge pn. Write n eqution tht shows wht frction of lrge pn of brownies ws eten t Henry s tble. Work will vry. Exmple: 5 2/16 = 10/16 4 April te 1 brownie from lrge pn, nd her friend, Christin, te 4 brownies from the sme pn. Write two frctions to tell how much of the lrge pn of brownies Christin te. 4/16 nd 1/4 (or 2/8) b Wht frction of lrge pn of brownies did the girls et together? 5/16 (continued on next pge) Bridges in Mthemtics Grde 4 Home Connections 55

Unit 3 Module 2 Session 2 Brownie Dessert pge 2 of 2 1 Freddy hd 2 of the brownies from lrge pn. His friend sid he te 1 8 of the brownies in tht pn. Tell why you gree or disgree. Work will vry. It is true tht 2/16 = 1/8 2 CHALLENGE In n 18-egg crton, 1 3 equls 6 eggs. Use the grids below to help you imgine nd drw crtons where: 1 2 is 9 eggs. b 3 8 is 18 eggs. Bridges in Mthemtics Grde 4 Home Connections 56

Unit 3 Module 2 Session 4 Plnning Grden pge 1 of 2 The Brown fmily is trying to decide how to pln their grden for the vegetbles they wnt to grow. Use the geobord model to design grden tht fits ech description. Lbel every re to show where ech vegetble will be plnted. 1 The Browns could plnt 1 2 tomtoes, 1 4 sqush, nd 1 4 lettuce. Work will vry. Exmple: 1/2 T 1/4 S 1/4 L 2 They could plnt 1 4 tomtoes, 1 4 sqush, 1 4 lettuce, 1 8 peppers, nd 1 8 cbbge. 1/4 T 1/4 L 1/4 S 1/8 P 1/8 C 3 The Brown fmily might plnt 1 8 tomtoes, 1 8 cbbge, nd 1 8 peppers. If they do, wht frction of their grden will be unplnted? 5/8 1/8 T 1/8 C 1/8 P (continued on next pge) Bridges in Mthemtics Grde 4 Home Connections 57

Unit 3 Module 2 Session 4 Plnning Grden pge 2 of 2 1 If the Browns plnt 3 16 tomtoes, 1 4 cbbge, nd 2 8 peppers, wht frction of their grden will be unplnted? 5/16 1/4 C 2/8 P 3/16 T 2 CHALLENGE Crete pln for grden tht hs room for 5 different vegetbles. Lbel the vegetbles in the grden nd write eqution to represent the model. Work will vry. Bridges in Mthemtics Grde 4 Home Connections 58

Unit 3 Module 2 Session 6 Frctions & More Frctions pge 1 of 2 1 Ethn used n egg crton model to dd frctions. Drw eggs in the crtons to show nd solve the problem. Then fill in the blnk to show the nswer. 1 2 + 1 6 = 4/6 (or 2/3) 2 Put the following numbers in order on the number line below. 1 2 1 1 2 3 5 1 4 1 3 4 1 1 4 7 8 0 1 2 3 Mri is writing s mny different ddition nd multipliction equtions s she cn for 2 2 8. Her rule is tht ll the frctions in ech eqution must hve denomintor of 8. Here re the equtions Mri hs written so for. Fill in the bubble beside ech eqution tht is true. NN 1/4 1/2 3/5 7/8 1 1/4 1 1/2 1 3/4 N 2 2 8 = 1 + 1 + 2 8 N 2 2 8 = 8 8 + 10 8 5 8 + 5 8 + 5 8 + 4 8 = 2 2 8 N 18 1 8 = 2 2 8 b Write t lest four more ddition or multipliction equtions for 2 2 8 in which ll the frctions hve denomintor of 8. Work will vry. Exmples: 8/8 + 8/8 + 2/8 = 2 2/8 9 2/8 = 2 2/8 2 9/8 = 2 2/8 3 6/8 = 2 2/8 (continued on next pge) Bridges in Mthemtics Grde 4 Home Connections 59

Unit 3 Module 2 Session 6 Frctions & More Frctions pge 2 of 2 4 Clvin nd Leh re plying gme tht hs them drw frction crds to dd up to numbers tht fill 12-egg crton. Clvin hd 1 3 of his egg crton full when he chose crd with 8 12 on it. He sys he will fill his egg crton. Do you gree or disgree? Why? Use lbeled sketch in the egg crton digrm below to help explin your nswer. Work will vry. Clvin is correct. He will fill his crton exctly becuse 1/3 + 8/12 = 1/3 + 2/3 = 1 5 Leh hd 4 6 of her egg crton full when she chose the 5 12 crd. Cn she fit 5 12 in this egg crton? Why or why not? Use lbeled sketch in the egg crton digrm below to help explin your nswer. Work will vry. She cnnot fit 5/12 in the crton becuse she lredy hs 8/12. She cn only fit 4/12 more. 6 CHALLENGE Imgine you re plying the gme with egg crtons tht hold 18 eggs, nd the frction crds refer to 18 eggs insted of 12 eggs. (For exmple, if you drw the 1 2 crd, tht mens hlf of 18, not hlf of 12.) If you hve 2 3 of your first 18-egg crton full, how mny more eggs will fit in tht crton? Wht frction crd will you need to drw to fill the first crton exctly? You cn fit 6 more eggs. You need the 1/3 crd. b You hve 1 3 of your second 18-egg crton full when you select the 5 6 crd. Cn you use this crd to plce more eggs in the second crton, or will you hve to use your third crton insted? You cn fit 2/3 of 18 (12 eggs). 5/6 of 18 is 15 eggs, though, so they will not fit. Bridges in Mthemtics Grde 4 Home Connections 60

Unit 3 Module 3 Session 2 More Compring Decimls & Frctions pge 1 of 2 1 Which frction is lrger: 8 10 or 73 100? Explin why you think so. 8/10 Work will vry. Exmple: 8/10 is greter becuse 8/10 = 80/100, nd 80/100 > 73/100 b Drw ech frction on grid below to verify your nswer. c Record ech frction s deciml number. 8 10 73 100 0.8 or 0.80 0.73 2 On the first grid below, shde number between 0.75 nd 0.8 nd lbel it. Then shde in nd lbel different number between 0.75 nd 0.8 on the second grid. Work will vry. Any number from 0.76 to 0.79 will work. Compre the two numbers you shded in the grids. Write n inequlity using the symbol < or > to show which number is lrger. Work will vry. (continued on next pge) Bridges in Mthemtics Grde 4 Home Connections 61

Unit 3 Module 3 Session 2 More Compring Decimls & Frctions pge 2 of 2 3 Write these numbers s decimls: Two nd eighty-three hundredths b One nd six hundredths 4 Write this deciml number in words: 2.94. 5 Fill in ech blnk with <, >, or =. 1.06 2.83 Two nd ninety four hundredths. 0.8 > 0.78 b 0.56 < 0.6 c 0.6 = 0.60 6 Allison sys tht 1.06 is bigger thn 1.2 becuse 6 is bigger thn 2. Do you gree or disgree? Explin. Work will vry. She is incorrect. 1.06 < 1.2 7 Erik is 4.23 feet tll. Stcy is 4.3 feet tll. Who is tller? Explin. Stcy is tller. 4.3 > 4.23 8 CHALLENGE One yer go, Chrlie s chmeleon ws 8.42 inches long. Now his chmeleon is 9.36 inches long. Show your work with numbers, lbeled sketches, or words for ech question below. How much did Chrlie s chmeleon grow in the lst yer? 0.94 inch b How much more does his chmeleon need to grow to be exctly 10 inches? 0.64 inch Bridges in Mthemtics Grde 4 Home Connections 62

Unit 3 Module 3 Session 4 Decimls, Frctions & Story Problems pge 1 of 2 1 Write the plce vlue of the underlined digit in ech number. The plce vlues re spelled correctly for you here: hundreds tens ones tenths hundredths hundredths ex 2.03 3.17 b 120.4 ones c 506.92 d 54.29 hunredths e 32.7 tenths hundreds tenths 2 Write ech deciml number. ex Twenty-three nd two-tenths: ex One hundred thirty nd five-hundredths: 23.2 6.07 Six nd seven-hundredths: 130.05 b Two-hundred sixty-five nd eight-tenths: 265.8 3 Write ech frction or mixed number s deciml number. 5.3 12.04 3.17 ex 510 3 ex 12100 4 ex 3 17 100 7 10 b 3100 5 4 0.7 3.05 c 100 0.04 d 4100 38 e 1100 9 f 110 9 4.38 1.09 1.9 4 Use greter thn (>), less thn (<), or equl sign to show the reltionship between the deciml numbers below. < ex 1.09 1.9 1.12 < 1.2 b 3.5 > 3.48 c 23.81 < 23.85 d 4.50 = 4.5 e 3.06 < 3.65 (continued on next pge) Bridges in Mthemtics Grde 4 Home Connections 63