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Visible Thinking 3a

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3K views83 pages

Visible Thinking 3a

Uploaded by

Fred Chow
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VISIBLE THINKING in Mathematics 3A Pe Ue Se ne ea one ee Reo ee eens ee ett ‘¢ Thinking Platform provides an avenue for reflection on the reasoning behind concepts and skills Sr nOmn a nek eee eee to the answers through detailed solutions. it opportunities for parents and teachers to clarify misconceptions, simplify a concept or Pes © Parallel questions highlight differences between similar problems and allow the child to focus on the correct application of concepts and skills. (@) There were 15 more pupils in Class 3A than in Class 38. 20 pupils from Class 3A moved to Class 38. How many more pupils were there in Class 3B than Class 3A in the end? (Answer: 20 - 15 = 5; 20 + 5 = 25 pupils) (b) There were 15 more pupils in Class 3A than in Class 38. 20 pupils from Class 38 moved to Class 3A. How many more pupils were there in Class 3A than Class 38 in the end? (Answer: 20 + 15 + 20 = 55 pupils) About the Authors “Ammiel Wan is 9 familiar name among teachers and parents in Singapore. He has spearheaded a team in redesigning the thinking cuticlum with the belief that ‘Every child can think’. Amiel has presented at international conferences, including the “International Conference on Thinking’ where his paper on “Thinking through the Conceptual Approach’ was selected for publication in an intemational journal. He has received accolades such as the ‘ellow of Teachers’ Network’ and has been featured in local papers fr his innovative approach in teaching mathematics. Being a strong advocate of teaching and continuous learning, he conducts regular workshops for teachers, parents and pupils in Singapore Tham Xingli holds an honours degree in Mechanical Engineering from Nanyang Technological University (NTU) and a Post Graduate Diploma in Education from the National Institute of Education (NIE). Through her dedicated teaching career, she has gained extensive experience in crafting student and teacher resource materials. She is also actively involved in sharing sessions on teaching methodologies and in conducting workshops for parents to guide their children to succeed academically About Marshall Cavens h Marshall Cavendish Education is the leading educational publisher in Singapore, with more than 40 years of experience in developing high-quality content that plays a citical role in raising the standard of learning, Our publications ate used by teachers, parents and pupil in more than 45 countries around ISaN o75281.01 15227 a | | Marshall Cavendish sHravatolriszer! Education [see _ VISIBLE THINKING in Mathematics 3 A ‘Ammiel wan Tham Xgl Trice Foreword he ft the sa Vine Thinking in Mathomatir is cnn vith te Thing Sco, Lnaing Neti? hioorly oped by Ge iste Eaton Seappr Th ef nathan deg ord ‘pring th habit Bok cannot nove oon. ded reson cher ho hall renner ono pegera ‘Shatter, ‘ara on xa plato oh ho hk and lt hk ‘doa faking Ov othr weg cate contre io rode the pronase nub fnch ech fogs te pose Frowdng nh on are cial ne degre el gcd king fie oad ‘Aare Coan tn, act on chp drome fd oe Tikng in Mothanats prs cca wih goa ring frittata Leving ences ul ng ot har, Fete tt cont rgeret ith ering mtn th ating ge pads nae os peel ng, exp Bon PR. Pipa ‘anal Comes ie Preface he Visible Thinking in Mathematics: elm ci ond eae, inkag i meena: Rt dened to flp rake Wing Se" by potdrg” te Sod th opptuniin to Wik, ee Cente. “We proc hho ter prema practie wth conse ord ‘Sretel ecesloning pts he ld om rng rly ood (Gots nn en ard tearing pect nd oad by ease caption: ‘Thinking routines: actzndl amos to drat the i hig oo ky ‘rcpt eh aig Parallel questions: comet ethanol rene wih he se ‘ob ilo ln word to hah gers ton peters ‘Sern od cil rds encom od beta, ‘Ws pouch ra oly in th cl ona eb ao Ini ducpon in iktg geste mthaon ana got sped to he chide Nate Nees pont porate poet ard ths to de mccoy, Sy SEEN ci doo os of ae fore Contents CChopter NumbersTo 10000 umber Nlotaten And ce Vales Reoding A Vining Numbers CCompoing And Oreng Numba womber Paes Cchopter 2 ‘Addition And Subtraction Wthin 10 000 [Aion Vth Regrouping ‘Addon vith Regrouig Subrocton Wout Regreuping Subrocton With groupe Chapter 3 Word Problems Involving Addition And Subtraction Word Probes ‘More Word robles "More We Problems (2) Chapter 4 ‘Multiplication And Division By 6, 7, "Mdpeaton Ad Oson By & ‘lplation Ae Dion By 7 "Mstpleaton Ans Disien By 8 alpen An Ovison By 9 More Muplcobon Bod Dison By 6,7, 8 nd 9 a 2% 2 2 a 3 2 % Fy 3 a si “0 a ” n a a Chapter 5 ‘Multiplication And Division Mutipleoon vneureprueng| ‘Mutpleaion Yi Regrowsig Dhison thot Reprvping ‘ison Mh Regrovpng ‘ora Probie ving Four (Operations Usa Models ‘unr Petters Imng Gaps nd Tels Chapter 6 Mental Calculations Addin Of2-igt Nambers Siowodton 012-01 Nuribos ‘Mert Mutplzaton Mest Dson| Answers gees ue cs 19 18 135 1» ro 1 Numbers To 10 000 Number Notation And Place Value __hiakinig Paton patna 109 “Think Tethis conser wy? 0999, ‘hissondsioe —thestonds for histondefor ‘undece| Stans ones 1900, om, ‘8. 199999, ees 7 C — | Gasser desea ye ievee temas ‘Stouonds Shunde Stans Sones 5000, 7900, or90 or ve dn Hc Ot — = eee ee ee a ve er i | be De Ls Ge " ve tn ri el cae a ee em | cl Gas = Os Tet, | Thousands | Hundreds: ‘Ones: J a a 7 tn fe SaaS wo eae 2 wD SAPS, serationmantotedt (ayers = au ‘Thousands | Hundreds | Tens ‘Ones: +) Go) of? [s (oo) Think con you Ken he mista? hy do you tink she mad he mistake? con youwie 248in cher wast 1248 con be writen os 248 cnos or 128 ona Bones ‘er Izhundrods@ ers 8 ones 12 heels 48 oes. ec mecer {Fic os o abo eba 3) 2. Flin tebionks 4. Aine blanks, ‘Example exemple 167964, thedgt_4_isinthetens place ond 2000 cn be represented os. ‘the dt sas te valve ot 900 (©) 13867, the digt____sinthoones place and ‘ne dg ss te vole of (2) 15082, the dig _IsinthePundeds place and (ese on eaten ms ————_ Seas ‘he dg 8 hos thevabe of bonnets {c1119609, the dg ____Isinthehousonds plac on “ nuncio the gt 6 host veo. * = 3. Flin hobionks . = Jo) 8 thowsnds « —_tens (2) 0 con be epreseniedos __ thousands 1 6 thoesnds uncecs ones le ahundees: tone Gs hundreds 4) 390 ens = __huneds ones le) Ther are —__ ens in 1200, o tens 1 There re rund 7300. ones |g) Tere re __rousons in 600. ut ni 1 Thereore. ‘peusoas in 00, 8 mneeptnenenst nent net er erm cd pe emer 8 ad | 5. Fllintheblonks Clos ut (the wrong answers Example —txemple [setts ams Eaanisepuonas | | -—s00 ‘ (Games > 7s > | | 5006 | ee 2ihowsonds hundreds 6 ere Tone |) (tia os (a) SB lens + 60005 = (a) $203 canboopressod sthousands 208 tens 5203 ones ase eee ae { Sadana seme eee ee [aan | [anmaaaon | [b) 9170.con bo expressed os: * @thundreds 70.0nes ff meets 7 [Ean so =d 6 tempers cameo ate igen tne attend vera 7 1) Shunde + 4tons 7, Reastne cues. Use the dts below to frm: Then cre the cored mumbw Example | (4 theses pose nbn iar | COCO eaneatet I | © 9 O® 2501 on Ja) Thawed! Sintheones pce Eom oteter ho 01s lo the sms! posse rumba, {hecgen the ons paces uc he dg inthe hundreds pace OOO® 695 65 26s e589 Ib the rote poste number "Enos nosound @ © © © a Taragho hes fess meshed te nares pce. |e the smaest pose umber betweon 2500 on 4000. wt O©OOO —— (2 thowaggt cheng 1 ges putin S759 Toryaatantaneaia Teueitee trio nowtonts dite 3 meant OOOO re J ogee xt rman no OOC® — | Reading And Writing Numbers ___tikinsiPatse, = — satis Josephs bing a compute 1. Wein numbers lo) two thousand end thinesn {2013 (a) two shoueond nd they —___[~ 203 (2 Four thousnd, nee hundred and Went-one (2) Fourthousand, wo hunted ond ton (6 Theo thousand, re hundredandferton (@ Thee thousand, ehundredand ony {e} Four tousand, seven hundred ndone—{ (Four housand, sven handed nd ten UU JU Think! Olde cut he cheque conechy? Wy? (gl Seon hewn ero 47 | 1H Soren heusand ond ninly | serous. atc n vr omh Ung eunpe teenie Ages iadicenewenmearchwss ncevosoneay Shiwownrrrenh Nine thousand and fy-rine ‘Rayaane owes hare word dn nate we ern at were etal te Garena aianaenomonaeacntescanart 1D Nine thousand, fe hundred and nine UU 10 anna cmtmaumanemanativentne thd manne migra ! | 2. Cela te mists ib son Example im = m0 eee syne sto) tl 692 -sxhaond hres hunced odin | aan wy 03 st Rowson ond four hunted oe © 70% seven housed, wo hunted and sn | a ene ‘ahha leven and si (4 6590 te 508 fad tree hun od ot 409 2. Wen numbar wets ae (Example ‘oo ene thowsond and nine 708 1o0 —_enethtsondondinete 80 a er thasond and nie hundred 705 x3 a mean | ee woe as my es i ‘Comparing And Ordering Numbers __‘thiskia tis: ee ‘Wayne wos ostd fo compare o numbars ond ccs gree ruber, 1. Sempare ond one has nob. He wos dls requredo eon fis chokes (a) Jes, Poe Soen ond owe each have sae money. Lookat he questions andhis ane, | ret area rey hve, Sen ah eect ‘omaintlmony| ‘ueston Ga (seas [Paar Siren [dena ) (nie [sane [sis aavs) Both numbers are the sone because the siits 7,8 and 9 are nthe some place wales. 1) ony coe, ee an ick eoch sol some books. ‘Order the numb of books ey hove sod begining with he veton 2 (eats! numba ol boks oo a ie vee) 3420 ‘15 ie greater than 6481 because the last digit in 3415 \soreater than the lst cgi 6451 a _ 3204 3082 sa) (2 Wary, tne, monde on ery uses diferent araunts of up ink Di Wopeuse hese neta conpr he unbes ‘oars br fe a inbangusant Gran amount uel bp wh te sole ‘yeu Eiko xd Woy cone? crore iver wh nt (Cana [ery >) (Gaoseme [3408 | 4308 mi | 3048 mi) § Seem meitt — fomnecsteree os i fs Sond, yo, Balle andro were kiting sects ‘defo ember sites hey hove done, bepiing vt the ‘sales number of sees (seria [Tye [ ete [ee (Coes [ seas [ see [sae] nae 2. arrange te follng numbers. Begin wh the greats. os fe0) Ste) (ees), 4 (8) mn wo ie Ga Gas Sais so vt 5 Aronge the follwing numbers. Bog wh fo smal! ame) a8 oy Some “ae \zte oar Ye warts msersenwthnnritenpamine example ®O2OO® Use hee igs orm (ol the recast Aig rrr, (01 the smales ¢-dgt cure. “OO@Q® Use hese ago farm (ol the retest rumer. (0) Sesmales' gt numer “OOOO Use thse dso form (o) tho grote 4g curr. (8) the smolst 4-igt eur “OOOO Uso se dito form (@) the grote! ig curter ben 6800 ond 8600, 1) fhe smatest 4d mune bowen 6800 and 3600 cd or i etree 17 Number Patterns a There or nay pes of number pate ‘het nuber potems inal edd or subtracing the sare number each iene so sme 0 o 2m 1, a, mie wk ee wh SCO. ‘he ptiens below ive a ctr the nurs aed or state, 6 cm wk RE BK As ee ee so BCC con you compl these numbor poems? ft 10,200, so, oe te 100, 200, —__. ____. (a ____. 200, ____. 00, (a) og, 0 Think How many numiberséo you nod to ety umber pane? Why? Compas ech mer paren Example — (ol 7088, 7059, 7070 7071 72.7078 (b) 2087 706,707, 7089 7099,__7108 (a 7099, 71627269, 7069, 75697569 1 1908, by 1943, (e783, 1983 2583, 2 4650, 4650,________470 » 4030, aago, ___ 4490 onsen soon sen 3. fo) 9017, 5015, __.____ 9009, ) ____ soa, 9025, 022, __ 9016 (905, 9015, _.__. ava fd eee ee 4905 (by 5905, __s2gs,_saas, 5005, 5255, S205 Addition And Subtraction 2 Within 10 000 Addition Without Regrouping _ iiss. Seven ode some numbers Here te hs soins Flin he bors. @ aene * ware Thinkt Can you spothis mstckas? We the caret elon in he box elo i |) steven no gn he gts bose on hs place wales ore ond {et ve ke hon the mara re added below I ee, to) 23492 inthe ramber 12 the ig isin te fons place and the dt 2 sn the oes ple, Fest odd the ones. ‘ones ones 6 ones Nest, od ts i Bienes Ten = ens Then he hunceds, huncreds » Dhunsreds = 2 hundeds pons 1 1039 +42. 2 swseai lost, athe thousonds. 45074301 ousond +0 meueands «thousand | 0,124 12 1246, (oy 1234 +123 “ho mumber 123, he itis in fhe hundreds poche dg 2s the fence ond the digs inte ones pace 5. 586+173 - 6 200+ 3201 = Frat ad the ons. mare Ne odd he ens. + 123 | Shere + 2 = 5 tons css | Thane the hued hundreds hunted =3 hundeds {sty oth heusonds ‘ilsond + 0 usonds = housand 7 $0064.n52~ 8, 167 +2. 50,204 + 120 = B57 matte ACSI ama tsarnbes ih toe pes eect bt anes DasapealeTaayetseae None atnape ten Addition With Regrouping ____ "siete, Stevo added some numbers Hoe are his sluions. "eee ei ‘Think? Con you pois makes? temas ~—s a et concern box aw = 24 netangrnte rare en os Soren dd not regroup fra) and Totus lok tow te numbers ae ede below fo weeser fs of for jouer sere ser ot te oe are) flere ae soa! cred one ‘hen, he hanced. hundreds +S hundreds + huaded = 8 hundreds st, the thousands. ‘howeand + hovsonds = cusond 0,123 +567» 180, vee sora fst odd he ones 2inndteds¥ hundreds + Thuaded = 9 hundreds {sty the housands "ousand ss thovsonde= 6 fhwvsonde 50,1234 + 5676 = 6912 tes Seehenmcnpnsennannepg os nay ne ale ngoons ___Attning Mastery 6 fe | a, 1 325 +68 = A sans * os 3. 10264595 = 4. 2859.78 5. 3564 +8962 6, 9506+ 3687 = 7, 494642049 = 8, 670942953 « cme en tigen soe mngrinnans 7 Subtraction Without Regrouping __ Tiki meus, Cae EMS ia Think 00 these sonencs mean ho sare hing? Would you obin he sare ‘nso or bth qustons? xan Stoven svbroced some numbers. Here aes solitons, pare woe a4 Thinket Can you spots mstokes? Cre hom. te const seins inthe box eo ant eed nantes 28 Stove dd not ogn he digs sed on ss pte volves fr oth oar [eros lok ot how te umber ar subrocied below. (1 34-1 ance Inns rnbee 2 ho dig is inthe fens place on ig 218 9 ‘hecnes place 1 1869-427 it nico rere ® ot ntte ttre . oS : ane ea Hare ered aaa ee aa aire ale se | (oy 34-123 Tithe number 123 he gt is the hunted place, he dat 2 sin the one xe ond he igh 3m te ones pace, 5. 5862-2021 Frat sub he nes a ones Sones = Tone . ‘No subtctthe ons 2 ‘ene 2tens= fen 3 “hen subroe thhundds Zhuncrede = hundred = hunted Last, soc he thousands Thousond~housandr = housond 0.129428 =1m, 20 1 oe rs 7. e9a4-1510 6 estore earnest Q SeStresematrccmnsenes 20 weemteprarnns ean memcmaemnanttnpenitiarei Peeiscaounta eerie 4, 4990-113 6, 6908 ans 8. 780-6020 = ‘Subtraction With Regrouping —_ Stove subholed some rumba Here ores sions oO mane % gare (as = ad ‘Think! Con you spot hs meskes? ([cecetoraan Wit th coret soon nthe box bow Steven det rt rgtoup fo bot (ond {err lok thaw the numbers ere subtracted bow (al 136-67 Fit subtot me nes. "ones cane! besubracted fon 4 ones. Rogtup the ons ond ons. Sane ones = tans ones subaat ‘ones -7 ones =7 ones Ne subd the tens (tens contr be surat om 2 tens. ogre he hundreds on ins ‘hundreds 2 ene = Vhunde iene Subhoe. Tens tons = 6 tons Thon sublet ho hundieds ThondedOhundeds= 1 honed Lost, sbi he thovsonds. "hetsond =O housonds = reson So 1234-67 = 67, ° y Saree (236-367 sist uate oes wane ene cael be Subtoce om 4 ones. mini Ragrup he ens ond ones. Stare anes = fons Maes ssuoe. ‘ones -7 ones =7 ones 1. m3 -st42__ 2, 365 = Noa sutra the rs (ene conna be surat rom 2 fens. Rogrup hehundredsonc tens. ‘hundreds? ens = Tranied 2 ens subroe. Tens = 6s = 6 ns 8, 2392-1665 =, 4.122867 = ‘Then sbi he handed ‘hundreds comet be sueded om hunced Fegroup he housonds ond hued Thowsond hundred = DIheusonds i hundeds Last, src the hands. 5, 02-698 = —_ 6, sm0- 1689 hundreds — 3 handeds = hundreds 0, 204-367 = 867 7, 2400- 636~. 8, 9009-4724 = § PEE econ rennet ae ‘Sole, Show your work 9, Wats 87 ss thon 360? 10, Whats 18 ess han $050? 11, The sum of wo numbers 4853, One ofthe nubs 699. ‘ils the ater rumbe? 12. Thesum of wo nmbetse 8200, One ofthe numbers is 705, ‘Watis the oer umber 18, The teres botasan to numbers 183, The grote numbers 4055, Vitis to salir number? 14. The ifrence beeen wo rumbets i 2682 ‘The greater number 7000, Whats the ser number? 36 eetaitnet enum creahveeegnemnaent 15, dor utr emis numbers Example re) cise ke ty ah win wean i Word Problems Involving 6 3 Addition And Subtraction Word Problems __ Lek at hese roles, Thinking Plt Problem Fis Oar mae 250 fos nthe maming. She made another 45 as nthe ‘fernoon How man ors ol se make agatha? Problem 2 Firs won nde 250s nhemarrng. She made 1&5 more ors (erneon How many los ddshernckeatogether? Problem 3 Fes van mode 250 asinine morning She rade 145 fever ersin the (emoon, ow many tots dsho make cogoter? ‘Think. How tthe pobis snr? How are they deren? Cee the key Ti yor hot make ham deren om ene note: (Con you use the seme model soe theo problems? ak SC Game 2 Gen i ere ee ahnansietomeraiytesien annie Son re 0 enero anne ee ne ‘row modes ond sabe these prions. Example Doritos 524 mares. Henry hss 298 mais. How many marbles thoy how allogethe? toyed 5244296822 Tey hove 822 marbles atogetor, 1. Doriahos 524 mats He hos 98 more marbles han Henry How many mats des Hey hove? %@ 2. ane has 524 mats He hos 298 fear eras han Here. How ma rable does Her hove? ™ 3. Kimberly sl 597 fcktstor concer Sove sold 216 kas Hou mary (6. A posimon dvered 02 erson Monday He dtvres 245 eters on feels i both of ram al aogether? “Tuestoy How mony lies ce deer on bot day? 44 eben sold 597 cessor a cnca. Stoe sold 2¥6 moc ks han 7. postman dobore 62 laters Monday. He dered 245 frees on nbery, How many elas da too sol? "Wes he on Monday. Hew mony ers he dlr on Tuesday? 15 Kimber sold 597 tat fora conc. Stove sol 216 fever hekets hon ©. Aposiman dered 602 laters on Mondoy He dred 245 noc ters on Ember How many hts id Seve sl” “uesoy han on Honey. How many leer ihe Sever on Tues3ay? 12 caeregnnnet cmnneaiomannentedtme nei

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