Msurs, Shp, Sp n Hnling Dt 6
PUBLISHED BY THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGE Th Pitt Builing, Trumpington Strt, Cmrig, Unit Kingom CAMBRIDGE UNIVERSITY PRESS Th Einurgh Builing, Cmrig CB RU, UK 0 Wst 0th Strt, Nw York, NY 00-, USA 77 Willimstown Ro, Port Mlourn, Vi 07, Austrli Ruiz Alrón, 80 Mri, Spin Dok Hous, Th Wtrfront, Cp Town 800, South Afri http://www.mrig.org Cmrig Univrsity Prss 00 First pulish 00 Rprint 005 Print in th Unit Kingom t th Univrsity Prss, Cmrig Typfs Frutigr, Hlvti, Minion, Swift Systm QurkXPrss.0 A tlogu ror for this ook is vill from th British Lirry ISBN 0 5 7896 pprk Txt illustrtion Gry Rs Gnrl itors for Cmrig Mthmtis Dirt Sny Cowling, Jn Crown, Anrw King, Jntt Mumfor Writing tm for Msurs, Shp, Sp n Hnling Dt 6 Ann Brr, Sllinn Colmn, Rogr G, Clir Grigson, Gill Hth, Su Hoo, Bo L Roh, Clr Luritzn, Krry Luny, Jntt Mumfor, Mry Nthn, Mlin Swrrik, Allison Toogoo, Elizth Toohig, Jn Wstr, Jonn Woowr Th writrs n pulishrs woul lik to thnk th mny shools n iniviuls who trill lssons for Cmrig Mthmtis Dirt. NOTICE TO TEACHERS It is illgl to rprou ny prt of this work in mtril form (inluing photoopying n ltroni storg) xpt unr th following irumstns: (i) whr you r iing y lin grnt to your shool or institution y th Copyright Linsing Agny; (ii) whr no suh lin xists, or whr you wish to x th trms of lin, n you hv gin th writtn prmission of Cmrig Univrsity Prss; (iii) whr you r llow to rprou without prmission unr th provisions of Chptr of th Copyright, Dsigns n Ptnts At 988. Arvitions n symols IP Intrtiv pitur CM Copymstr A is prti work B vlops is C is xtnsion work if n, hlps with work in A A r mrgin inits tht tivitis r thr-l. A grn mrgin inits tht tivitis r inpnnt.
Contnts Msurs (M) M Lngth M. Rouning istns n lngths 5 M. Convrting kilomtrs to smllr units 6 M. Mtri n impril units 7 M. Ring sls n solving prolms 9 M Mss M. Rltionships n rouning M. Convrting twn kilogrms n grms M. Mtri n impril units 7 M. Ring sls n solving prolms 0 M Cpity M. Litrs n millilitrs M. Rouning pity msurmnts 6 M. Mtri n impril pitis 8 M. Cpity prolms 0 M Ar n primtr M. Primtrs of ompoun shps M. Ars of ompoun shps M. Surf rs 5 M. Ars of isosls tringls 7 M.5 Ar of right-ngl tringls 9 M5 Tim M5. Worl tim zons M5. Tim zons n t hngs M5. Solving tim prolms 5 Shp n sp (SS) SS Proprtis of -D shps SS. Prlllogrms n rhomuss 7 SS. Trpziums n kits 9 SS. Digonls 5 SS. Cirls 5 SS.5 Tngrms 5 SS.6 Rsoning out shps 55 SS Proprtis of -D shps SS. Proprtis of -D shps 57 SS. Nts for los us 58 SS. Visulising -D shps 59
SS Rfltiv symmtry SS. Rfltions in mirror lin 6 SS. Rfltions in mirror lins 6 SS. Rsoning out symmtry 6 SS Trnsltion SS. Trnsltions n -D shps 6 SS. Trnslting pttrns 66 SS. Trnsltions in qurnts 68 SS. Trnslting n tssllting 70 SS5 Position n irtion SS5. Intrsting lins 7 SS5. Byon th first qurnt 7 SS5. Plotting o-orints in ll qurnts 7 SS5. Pttrns in o-orints 76 SS6 Angl n rottion SS6. Msuring ngls 77 SS6. Rflx ngls 78 Hnling t (HD) HD Proility HD. Fining proilitis 80 HD. Using 0 sl for proilitis 8 HD. Exprimnting to fin proilitis 85 HD Orgnising n intrprting t HD. Mn, min, mo n rng 87 HD. Pi hrts 89 HD. Lin grphs 9 HD Orgnising n intrprting t HD. Tsting hypothsis 9 HD. Mn, min, mo n rng 9 HD. Pi hrts 95 HD. Lin grphs 96 HD Orgnising n intrprting t HD. Mn, min, mo n rng 99 HD. Intrprting n ompring t 0 HD. Lin grphs 0
M. Rouning istns n lngths Ky i In rtin situtions n pproximt msur, to th nrst whol unit or tnth of unit is n. A Writ th istn to h pl to th nrst kilomtr. A Spttors t footll mth ompr th istns thy hv trvll. Roun to th nrst kilomtr. 6.78 km.5 km 78.9 km 0.8 km 8.9 km A Jn msur th thiknss of som lirry ooks. Roughly how mny ntimtrs r thy to th nrst whol ntimtr? 7 mm 5 mm mm 6 mm 09 mm A B Do CM. Cylists trvll ths istns in trining. Approximtly how fr i thy yl to th nrst kilomtr? 768 m 509 m 998 m 90 m 789 m B Anil msur som ojts in his lssroom. Aout how mny mtrs r thy to th nrst tnth of mtr? m = 0.0 m m 5 m 67 m 6 m 98 m C An xprimnt to grow plnts prou th following rsults. Roun th hights of h plnt to th nrst tnth of mtr. 80 mm 576 mm mm 8 mm 7 mm M Lngth CM 5
M. Convrting kilomtrs to smllr units Ky i m is on thousnth of km. A A hrt givs th hight ov s lvl of svrl towns. Writ ths hights in mtrs. 0.00 km 0.007 km 0.06 km 0.080 km 0.668 km 0.900 km f A B You n 5 ojts smllr thn your hn to msur. Ror your msurmnts in ntimtrs n thn onvrt thm to mtrs. Whih of th two msurmnts is highr ov s lvl?.59 km or 50 m 978 m or.66 km 0.0 km or 0 m 70 m or 0.0 km B How fr is it in mtrs from Wlly to: Applton? Brfor? Cstlorough? B Drthorp? Estwll? Fullrook? Arrng ths lngths in orr from smllst to lrgst. 0.0 m 0.00 km 0. m 5.08 m 8 mm 9 m f Convrt ll lngths to mtrs. C You n 5 ojts lss thn 00 mm long n rulr mrk only in millimtrs. Msur your ojts in millimtrs thn onvrt to mtrs. 6 M Lngth
M. Mtri n impril units Ky i A mil is out 600 m. 8 km is out 5 mils. A mtr is longr thn yr. A mtr is out ft inhs. You n your grph n prtnr. British rivrs trvlling in Europ n to onvrt istns givn in kilomtrs into mils. Us your grph to onvrt th istns in th following prolms. Convrt ths istns into kilomtrs. 0 mils 5 mils 50 mils 75 mils Us your grph to fin whih is furthr: 5 mils or 6 km 8 km or 5 mils 56 km or 6 mils 8 km or 9 mils Complt ths, hoosing from th list low. inhs = ft = foot = yr = mtr = mtrs = f 6 inhs ft foot inhs 6 ft ft inhs List lssroom ojts tht you woul msur in inhs n ojts tht you woul msur in ft. Wht impril unit woul you us to msur th hight of oor? M Lngth 7
5 Put ths istns in orr, from shortst to longst: 0 mils 5 km 5 mils 0 km 5 mils 5 km 6 John trvll mils. How mny kilomtrs i h go? Clis is 8 km wy. How fr is this in mils? It is 95 km to Pris. Morg hs trvll 56 mils. How muh furthr hs sh to go? Lnny rivs mils from his mpsit to Buvill. Thn h rivs 8 mils to th h n gos stright hom to th mpsit from thr. If his totl journy ws out 75 km tht y, wht is th istn in kilomtrs from th mpsit to th h? 7 Choos from <, >, = to omplt ths qustions. 6 ft m m 9 ft 9 inhs yrs ft ft mtrs 0 m 0 yrs f foot 0 inhs Rmmr: foot = inhs yr = ft 8 Mk up of your own numr prolms using impril n mtri units. Ky i A mil is out 600 m. 8 km is out 5 mils. A mtr is longr thn yr. A mtr is out ft inhs. 8 M Lngth
M. Ring sls n solving prolms Ky i You n to hoos th right sl to msur in mtri or impril units. Srh trvll. km y r,.7 km y us n 000 m on foot. How mny kilomtrs i sh trvl? m inhs I ut 65 m off.5 m of rop. How muh is lft? A lss msur rinfll using rin gugs thy m thmslvs. Som sls wr in inhs, othrs in ntimtrs. Us th sl to nswr ths qustions. On Mony thr ws inh of rin. How mny ntimtrs is this? On Tusy thr ws inh of rin. How mny ntimtrs is this? 0 9 8 5 On Wnsy n Thursy it in t rin, ut on Friy thr wr inhs of rin. How mny ntimtrs is this? Wht ws th totl rinfll for ths 5 ys in ntimtrs? 7 6 5 Th nxt wk it rin.7 m on Mony. If it rin th sm mount vry y until Friy, how mny inhs of rin fll on ths 5 ys? 5 If th totl rinfll for 0 ys ws 5 inhs, wht ws th vrg rinfll h y? Giv your nswrs in ntimtrs. 0 0 M Lngth 9
6 Th thir wk Nim msur.8 m, 0. m, 5. m, 0. m n.6 m of rin. Wht ws th totl rinfll for th 5 ys in ntimtrs? How muh is this to th nrst inh? Th shool wthr sttion ror xtly inhs of rinfll. Whih hil h th most urt rin gug? Josh.5 m Ky.8 m Mnsi. m Nim.6 m 7 In th fourth wk, Mony h. m of rin, Tusy 8 Thursy 7 8 inh n Friy.5 m. inh, Wnsy. m, Whih y i it rin th most? Whih y i it rin th lst? Wht ws th totl rinfll in ntimtrs? Wht ws th totl rinfll in inhs? 8 Th vrg rinfll for th fifth wk ws inh of rin ovr th 5 ys. Rinfll on Mony ws. m low vrg, on Tusy 0.5 m ov vrg, on Wnsy.6 m ov vrg n on Thursy.0 m low vrg. Giv th totl rinfll in ntimtrs for wk 5. Work out th rinfll in inhs h y tht wk inluing Friy. 9 0 A ow is m from 6 inhs of rion. How mny ows n m from m of rion? Thr r.5 m to inh. yr is 6 inhs. Aout how mny ntimtrs r thr in yr? Ky i You n to hoos th right sl to msur in mtri or impril units. 0 M Lngth