MANUAL FOR SECONDARY MATHEMATICS KIT

1 MANUALFORSECONDARYMATHEMATICS KITSE COND ARY M ATH EM ATI CS K ITII PREFACEOn e of t h e m ost si gn i fi can t r ecom m en dat i on s of t h eNat i on al Cu r r i cu l u m Fr am ewor k (NCF)- 2 0 0 5 i s t h em at h em at isat i on of t h e ch i l d s t h ou gh t p r eivin g t h is goal, con cr et e m at h em at ical exper ien cesp l a y a m a j o r r ol e. A c h i l d i s m o t i v a t ed t o l ea r nm at h em at ics b y get t i n g i n volved i n h an dl in g var iou scon cr et e m an ipu lan t s in var iou s act ivit addit ion t oact ivit ies, gam es in m at h em at ics also h elp t h e ch ild sin volvem en t in lear n in g by st r at egisin g an d r eason in lear n in g m at h em at ical con cept s t h r ou gh t h e above-m en t ion ed appr oach , a ch ild-cen t r ed M at h em at ics k ith as been developed for t h e st u den t s of Secon dar y st agebased on som e of t h e con cept s fr om t h e n ewly developedNCERT m at h em at ics t ext book s.

2 Th e k it in clu des var iou sk i t i t em s a l o n g w i t h a m a n u a l f o r p er f o r m i n gact e k it br oadly cover s th e act ivities in t h e ar easof geom et r y, algebr a, t r igon om etr y an d m en su r at ion .Th ek it h as t h e followin g advan t ages : Availabilit y of n ecessar y m at er ials at on e place M u lt ipu r pose u se of it em s Econ om y of t im e in doin g t h e act ivit ies Por t abilit y fr om on e place t o an ot h er Pr ovision for t each er s in n ovat ion Low-cost m at er ial an d u se of in digen eou s r esou r cesH er e ar e som e of t h e sp eci al f eat u r es of t h e k i t i t em s :-Two var iety of plast ic st r ips wit h slot s an d m ar k in gs h aveb een p r ovi d ed . Th ey h el p i n cr eat i n g a n gl es, t r i a n gl es,qu adr ilat er als an d det er m in at ion of valu es of t r igon om et r icr at ios. Th e fu ll or h alf pr ot r act or can be fixed on t h e st r ips form easu r i n g t h e an gl es i n t h e act i vi t i es r el at ed t o an gl es,t r ian gles, an d qu adr ilat er Cir cu lar Boar d is design ed in su ch a m an n er t h at itcan be u sed t o ver i fy r esu lt s r elat ed t o a cir cl e as wel l ast r igon om et r ic r at COND ARY M ATH EM ATI CS K ParasharProf.

3 & Head, DEKNCERT, New Delhi05/03/2014A Geoboar d is a boar d of dim en sion s 19cm 19cm 1cmh avin g h oles dr illed on side A of it at a dist an ce of 1cm each .Geoboar d pin s can be fit t ed in t h e h oles an d wit h t h e h elp ofr u bber ban ds differ en t geom et r ical sh apes can be for m u t - o u t s o f c o r r u ga t ed s h eet s i n t h e f o r m o fpar r r llelogr am , t r ian gle, t r apeziu m an d cir cle h elp in lear n in gcon cept s r elat ed t o ar cu be wit h adju st in g cu t -ou t s of cu boid, cylin der, con ean d h em isph er e h ave been given t o con st r u ct t h e con cept ofsu r face ar ea an d volu m t -ou t s of plast ic car dboar d in t h e for m of t r ian gles,qu ad r i lat er als an d r ect an gle et c. h ave been given t o ver i fyPy t h a go r u s t h eo r em a n d a l geb r a i c i d en t i t i es l i k e 22aba b a b.

4 An ot h er in t er est in g it em , Algebr aic Tiles h as also beenpr ovided. Th ey ar e pr ovided in t wo differ en t colou r s an d t h r eed iffer en t si zes. Th ey can b e u sed for con cr et i sat ion of t h econ cept of fact or isat ion of qu adr at ic equ at ion e k it it em s, apar t fr om bein g academ ically u sefu l, ar ealso design ed in at t r act ive m an n er. It is h oped t h at t h is k it willgen er at e en ou gh in t er est for lear n in g m at h em at ics at secon dar yst age. It will pr ove t o be an im por t an t par t of t h e m at h em at icsr esou r ce r oom in t h e sch ools acr oss t h e cou n t r COND ARY M ATH EM ATI CS K ITIVDEVELOPMENT of. Wazalwar, Head , of. Ram Avt ar (Retd .). r i M ah en dr a Sh an k ar, Retd . Lecturer (SelectionGrad e). of. Dh ar am Pr ak ash (Retd ). r i M an oj Ver m a, PGT, KV, Tughlak abad . Ch au r asia, Associate Prof.

5 , Coord t h an k s ar e du e t o Pr of. Gu pt a (Ret d) forsu ggest ion an d su ppor t t o e cou n cil ack n owledges wit h t h an k s t h e con t r ibu t ionof DEK st affs, Sh r i Pat il, Technical Officer, Sh r i An il Nayal,Draftsmen for mak ing illustrations, Sh r i Sat ish Ku m ar, Fore-men, Sh r i Ved Pr ak ash , Sh r i Nar en dr a Ku m ar Jr. Foremen,Sh r i Dewen dr a Ku m ar, DTP COND ARY M ATH EM ATI CS K ITVACT I VI T Y 1:To for m differ en t an gles an d m easu r et h em .ACT I VI T Y 2:To ver ify t h e r elat ion of differ en t pair sof an gles for m ed by a t r an sver sal wit ht wo par allel lin I VI T Y 3:To explor e t h e pr oper t ies of a t r ian I VI T Y 4:To ver ify t h e m id-poin t t h eor em A lin ejoin in g t h e m id poin t s of a t r ian gle ispar allel t o t h e t h ir d side an d h alf ofit ACT I VI T Y 5:To ver ify t h at a line dr awn t h r ou ght h e m id-poin t of on e side an d par allelt o t h e secon d side bisect s t h e t h ir I VI T Y 6:To ver i fy t h e b asi c p r op or t i on al i t yt h eor em.

6 ACT I VI T Y 7:To ver ify t h at a lin e dividin g t wo sidesof a t r i an gl e i n t h e sam e r at i o i spar allel t o t h e t h ir d I VI T Y 8:T o ex p l o r e va r i ou s p r op er t i es ofdiffer en t t ypes of qu adr ilat er FOR CLASS X1591517192123SE COND ARY M ATH EM ATI CS K ITVIACT I VI T Y 9:To ver ify t h at a qu adr ilat er al for m edby join in g t h e m id-poin t s of t h e sidesof a qu adr ilat er al t ak en in or der, is apar allelogr am .ACT I VI T Y 1 0:T o f o r m d i f f er en t s h a p es o n ageoboar d an d explor e t h eir ar I VI T Y 1 1:To ver ify t h at t h e r at io of ar eas of t wosim ilar t r ian gles is equ al t o t h e r at ioof squ ar es of t h ei r cor r esp on d i n I VI T Y 1 2:To ver i fy t h at m ed i an of a t r i an gl ed ivi des i t in t wo t r ian gl es of equ alar I VI T Y 1 3:T o f o r m d i f f er en t f i gu r es i n aGeob aor d sat i sfyi n g t h e fol l ow i n gcon dit ion s:-(a)lyin g on t h e sam e base.

7 (b)lyin g bet ween t h e sam e par allesbu t n ot on t h e sam e base.(c)l y i n g o n t h e s a m e b a s e &bet ween t h e sam e par allelsACT I VI T Y 1 4:To ver ify t h at t r ian gles on t h e sam ebase an d bet ween t h e sam e par allelsar e equ al in ar I VI T Y 1 5:To ver ify par allelogr am s on t h e sam ebase an d bet ween t h e sam e par allelsar e equ al in ar I VI T Y 1 6:To ver i fy t h at for a t r i an gl e an d apar allelogr am on t h e sam e base an dbet ween t h e sam e par allels, t h e ar ea2931353739424446SE COND ARY M ATH EM ATI CS K ITVIIo f t r i a n gl e i s h a l f t h e a r ea o fpar allelogr am .ACT I VI T Y 1 7:T o ex p l o r e a r ea o f t r i a n gl e,par allelogr am an d t r apeziu m .ACT I VI T Y 1 8:To ver ify Pyt h agor as t h eor em .ACT I VI T Y 1 9:To ver ify t h e algebr aic iden t it ies.(i)(ii)ACT I VI T Y 2 0:To ver ify t h e algebr aic iden t it y 22abab a b ACT I VI T Y 2 1:To fact or ise expr ession of t h e t ype 2,A xB xCfo r e x a c tly (i)256xx (ii)26xx (iii)2276xx ACT I VI T Y 2 2:To explor e ar ea of a cir I VI T Y 2 3:T o v er i f y t h a t t h e l o n ger c h o r dsu bt en ds lar ger an gle at t h e cen t r e ofa cir I VI T Y 2 4:To ver ify t h at equ al ch or ds su bt en dequ al an gles at t h e cen t r e of a cir I VI T Y 2 5:To ver ify th at ch or ds su bt en din g equ alan gles at t h e cen t r e of a cir cl e ar eequ 2222a baab b 2222a baab b SE COND ARY M ATH EM ATI CS K ITVIIIACT I VI T Y 2 6:To ver ify t h at t h e per pen dicu lar fr omt h e cen tr e of a cir cle t o a ch or d bisect st h e ch or I VI T Y 2 7.

8 To ver ify t h at t h e lin e dr awn t h r ou ght h e cen t r e of a cir cle t o bisect a ch or dis per pen dicu lar t o t h e ch or I VI T Y 2 8:To ver ify t h at equ al ch or ds of a cir clear e equ idist an t fr om t h e cen t r e of t h ecir I VI T Y 2 9:To ver ify t h at t h e ch or ds equ idist an tfr om t h e cen t r e of a cir cle ar e equ alin len gt h I VI T Y 3 0:To ver ify t h at equ al ar cs of a cir clesu bt en d equ al an gles at t h e cen t r I VI T Y 3 1:To ver ify t h at t h e an gle su bt en ded byan ar c of a cir cl e at t h e cen t r e, i sdou ble t h e an gle su bt en ded by it onan y poin t in t h e r em ain in g par t of t h ecir I VI T Y 3 2:To ver ify t h at t h e an gles in t h e sam esegm en t of a cir cle ar e equ I VI T Y 3 3:To ver ify t h at an an gle in a sem i cir cleis a r igh t an I VI T Y 3 4:To ver ify t h at t h e su m of eit h er pairo f o p p o s i t e a n gl es o f a c y c l i cqu adr ilat er al is 180 ACT I VI T Y 3 5:To ver ify t h at t h e su m of a pair of74767881838588909294SE COND ARY M ATH EM ATI CS K ITIXo p p o s i t e a n gl es o f a n on c y c l i cqu adr ilat er al is n ot equ al t o 180 ACT I VI T Y 3 6:To ver ify t h at t h e t an gen t at an y poin tof cir cle is per pen dicu lar t o t h e r adiu st h r ou gh t h e poin t of con t act.

9 ACT I VI T Y 3 7:To ver ify t h at t h e len gt h s of t h e t wotan gen t s dr awn fr om an exter n al poin tt o a cir cle ar e equ I VI T Y 3 8:T o u n d er s t a n d t h e m ea n i n g o fd iffer en t t r igon om et r i c r at i os u sin gt h e cir cu lar boar I VI T Y 3 9:To est im at e t h e t r igon om et r ic r at iosof som e special an gles su ch as 0 , 30 ,45 , 60 an d 90 ACT I VI T Y 4 0:T o v er i f y t h a t t h e v a l u es o ft r igon om et r ic r atios of an an gle do n otvar y wit h t h e len gt h s of t h e sides oft h e t r ian I VI T Y 4 1:T o ver i f y st a n d a r d t r i gon om et r i ciden t it i v i t y 4 2:(i ) T o u n d er st a n d t h e con cep t ofsu r face ar ea an d volu m e of solids.(i i ) T o v er i f y t h e f a c t t h a tin cr ease\ decr ease in t h e volu m e of asolid m ay n ot r esu lt t h e sam e ch an gein it s su r face ar COND ARY M ATH EM ATI CS K ITXSECONDARY MATHEMATICS KITS.

10 Ast i cSt r i p(A T y pe)3264 20 2mm cu b oi d a lper spex h avin g 3 slot s of5m m widt h at (0-30)m m ,(5 0 - 2 0 0 )m m an d (2 2 0 -250)m mAs per sam pl e3264 20 2mm c u b o i d a lper spex h avin g 3 slot s of5m m widt h at ( )dm ,( )dm & ( )dmAs per sam pl eA 2 m m t h i c k c i r c u l a rt r an spar en t plast ic sh eetof dia 120 m m m ar k ed in(0-360) degr per sam pl eA 2m m th ick semi cir cu lart r an spar en t plast ic sh eetof dia 90 m m m ar k ed in(0-180) degr eesAs per sam pl eIt is a com bin at ion of n u twit h win g an d ch r om iu mplat ed scr ew wit h m at r ict h r ea d (M4) of l en gt h1 5 m m m ad e u p of wi l dst eel h ain g slot t ed r ou n dh ead or HDPE m oldedAs per sam pl e10 8Pl ast i cSt r i p(B T y pe)Fu l lPr ot r ac t or(3 6 00)H al fPr ot r act or(1 8 00)Fl y n u tan dscr ew23450 30 40 41 5 Set sTechnical SpecificationSE COND ARY M ATH EM ATI CS K ITXIGeo-boar dPi n s71 0Ru bberban dsCu t ou t s(For ar ea ofpolygon s)893190 190 10mm A B Sm at er i al b oar d h avi n ggr i d of 1 0 m m squ ar eswit h a h ole of 1m m t h e cor n er s of eachsqu ar e except bou n dar ycor n er s of squ ar per sam pl eSolid cylin dr ical pin s ofl en gt h 1 8 m m an d d i a2 m m m a d e u p o fst ain less st per sam pl eSm a l l m u l t i c o l ou r sr u b b er b an d.