P5 Par e nts Se minar Mathe matic s Str ate gie s for Mode l Dr - PowerPoint PPT Presentation

P5 Par e nts’ Se minar Mathe matic s Str ate gie s for Mode l Dr awing II 18 F e b 2017 Springdale Prim ary School 1

Obje c tive s At the e nd o f this se ssio n, pa re nts will b e a b le to : • unde rsta nd the ra tio na le o f using the mo de l a ppro a c h in so lving pro b le m sums • so lve uppe r prima ry pro b le m sums using the mo de l a ppro a c h • g uide the ir c hild to so lve pro b le m sums using the mo de l a ppro a c h Springdale Prim ary School 2

Outline • Why? (I ntro duc tio n to mo de l me tho d) • What? (E xpla na tio n o f diffe re nt type s o f mo de l) • How? (Ha nds-o n pra c tic e with dra wing o f mo de l) • How? (Ho me suppo rt fo r yo ur c hild) Springdale Prim ary School 3

Why? (I ntro duc tio n to mo de l me tho d) Springdale Prim ary School 4

Curric ulum F ra me work 0 Springdale Prim ary School 5

Proble m- solving Proc e ss • Unde r standing the Pr oble m L o o k fo r g ive n info rma tio n – Visua lize the info rma tio n – Org a nize the info rma tio n – Co nne c t the info rma tio n – • De vising a Plan (Str ate gy) • Car r ying out the Plan (Str ate gy) Use c o mputa tio na l skills – Use g e o me tric a l skills – Use lo g ic a l re a so ning – • Re fle c ting Che c k re a so na b le ne ss – Impro ve o f the me tho d use d – Se e k a lte rna tive so lutio ns – E xte nd the so lutio n to o the r pro b le ms – Springdale Prim ary School 6

Proc e sse s – He uristic s He uristic s a re pro b le m-so lving stra te g ie s whe n • the so lutio n to the pro b le m is no t o b vio us. T he se inc lude making a gue ss (e .g . tria l a nd e rro r/ g ue ss – a nd c he c k, ma king a suppo sitio n) walking through the proc e ss (e .g . a c ting it – o ut, wo rking b a c kwa rds) using a re pre se ntation (e .g . drawing a – diagram , ta b ula ting ) c hanging the proble m (e .g . simplifying the – pro b le m, c o nside ring spe c ia l c a se s) Springdale Prim ary School 7

Using a Re pre se nta tion Re pre se ntations a llo w stude nts to • re fle c t o n the m; – mo dify the m; a nd – link the m to suita b le pro b le m-so lving – stra te g ie s • Re pre se nta tio ns inc lude Pic ture – – Mode l Dia g ra m – T a b le / L ist – Springdale Prim ary School 8

Ma the ma tic s Sylla bus Pr imar y 1 and 2 Pr imar y 3 and 4 Pr imar y 5 and 6 • Who le Numb e r • Who le Numb e r • Who le Numb e r • Mo ne y, Me a sure s • Mo ne y, Me a sure s • Mo ne y, Me a sure s & Me a sura tio n & Me a sura tio n & Me a sura tio n • F ra c tio ns • F ra c tio ns • F ra c tio ns • De c ima ls • De c ima ls • Ra tio & Pro po rtio n • Pe rc e nta g e T he mo d e l me tho d is o ne o f the mo st fre q ue ntly use d • pro b le m-so lving he uristic s thro ug ho ut the prima ry sc ho o l ye a rs. Springdale Prim ary School 9

2018 PSL E Ma ths F orma t Springdale Prim ary School 10

2018 PSL E Ma ths F orma t Cha ng e s to fo rma t o f pa pe rs: • Pape r 1 Bookle t B – Pre vio usly 10 (1m) a nd 5 (2m) q ue stio ns – No w 5 (1m) a nd 10 (2m) q ue stio ns • Pape r 2 – Pre vio usly 13 lo ng -struc ture d q ue stio ns – No w 12 lo ng -struc ture d q ue stio ns • T otal Numbe r of que stions for both Pape r s – Pre vio usly 48 q ue stio ns – No w 47 q ue stio ns Springdale Prim ary School 11

2018 PSL E Ma ths F orma t Cha ng e s to fo rma t o f pa pe rs: • Distr ibution of mar ks – Pre vio usly Pa pe r 1 (40m) a nd Pa pe r 2 (60m) – No w Pa pe r 1 (45m) a nd Pa pe r 2 (55m) • Dur ation for Pape r 1 – Pre vio usly 50 min – No w 1 h • Dur ation for Pape r 2 – Pre vio usly 1 h 40 min – No w 1 h 30 min Springdale Prim ary School 12

2018 PSL E F Ma ths F orma t Springdale Prim ary School 13

2018 PSL E F Ma ths F orma t Cha ng e s to fo rma t o f pa pe rs: • Pape r 2 – Pre vio usly 8 lo ng -struc ture d q ue stio ns – No w 6 lo ng -struc ture d q ue stio ns • T otal Numbe r of que stions for both Pape r s – Pre vio usly 48 q ue stio ns – No w 46 q ue stio ns • T otal Numbe r of mar ks for both Pape r s – Pre vio usly 100 ma rks – No w 90 ma rks Springdale Prim ary School 14

2018 PSL E F Ma ths F orma t Cha ng e s to fo rma t o f pa pe rs: • Dur ation for Pape r 2 – Pre vio usly 1 h 15 min – No w 1 h • T otal Dur ation – Pre vio usly 2 h 15 min – No w 2 h Springdale Prim ary School 15

Wha t? E xpla na tio n o f diffe re nt type s o f mo de l Springdale Prim ary School 16

F e a ture s of Mode l Dra wing • Simplify the pro b le m. • Visua lize the pro b le m fro m a b stra c t to c o nc re te . • Ma ke se nse o f a nd ma nipula te the info rma tio n pic to ria lly. • L e ng th o f the re c ta ng ula r b a rs is dra wn in re la tio n to o ne a no the r. Springdale Prim ary School 17

F e a ture s of Mode l Dra wing • T he a va ila b le info rma tio n is re c o rde d o nto the mo de ls. • Que stio n ma rks a re use d to indic a te the unkno wn info rma tio n. • T ra nsla te the pro b le m into ma the ma tic s ste ps, i.e . e q ua tio ns • Ma inly 2 type s – Pa rt-Who le Mo de ls a nd Co mpa riso n Mo de ls. • T he re st a re hyb rids o f the se two type s. Springdale Prim ary School 18

Pa rt- Whole Mode l Pa rt Pa rt X Y Whole Springdale Prim ary School 19

Pa rt- Whole Mode l Pa rt X Whole Y Pa rt Springdale Prim ary School 20

Compa rison Mode l X Y Compa rison Springdale Prim ary School 21

Compa rison Mode l X Y Compa rison Springdale Prim ary School 22

Proc e ss of Mode l Dra wing Pha se Ac tion Que stions E Re a d the  Ha ve I re a d the who le WHOL who le pro b le m sum? sum Re a d the sum  Wha t d o I kno w? PART line b y line  Ca n I d ra w a d ia g ra m to sho w wha t I kno w?  Wha t d o I no t kno w?  Ca n I d ra w a d ia g ra m to sho w wha t I d o no t kno w? Re a d wha t  Ho w c a n I link up L INK yo u ha ve wha te ve r I ha ve d ra wn? writte n a nd  Ho w c a n I so lve the d ra wn pro b le m? Springdale Prim ary School 23

E xa mple # 1 F re d is 3 ye a rs yo ung e r tha n E unic e . Da wn is 3 time s a s o ld a s E unic e . T o g e the r, E unic e a nd F re d ’ s to ta l a g e is 15 ye a rs le ss tha n Da wn’ s a g e . Ho w o ld is Da wn? F r e d E unic e 15 3 Dawn 3 3 3 ? Springdale Prim ary School

E xa mple #2 � � � o f the sa le s fro m o nio ns is a s muc h a s � o f the sa le s fro m c a rro ts. T he sa le s fro m c a rro ts is $240 mo re tha n the sa le s fro m o nio ns. F ind the to ta l sa le s fro m the o nio ns a nd c a rro ts. O ? C 240 Springdale Prim ary School 25

E xa mple #3 � Ab b y ha d so me swe e ts. She g a ve � o f he r swe e ts to Be n � a nd � o f the re ma ind e r to Ca in. She ha d 12 swe e ts le ft. Ho w ma ny swe e ts d id Ab b y ha ve a t first? Be n Cain 12 ? Springdale Prim ary School 26

E xa mple #4 � Ab b y ha d so me swe e ts. She g a ve � o f he r swe e ts to Be n � a nd �� o f the re ma ind e r to Ca in. She ha d 49 swe e ts le ft. Ho w ma ny swe e ts d id Ab b y ha ve a t first? Be n Cain 49 ? Springdale Prim ary School 27

E xa mple #5 Ra y a nd Se a n sha re d the c o st o f a pre se nt fo r the ir � frie nd . Se a n pa id $73 a nd Ra y pa id $17 mo re tha n � o f the c o st o f the pre se nt. F ind the c o st o f the pre se nt. Ray Se an 17 73 ? Springdale Prim ary School 28

E xa mple #6 T he re a re thre e b o ys in the L e e fa mily. T he ra tio o f the e ld e st b o y’ s a g e to tha t o f the yo ung e st is 4 : 1. T he ra tio o f the mid d le b o y’ s a g e to tha t o f the yo ung e st is 2 : 1. T he e ld e st b o y is 4 ye a rs o ld e r tha n the mid d le b o y. Ho w o ld is the yo ung e st b o y? E lde st Middle 4 Younge st ? Springdale Prim ary School 29

E xa mple #7 � T he re a re � a s ma ny P3 stud e nts a s P4 stud e nts in a sc ho o l. T he ra tio o f the numb e r o f P5 stud e nts to tha t o f P3 stud e nts is 4 : 1. T he re a re 490 P4 a nd P5 stud e nts a lto g e the r. Ho w ma ny mo re P5 stud e nts tha n P3 stud e nts a re the re ? ? P3 P4 490 P5 30 Springdale Prim ary School

E xa mple #8 T he numb e r o f to urists who visite d a to wn this ye a r is 75% tha t o f la st ye a r. T he re we re 120 000 to urists la st ye a r. Ho w ma ny to urists visite d the to wn this ye a r? 75 units T his ye ar ? 120 000 L ast ye ar 100 units Springdale Prim ary School 31

E xa mple #9 Alvin’ s sa la ry is 20% mo re tha n Ba rry’ s sa la ry. Álvin’ s sa la ry is $3600. F ind Ba rry’ s sa la ry. 3600 20 units Alvin Bar r y ? 100 units Springdale Prim ary School 32