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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

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Springdale Prim ary School

P5 Par e nts’ Se minar Mathe matic s Str ate gie s for Mode l Dr awing II

18 F e b 2017

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Springdale Prim ary School

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

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Springdale Prim ary School

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)

3

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Springdale Prim ary School

Why? (I ntro duc tio n to mo de l me tho d)

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Springdale Prim ary School

Curric ulum F ra me work

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Springdale Prim ary School

Proble m- solving Proc e ss

  • Unde r

standing the Pr

  • ble m

–

L

  • 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

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Springdale Prim ary School

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

  • 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)

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Springdale Prim ary School

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

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Springdale Prim ary School

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
  • Mo ne y, Me a sure s

& Me a sura tio n

  • F

ra c tio ns

  • Who le Numb e r
  • Mo ne y, Me a sure s

& Me a sura tio n

  • F

ra c tio ns

  • De c ima ls
  • Who le Numb e r
  • Mo ne y, Me a sure s

& Me a sura tio n

  • F

ra c tio ns

  • 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.

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Springdale Prim ary School

2018 PSL E Ma ths F

  • rma t

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Springdale Prim ary School

2018 PSL E Ma ths F

  • rma t

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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
  • tal Numbe r
  • f que stions for

both Pape r s – Pre vio usly 48 q ue stio ns – No w 47 q ue stio ns

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Springdale Prim ary School

2018 PSL E Ma ths F

  • rma t

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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

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Springdale Prim ary School

2018 PSL E F Ma ths F

  • rma t

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Springdale Prim ary School

2018 PSL E F Ma ths F

  • rma t

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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
  • tal Numbe r
  • f que stions for

both Pape r s – Pre vio usly 48 q ue stio ns – No w 46 q ue stio ns

  • T
  • tal Numbe r
  • f mar

ks for both Pape r s – Pre vio usly 100 ma rks – No w 90 ma rks

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Springdale Prim ary School

2018 PSL E F Ma ths F

  • rma t

15

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
  • tal Dur

ation – Pre vio usly 2 h 15 min – No w 2 h

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Springdale Prim ary School

Wha t?

E xpla na tio n o f diffe re nt type s o f mo de l

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Springdale Prim ary School

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.

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Springdale Prim ary School

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.

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Springdale Prim ary School

Pa rt- Whole Mode l Pa rt Pa rt Whole

19

X Y

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Springdale Prim ary School

Pa rt- Whole Mode l Pa rt Pa rt Whole

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X Y

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Springdale Prim ary School

Compa rison Mode l Compa rison X Y

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Springdale Prim ary School

Compa rison Mode l Compa rison X Y

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Springdale Prim ary School

Proc e ss of Mode l Dra wing

Pha se Ac tion Que stions

WHOL E Re a d the

who le pro b le m sum

  • Ha ve I re a d the who le

sum?

PART

Re a d the sum line b y line

  • Wha t d o I kno w?
  • 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?

L INK

Re a d wha t yo u ha ve writte n a nd d ra wn

  • Ho w c a n I link up

wha te ve r I ha ve d ra wn?

  • Ho w c a n I so lve the

pro b le m?

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Springdale Prim ary School

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

  • ld a s E

unic e . T

  • 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?

15 E unic e F r e d

3

Dawn

3 3 3

?

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Springdale Prim ary School

E xa mple #2

  • f the sa le s fro m o nio ns is a s muc h a s
  • 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

  • nio ns a nd c a rro ts.

240

?

25

O C

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Springdale Prim ary School

E xa mple #3

Ab b y ha d so me swe e ts. She g a ve

  • f he r swe e ts to Be n

a nd

  • 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

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Cain 12

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Springdale Prim ary School

E xa mple #4

Ab b y ha d so me swe e ts. She g a ve

  • f he r swe e ts to Be n

a nd

  • 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

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Cain 49

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Springdale Prim ary School

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

  • f

the c o st o f the pre se nt. F ind the c o st o f the pre se nt.

28

73 Ray Se an ? 17

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Springdale Prim ary School

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?

29

4 Middle E lde st Younge st ?

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Springdale Prim ary School

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 ?

?

30

P4 P3 P5 490

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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?

T his ye ar L ast ye ar 75 units 100 units

31

120 000 ?

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Springdale Prim ary School

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.

32

Alvin Bar r y 20 units 100 units 3600 ?

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Springdale Prim ary School

E xa mple #10

In F e b rua ry, the numb e r o f to urists who visite d the zo o inc re a se d b y 25% c o mpa re d to Ja nua ry. In Ma rc h, 60 000 to urists visite d the zo o . T his wa s a 40% d e c re a se in the numb e r o f to urist c o mpa re d to F e b rua ry. Ho w ma ny to urists visite d the zo o in F e b rua ry?

33

Jan F e b 4 u 1 u 60 000 ? Mar 3 u

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Springdale Prim ary School

How?

Ha nds-o n pra c tic e with dra wing o f mo de ls

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Springdale Prim ary School

How?

Ho me suppo rt fo r yo ur c hild

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Springdale Prim ary School

A F ina l Word

Common Mode l-dr awing Pitfalls

  • I

nc o rre c t re pre se nta tio n o f the pro b le m sum

  • I

nc o mple te re pre se nta tio n o f the pro b le m sum

  • T

ra nsfe r e rro r

  • Missing e q ua tio ns
  • Missing units

36

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Springdale Prim ary School

A F ina l Word

What Make s Mode l-dr awing Diffic ult?

  • K

no wle dg e F a c to rs

– L

ing uistic kno wle dg e

– Co nc e ptua l kno wle dg e – Sc he ma tic kno wle dg e

http:/ / re po sito ry.nie .e du.sg / jspui/ b itstre a m/ 10497/ 132/ 1/ ME

  • 2-1-93.pdf

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Springdale Prim ary School

A F ina l Word

What Make s Mode l-dr awing Diffic ult?

  • Affe c tive fa c to rs

– Co nfide nc e – Pe rse ve ra nc e – Mo tiva tio n

http:/ / re po sito ry.nie .e du.sg / jspui/ b itstre a m/ 10497/ 132/ 1/ ME

  • 2-1-93.pdf

38

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Springdale Prim ary School

A F ina l Word

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Springdale Prim ary School

A F ina l Word

Re sour c e s for Mode l-dr awing

  • http:/ / www.te a c h-kid s-ma th-b y-mo d e l-

me tho d .c o m/

  • http:/ / c ite se e rx.ist.psu.e d u/ vie wd o c / d o wnlo a d ?

d o i=10.1.1.555.5563&re p=re p1&type =pd f

  • F

a c e b o o k g ro up – “Ma ths Mo d e l Me tho d – Sing a po re ”

  • iOS App - ima th

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Springdale Prim ary School

Q & A T HANK YOU

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