Literasi Nombor Topik 2

7/17/2019 Literasi Nombor Topik 2

http://slidepdf.com/reader/full/literasi-nombor-topik-2 1/41

WAJ 3052LITERASI NOMBOR

2. OPERASI & PENGIRAAN

1



1. Pelbagai cara ela!"!a# $e#giraa# %

i. Algri'a ber'"li( )a#g al'er#a'i* +b"!a# $ia,ai-

ii. al!"la'r

iii. Pe#giraa# e#'ali/. Pe#ga#ggara#

/. Baa# a#i$"la'i*

2. e(e("aia# a# !e'ia!(e("aia# $e#gg"#aa#!al!"la'r ala $e#giraa#

3. Meba#i#g!a# !e(e("aia# $e#gg"#aa# a(ila#ggara# a# $e#giraa# )a#g 'e$a'

. Pera#a# algri'a al'er#a'i* !al!"la'r$e#giraa# e#'al $e#ga#ggara# a# baa#a#i$"la'i* ala $e#ga4ara# $e#giraa#.

2



1.

Algri'aber'"li()a#g

al'er#a'i*

+b"!a#$ia,ai-

2.al!"la'r

. Pe#ga#ggara#

5. Baa#a#i$"la'i

*

3.Pe#giraa#

e#'al

3

Kaedah UntukMengira



1. La#g!ala#g!a lai# )a#g ig"#a!a# "#'"!e#a$a'!a# 4a,a$a# bagi $era(i 'aba'la! arab a# baagi.

2. 6#' $e#giraa# algri'a al'er#a'i* )a#geliba'!a# $era(i 'aba iala $e#giraa#ala be#'"! cera!i#!a# #br e#gi!"' #ilai'e$a'.

3. Algri'a aala !"$"la# $eri#'a "#'"!e#)ele(ai!a# a(ala. Peri#'a$eri#'a i'"i'er4ea!a# (ecara ber'aa$ a# ber'"r"'a#(ecara 'era'"r.

. Algri'a (eri#g e$"#)ai la#g!a e#g"la#ga'a" eerl"!a# !e$"'"(a# (a$ai '"ga(

1. i) Algoritma Alternatif



ii-Contoh 1

Algri'a Al'er#a'i* bagi O$era(i Taba Aala (e$er'i beri!"'%

Aa e$"#)ai 27 !e$i#g ca!era $aa'.

Ba$a#)a eberi!a# 35 !e$i#g lagi ca!era$aa' !e$aa#)a. Bera$a!a 4"la ca!era$aa' )a#g Aa aa8

Algoritma 1: Cerakinan

27 9 20 : 7 35 9 30 : 5

50 : 12 ; <2

:

5



Contoh 2Algri'a Al'er#a'i* bagi O$era(i Tla! Aala (e$er'i beri!"'%

Aa e$"#)ai =1 !e$i#g ca!era $aa'.2 !e$i#g 'ela r(a!. Bera$a !e$i#g ca!era

$aa' )a#g 'i#ggal8

Algoritma 1: Cerakinan

=1 ; >0 : 11 ; >0 a# 11

2 ; 20 : ; 20 a# G"#a!a# !#(e$ b"a#g +take away)=1 9 >0 a# 11

2 9 0 a# <0 a# 7 ; <7

<



iii) Peranan Algoritma

1. ?#'"! e$er"a!a# !er4aala eb"a' $rgra a'a" )a#gbia(a i(eb"' (ebagai @ problem

solving’ .2. Me#ga'a(i a(ala lgi!a a#

a(ala Ma'ea'i!.

3. 6#'

7



2. i) Bahan Manipulatif

1. Mel !#!ri' )a#g eliba'!a# !#(e$ Ma'ea'i!"#'"! e#ari! $elbagai eria.

2. Meliba'!a# $e#gg"#aa# 'a#ga# a'a" (e#'"a#'a#ga# "ri"ri e#ga# ce!a$.

3. Me#ari! i#a' a# $era'ia# "ri "#'"! bela4arMa'ea'i!.

. Baa#i'e )a#g $ela4ar g"#a!a# "#'"!e#)!#g $ebela4ara# (ecara $e#galaa#

a#(# $ra!'i!al +$ebela4ara# e$erie#'ial-.5. Me#"#4"!!a# el )a#g !#!ri' +ble ilia'(e#'"$ega#g-.

<. Ble ia#i$"la(i bagi eba#'" !e*aaa#!#(e$.

>



ii)

Contoh 1

=

Bar Ma'ea'i!Bl! Ci#e( 6i$ Ber,ar#a

R 6"i(e#aire I!a'a# S'ra, Aba!"(



1. Ba'a#g Ice 6rea . Blc! Cie#e(

2. Aba!"( 5. Iba#ga#

3. Ca" <. P"DDle

Contoh 2

10



Bl!Cie#e(

Contoh3

11



CaraPenggunaan

12



Contoh 4Bar Matematik !od Cui"enaire

13



1c 1c 1c 1c 1c 1c 1c 1c 1c 1c

1#$m

2c

5c

10c

1



Contoh %Cip Ber&arna

15



Contoh '(katan tra&

10 ba'a#g Buang % *atang

7 ba'a#g

1<



iii) Peranan Bahan Manipulatif

1. Ala' $eba#'" !e$aa g"r" alae#ca$ai b4e!'i* $ebela4ara#.

2. Mei" )a#g a!a# e#ari!$era'ia# a# i#a' "ri "#'"!'er"( e#"$"!a# $era'ia#'eraa$ (e(i $e#ga4ara# a#

$ebela4ara# )a#g berla#g("#g.3. Ala' a'a" baa# )a#g ber(i*a' !#!ri'.



. Pe#gliba'a# $e#gg"#aa# 'a#ga# a'a"(e#'"a# 'a#ga# "ri"rie#ga# ce!a$ 'eraa$ b4e! )a#g

a$a' i$ega#g a# ia#i$"la(i.5. Meba#'" "ri"ri )a#g beraa

ala !a'egri $ra $era(i )a#g bar"

"la ebi#a $e#ge'a"a# a#!#(e$ Ma'ea'i! (ecara la#g("#ga'a" 'ia! la#g("#g.



Contoh +A*aku"

Aba!"( iala ala' e#gira ala a!'i/i'i$e#ga)aa#. Ia er"$a!a# ala' ba#'"a# e!a#i!al)a#g ig"#a!a# "#'"! ebila#g.

1=



20

Bahagian,*ahagianA*aku"



Se'ia$ bi4i

e,a!ili 5

Se'ia$ bi4ie,a!ili 1

Nai!!a# 2 a#i! ba,a )a#g $ali#g !a#a# !e ara $ala#gbia##ai!!a# 1 a#i! ba,a )a#g beraa i (ebela !iri "#'"!e#"#4"!!a##ilai 12.

?#'"! e#aba!a##)a e#ga# #ilai 31gera!!a# 1 a#i! i baagia# #ilai 'e$a' (a !e a'a( a#3 a#i! baagia# #ilai 'e$a' $"l" !e a'a(.

CaraPenggunaan

21



22

i/-



Peranan A*aku"

1. Pe#"$"a#

Se"a eria "'aa ig"#a!a# a$abilae#ge#ali!a# aba!"(.

2. I#ga'a#.!e"a"a 'a! !iri a# 'a! !a#a# a!'i* a$abila

e#gg"#a!a# aba!"(. O'a! !a#a# e#gi#ga'icra! a# ie4 a#a!ala 'a! !iri e#gira (ecarae#'al.

3. Gabara# a# I#($ira(iPe#giraa# (ecara $a#'a( a# a$a' e#)ele(ai!a#

ba#)a! a(ala.. Peera'ia#

La'ia# (ecara $eera'ia# a# eb"a' la'ia#'a#$a !e(ila$a#.

5. e$a#'a(a# 23



3. i) Kalkulator1. Me(i# )a#g a$a' ig"#a!a#

"#'"! e#4ala#!a# $era(i'aba 'la! arab baagia# lai#lai#.

2. Ber*"#g(i (ebagai

$e#gi'"#g.3. Mer"$a!a# (eb"a ala'

ele!'r#i! )a#ge#gg"#a!a# 'e!#lgie# "#'"! e#a$a'!a#

4a,a$a# )a#g 'e$a' a#$a#'a(.

. M"ri"ri a$a'e#i#g!a'!a# !eaira#

Ma'ea'i! a#)a e#ga#2



ii) Peranan Kalkulator

1. Sebagai baa# ba#'" bela4ar +BBB- i(e!la re#a.

2. M"ri ber$el"a#g eb"a' $e#er!aa#

)a#g lebi e#ala 'e#'a#g !#(e$ &!eaira# '$i!'$i! Ma'ea'i! )a#gber!ai'a#.

3. Me#4ia'!a# a(a $e#giraa#.

. Mebe!al "ri cara )a#g (e#a#g a#ber!e(a# "#'"! eb"a' $e#)ele(aia#a(ala.

25



iii) Kesesuaian Dan Ketidaksesuaian

Penggunaan Kalkulator Dalam Pengiraan

Kesesuaian Ketidaksesuaian

1. Bahan sokongan pembelajaranyang pantas

Contoh:Fungsi Pemalar (constant) untuk

operasi asasara biasa:

ara pantas:

1. !a"apan akhir akandipengaruhikan sekiranyatersilap tertekan butang

kalkulator

Contoh:

Kebanyakan butang padakalkulator disusun dalam suatuaturan tertentu dan mempunyaisai# yang sama

6

H

;

H

;

6

H

;

;

2<

3

3

3 273 =

27



Kesesuaian Ketidaksesuaian

$. %embolehkan murid&muridmengira dan menggunakannombor dari angka kecil sehinggaangka yang lebih besar denganmudah.

Contoh:

%urid&murid boleh membuatpengiraan yang melibatkan angka

juta dan billion.

$. %urid&murid yang terlalubergantung kepada kalkulatorkurang mengingati dan mahirdalam menulis jalan penyelesaian%atematik.

Contoh:

%urid&muird lebih bergantungkepada kalkulator daripada

menulis percubaan strategi untukmenyelesaikan masalah.

'. %empercepatkan penyelesaianmasalah

Contoh:%urid&murid boleh mendapat ja"apan dengan cepat tanpamenulis jalan penyelesaian yangpanjang.

'. %engurangkan penerokaan dalamminda

Contoh:%urid&murid kurang mengamalkanpengiraan mental ataupunanggaran.

27



1. Pr(e( e#a$a'!a# 4a,a$a# 'e$a'e#ga# a#)a ber!ir 'a#$ae#gg"#a!a# $e#(il !er'a(

!al!"la'r a'a" (ebara#g ba#'"a#ala' e#gira.

2. Cig"#a!a# "#'"! e#a$a'!a#

4a,a$a# 'e$a' a'a" (ecaraa#ggara#.

4. i) Pengiraan Mental

2>



1. Si*a' !"'a'i* a((ia'i* a# i('rib"'i*#br eble!a##)a "#'"! i("("# a#icera!i#!a# ("$a)a "a i!ira (ecarae#'al.

2. Nbr a# "#g!a$a# ble i,a!ili ala$er(aaa# )a#g (e'ara eble!a#$e#giraa# #br "a i!ira (ecarae#'al.

3. G"#a!a# 'e!#i! i#i 4i!a (a'" #br )a#g $erl"i'aba a'a" i'la! iala 12 a'a" 3 10 2030 a'a" 100 200 a'a" 300 a# (ela#4"'#)a.

ii) trategi dan Pro"edurPengiraan Mental

2=



Contoh 1G"#a!a# $e#giraa# e#'al "#'"! e#)ele(ai!a#(ala# i ba,a.

1. 1>77 : 300 ;

2. 2 > ;

3. 775 3> ;

. 1>200 :2300 ;

30

2177

1=2

737

20500



iii) -eknik Mem*ilang

1. Te!#i! ebila#g aala kaedah ang $ekapuntuk menam*ah 4i!a ae#( iala

1 2 3 10 20 30 100 200 300 a# (ela#4"'#)a.

. 6#'#)a 5 : 30 "la!a# e#ga# 5 a# bila#g(ecara e#ai! (eba#)a! 10 "#'"! e#a$a'!a#a(il 'aba% 5 55 <5 75.

2. ?#'"! ebila#g (ecara e#ai! "la!a# e#ga#ae# )a#g lebi be(ar a# 'er"( ebila#g(ecara e#ai! (ei#gga e#a$a' 4a,a$a#.

3. Te!#i! ebila#g (ecara e#"r"# er"$a!a#

!aea )a#g ce!a$ a$abila i'la! 1 2 a'a" 1020 a'a" 30 a# (ela#4"'#)a.

. Mi(al#)a >712 "la!a# e#ga# #br )a#glebi be(ar >71 a# la!"!a# $r(e( ebila#g

(ecara e#"r"#% >71 >70 ><=. 31

C t h 1



Contoh 1

a !rei' (e(era#g e#"#4"!!a# baa,a iaber"'a#g RM >>00 "#'"! $i#4aa# !ere'a a# RM

3100 (ecara !rei'. Bera$a 4"la "'a#g#)a "#'"!!e"a"a i'e i#i8

Penele"aiaan:

1. 6ari >>00 : 3100.2. Taba!a# #ilai rib".

3. M"la!a# e#ga# >>00 a# bila#g (ecara e#ai!(eba#)a! 1000 'iga !ali% >>00 =>00 10>00

11>00.. Jai >>00 : 3000 ; 11>00.

5. Se!ara#g ber"la e#ga# 11>00 a# bila#ge#ai! 100% 11>00 11=00.

<. J"la "'a#g iala RM11.=00. 32



Contoh 2

Perbela#4aa# (ea(a ar#i/al e(ia'a#'a"# lal" iala RM 1155. Ta"# i#i Ja,a'a#!"a(a ber4a)a e#g"ra#g!a#$erbela#a4aa# (eba#)a! RM 200. Bera$a!a!( bar" "#'"! $erbela#4aa#8

Penele"aian:

1. 6ari 1155200.

2. M"la!a# e#ga# 1155 a# bila#g (ecara

e#"r"# (eba#)a! 100 "a !ali iai'"%1155 1055 =55.

3. ( bar" "#'"! $erbela#4aa# iala RM=55

33



i/) Memilih 0om*or ang era"i

1. bi#a(i (e(e'e#ga #br eb"a'!a#$e#abaa# "a ila!"!a# c#'#)a 25a# 175 4"ga "a "#'"! iarab c#'#)a2> 10.

2. 0om*or ang mudah untuk dikira (ecarae#'al i#aa!a# #br c$a'ible.

3. Te!#i! eili Nbr )a#g 6$a'ibleeerl"!a# $eilia# $a(a#ga# #br )a#gc$a'ible "#'"! i$era(i!a# a# eliba'!a#*a!'a . ble e#aba a# e#la! (ecarae#'al #br ga#aa# 10 a'a" 100 c#'#)a70 : 20 ; =0 a# ble e#arab ga#aa# 10a# 100

. 6#'#)a 3 100 ; 300. 3



/) Memilih 0om*or ang era"i dalamPendara*an

Contoh 1

6ari #br )a#g c$a'ible "#'"! e#cari #ilai)a#g 'e$a' bagi $e#giraa# +2 >- +5 7-.

Pe#)ele(aia#

Pei!ira# Si'i % Sa)a elia' baa,a 2 arab 5(aa e#ga# 10 a# e#arab #br e#ga# 10aala "a. e"ia# > arab 7 aala 5< a#5< arab 10 aala 5<0. a(il arab#)a iala 5<0.

Pei!ira# Ai()a% Sa)a elia' baa,a > arab 5aala 0 a# 0 arab 2 aala >0 a# >0 arab 7aala 5<0. a(il arab#)a iala 5<0.

35



i) Peranan Pengiraan Mental

1. Me#)ele(ai!a# $era(alaa# aria#.

2. Ca$a' e#l#g "ri "#'"! eberi!e$"'"(a# )a#g ce$a'.

3. 6ara 'erbai! "#'"! eba#'" "rie#geba#g!a# !e$e!aa# #br a#!eaira# ber!ir (ecara !ri'i(.

. Meba#'" $eaaa# )a#g e#ala'e#'a#g ('r"!'"r a# ciriciri #br.



1. Meerl"!a# !e$aa $eaaa##"era(i a# $e#ge'a"a# 'e#'a#g*a!'a*a!'a a(a(.

2. Te!#i! $e#ga#ggara# #breliba'!a# $e#"!ara# #bre#ga# )a#g $ali#g e!a' a#

"a i!ira (ecara e#'al.

% i) Penganggaran

37



ii) Peranan Penganggaran

1. Me#)ele(ai!a# a(ala Ma'ea'i!e#ga# lebi ce$a'.

2. ei"$a# (e#'ia(a e#gg"#a!a#

a#ggara#.3. 6#'%

A#ggara# !( $eba)ara# "#'"! (e("a'"$r"!.

3>



iii) trategi dan Pro"edur UntukPenganggaran

1. Tera$a' Te!#i! Pe#ga#ggara#.

2. Meerl"!a# !e$aa $eaaa##"era(i a# $e#ge'a"a# 'e#'a#g

*a!'a*a!'a a(a( (e$er'i 'e!#i!'e!#i!"#'"! $e#giraa# e#'al.

3. J"ga eliba'!a# eb"a' !e$"'"(a#(aaa a#ggara# i'" ble i'eria

"#'"! (i'"a(i )a#g ber!ai'a# a# 'e!#i!a#a )a#g ar"( ig"#a!a# "#'"!a$a'!a# a#ggara# i'".

3=



i/) Kefahaman Penting

1. Se"a 'e!#i! $e#ga#ggara# #breliba'!a# e#"!ara# #br e#ga#)a#g $ali#g a$ir a# "a "#'"!i!ira (ecara e#'al.

2. Per!ai'a# e#ga# !eaaa# (ebe#are#e#'"!a# (aa aa 4a,a$a# )a#g'e$a' a'a" a#ggara# (aa4a )a#gi$erl"!a# "#'"! e#)ele(ai!a#

a(ala.

0



!uukan

''$%,,,.I(i$a.#e'$$gKl(le.$$1MOC?LKPPGKSEMESTERK1WAJ305KLi'era(iKNbr.$*

''$%4"r#al(.blg($'.c201001$e#ga#ggara#e#i(i*"#g(ia#*aa'.'l

''$%,,,./$$l."$.e".)"$l

a(c(*ce300K130==3=731.$* ''$%ella'ea'ic(.,eebl).c

e(ei.'l

li bl

http://www.imsipda.net/ppg_lms/file.php/1/MODUL_PPG_SEMESTER_1/WAJ3105_Literasi_Nombor.pdf



http://journal-sdm.blogspot.com/2010/01/penganggaran-definisi-fungsi-manfaat.html



http://www.vodppl.upm.edu.my/uploads/docs/fce3400_1309939731.pdf


http://hellomathematics.weebly.com/esei.html


http://wansalina2012.blogspot.com/2012/11/pengiraan-secara-mental.html

http://wansalina2012.blogspot.com/2012/11/pengiraan-secara-mental.html











Documents

Literasi Nombor Topik 2