tugas akhir matematika modul 3 ppg.pdf

TUGASAKHIR  MODUL3MATEMATIKA BagianA 1. Berikanlah Berikanlahsebuahanalisisuntukkesalahanpemahamansepertigambarberikutini!Menurut Berikanlahsebua sebuahanal hanalisis isisuntuk untukkesa kesalahan lahanpemah pemahamans amansepert epertigamb igambarbe arberikut rikutini! ini!Menu Menurut rut anda,mengapahalinibisaterjadi?

2.

Tentukanhasildari Tent Tentuk ukan an hasi hasil lda dari ri 5 78  3 73 denganmenggunakanilustrasigambar!

JawabanBagianA JawabanBagianA 1. Analisis Analisisuntukkesalahanpemahamanpadasebuahgambar  Analisisuntu untukkes kkesalahan alahanpem pemahaman ahamanpada padaseb sebuahg uahgambar  ambar  a. a. Gamb Ga Gambar mbar ar  pertama pert pertam ama a bisa bisa bisa terjad ter terjadi jadi i kesala kesalah h pahama pahaman n karena karena  perbandingan perban perbandin dingan gan besar besar kedua

gambaryangdibandingkantidaksamasehinggaseolah-olah 23 lebihbesar. b. b.

G Gamb Ga amba am mbar bar arr kedu kedua a bisa bisa ter te terj rrjad jadi ja adi dii kes ke kesa ssala alah allah ah h p paha pa aham ah hama aman man an n kar ka kare rrena ena en na a gamb gambar arny nya a ber be berb rrbed beda be eda, da, a,, gamb gambar  ar  pertama perta pertama ma dibagi dibagi secara secara horizontal horiz horizo horizonta ontal ntal l sedang sed sedangkan sedan angkan gkan kan gambar gambar kedu ke kedua ked dua ua a dibagi dib diba dibagi agi gi secara secara vertikal vertik vertikal al sehinggaseolah-olahtidaksama. c. Gambarketigabisaterjadikesalah Gamba Gambar Gambarketig rketigabisaterjadikesalah ketigabisa abisaterja terjadikes dikesala alahpaha hpahaman pahamankarenapropors paham mankaren ankarenaproporsiketigabagiantidaksama karenaprop apropors orsiketi iketigabag iketigabagiantidaksama gabagian iantidak tidaksama sama sehingga

2.

1 3

bagiandanbagianyangdiarsirbukan 13 yangaktual. yangaktual.

Langkah-la Langka Langk Langkah-l ah-langkah h-lang angkah ngkah kah mengilust mengil mengi mengilust lustrasi ustras rasiperka rasi i perkalian perkal perkalian lianpecaha ian pecahan pecaha pecahan n

7

58

3

3 7

menggunaka menggunakan n ilustrasi ilustrasi gambar  gambar 

adalahsebagaiberikut: Langkah1. Mengubahpecahanyangakandioperasikanmenjadipecahanbiasa  5

 3

7 8

47 

3 7

8 24



7

Langkah2. Memisahkankomponenpecahanmenjadibeberapakomponensederhana 



47 8

8 

24 7

8

8 

7 

7

8

8 

7 

7

8

8 

7 

7

8 3



7

8 

8

7 

8

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Mengga gamb mbar arka kan n oper operasi asi perk perkal alia ian n peca pecaha han n meng menggu guna naka kan n ilus ilustr tras asi i gamb gambar  ar  Langkah3. Meng sentuhanawal 3 73

8 8

8 8

8 8

7

58



47 8

8 8

8 8

7 8



24 7

7

7

7

3

7

7

7

7

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Langkah4. Mengga Menggamba mbarka rkan n operas operasi i perkal perkalian ian pecaha pecahan n menggu menggunak nakan an ilustr ilustrasi asi gambar  gambar  sentuhanakhir. 3

3 7

5

7 8

Langkah5. Menganalaisisilustrasigambarpadalangkah3dan4yangtelahdibuatuntuk  menentukanhasildariperkalian  Padalangkah3,untukmembentuk1bagiankomponensatuanternyataterisi56persegi satuan  Padadaerahyangberwarnabiruadala Padadaerahyangberwarnabiruadalahhasildariperkalia hhasildariperkalianternyatateris nternyataterisi1.128persegi i1.128persegi satuan.  Jumlahpersegisatuandarihasilperkalianyaitu1.128persegisatuan,kemudiandibagi denganjumlahpersegisatuanuntuksatubagiankomponensatuanyaitu56persegisatuan

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Langkah6. Mengecekhasilperkalianmenggunakancaraperkalianlangsung 7

 5 8

 3 73 

47 8

128  247  1.56  20 568  20 17

Setelahdilakukanpengecekanternyatamendapatkanhasilyangsamapadalangkah5. BagianB 1.

Buktikanlahrumusluassegitigasamasisi Buktik Buktikanl anlah ahrum rumus uslua luass ssegi egitig tigas asama amasi sisi si  14 s

2.

Berdasarkanrumusluassegitiga,tentukanlahrumusluassegi6beraturan! Berdasarkan Berdasarkanrumus rumusluass luassegiti egitiga,t ga,tentuka entukanlah nlahrumus rumusluas luassegi segi6b 6beraturan!

2

3

!

JawabanBagianB JawabanBagianB Bukti,perhatikanlahpadagambarsegitigadibawahini! 1.

Diketahui  ABCmerupakansegitigasamasisi Misalkansisinyaadalahsmakatinggisegitigaadalah 

1  t  s    ss  2 



t2  s 2  s 2



t2  s 2





2

2

2

1

4

3 4

3

t2 

 t

s

4

s 2

3

2

RumusUmumLuasSegitigaadalah 

L 

1 2

   alas  tinggi

Maka,luassegitigasamasisiadalah

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1

 L 

2.

s

2

4

3 (Terbukti)

Bukti,perhatikanlahpadagambarsegienamberaturandibawahini! Bukti,perha Bukti,perhatikan tikanlahpa lahpadagam dagambarseg barsegienam ienamberat beraturandi urandibawah bawahini! ini!

Melihatkembalibahwarumusluassegitigasamasisiadalah L

1

s

2

3

4

maka maka, , dari dari gamb gambar ar di atas atas dapa dapat t dipe diperol roleh eh bahw bahwa a luas luas segi segi enam enam bera beratu tura ran n

adalah:  L segienamberaturan=6xLsegitigasamasisi  L



 L



6 3 2

s

1

s

2

4 2

3

3

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BagianC Tentukanlah:Mean,Median,Modus, Tentukanlah:Mean,Median,Modus,Kuartildaridata Kuartildaridataberikut. berikut.

84 68 67 70 52 87 83 82

82 87 91 86 84 90 79 70

72 89 82 88 93 58 55 90

70 85 73 79 78 89 97 95

72 82 77 70 75 60 74 92

80 87 80 81 71 79 71 75

62 85 78 85 99 77 86 85

96 84 79 88 81 72 75 83

86 88 86 61 86 83 83 71

68 89 83 80 83 87 63 88

JawabanBagianC JawabanBagianC Langkah1.Membuattabeldistribusifrekuensi 1) Rentang(R) Rent Rentan ang g(R (R))

R  x max  x min R  99  52 R  47 2) BanyakKelas(k) Bany Banyak akK Kel elas as( (k) k) k  1  3,3 log n k  1  3,3 log 80 k  1  (3,3)(1,9091) k  7,2801  7 3) PanjangKelas(c) Panj Panjan ang gKe Kela las s(c (c)) R c k 

c

47 

7



6,71428  7

Tabel.DistribusiFrekuensi

Nilai 52 59 66 73 80

–

–

–

–

–

58 58 65 65 72 72 79 79 86 86

Frekuensi( fi )

TitikTengah(x xi)

fi.xi

FrekuensiKumulatif(f fk k)

3 4 13 13 27

55 62 69 76 83

165 248 897 988 2.241

3 7 20 20 33 33 60 60

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Langkah2. Langkah2. Menentukannilaidatayangditanya

1) 1) Mean( Mean (x )

x 

 f.x  f i

i

i

x 

6.367 80

x  79,5875  79,6 Me) 2) 2) Median( Median (Me

Letakkelasmedianadalah

1 2

86. n  12  80  40 ,Jadiadadidatake40yaitukelas80 86. –

 12 n  fks  .c Me  TB   f  Me   1 (80)  33   7 Me  79,5   2 27   Me  79,5 

49

27 Me  81,314814  81,3 Mo) 3) 3) Modus( Modus (Mo Letakkelasmodusyaitupadakelas80 86. 86. –

 d1  .c Mo  TB    d d  1 2   14  7 14  11

Mo  79,5   Mo  79 5 

98

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Q1 Q1 Q1 Q1

 14 n  fk1  .c  TB    f  Q1    14 (80)  7   7  65,5   13   13  65,5     7 13  72,5

b)

Q2 =Me=81,3

c)

Q3

Letakkelaskuartil3adalah

3 4

kelas80-86.

Q3 Q3 Q3 Q3

 34 n  fk3  .c  TB    fQ 3     3 (80)  33   7  79,5   4 27   27  79,5     7 27  86,5

n  34 (80)  60 ,makaterletakdidatake60yaitupada

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BagianD 1. Pada Pada mate materi ri utam utama, a, tela telah h diba dibaha has s meng mengen enai ai Tauto Tau Taut Tautol tolo olog logy ogy, gy, y,, kont kontrad ntra radik radi diks iksi ksi, si, i,, dan dan kont kontin inge gens nsi. i. Buktikanlah: a. b.

p  q   q  r  p  r merupakantautology  p  r  p  q  rmerupakankontingensi ~

~

~

~

2.

Carilahdanbuktikanpolabilanganuntukpermasalahanberikutini: Carilahdan Carilahdanbukti buktikanpo kanpolabil labilangan anganuntuk untukperma permasalaha salahanberi nberikutin kutini: i: a. Sistemkompetisipenuh Sist Sistem emk kom ompe peti tisi sip pen enuh uh b. b. Sistemsetengahkompetisi Sist Sistem ems set eten enga gah hko komp mpet etis isii 3. PadapelaksanaanPPGseluruhpesertadimintauntukmembuatRPPuntukkelasII,III,dan Padapelaksa PadapelaksanaanPP naanPPGselur Gseluruhpese uhpesertadim rtadimintau intauntukme ntukmembuat mbuatRPPun RPPuntukkel tukkelasII,III,da asII,III,dan n IV.Dari120pesertaPPG,100orangtelahmenyelesaikanRPPkelasII,kelasIII,dankelas IV,20orangmenyelesaikanRPPkelasIIdanIII,25orangmenyelesaikanRPPkelasIII danIV,15orangmenyelesaikanRPPkelasIIdanIV.Sementaraitu,65orangmembuat RPPkelasII,45orangmembuatRPPkelasIII, RPPkelasII,45or angmembuatRPPkelasIII,dan42orangmembuatRPPkelasIV. dan42orangmemb dan42orangmembuatRPP uatRPPkelasIV. kelasIV. Dari permaslahan permas permaslahan lahan tersebut tersebut berapakah berapakah berapakah banyaknya banyaknya  peserta peserta yang yang belum belum belum menyelesaikan menyelesaik menyelesaikan an satupun satupun RPPyangharusdibuat?Ilustrasikandenganmenggunakandiagramvenn. JawabanBagianD JawabanBagianD 1 1.. Membuktikan Membuktikan a. a. Bukti Bukti

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Kesimpulan: Setelah Setela Setelah h mel me melaku lakuk ak akukan ukan kan an percoba perc perco ercoba obaan baan an an  pada pada ada tabel tabel kebena kebenaran ran dida di didapa did dapa apatka patk tkan tkan an n bahw ba bahwa bah hwa wa a  pada pada pada tabel

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Un=n(n-1) Sebaga Sebagai i contoh contoh, , jika jika pertan pertandin dingan gan sepak sepak bola bola dengan dengan sistem sistem kompet kompetisi isi penuh penuh diikut diikutii sebany sebanyak ak 11 kesebe kesebelas lasan, an, maka maka banyak banyak pertan pertandin dingan gan satu satu kesebe kesebelas lasan an adalah adalah 10 kali kali pertandingandanbanyakpertandinganseluruhk pertandingandanbanyak pertandingandanbanyakpertandinganseluruhkesebelasanadalah110kalipertandingan. pertandinganseluruhkesebelasanadalah110k  esebelasanadalah110k alipertandingan. Banyakkesebelasan  n=11 Pertandingansatukesebelasan  n-1=11-1=10 Pertandinganseluruhkesebelasan  Un=n(n-1)  U11 =11(11-1)=11(10)=110 b. Sistems Sist Sistemsetengahkompetisi emseteng etengahk ahkompet ompetisi isi Sistem Sistem setengah setengah kompetens kompetensi i adalah peserta peserta bertanding bertanding dengan dengan lawan lawan yangsama hanya satukalikecualijikapeserta satukalikecualijikapesertatersebutbertemu. tersebutbertemu. n/2(n-1) Polabilanganuntuksistem Polabilanganuntuksistemsetengahkompetisi setengahkompetisi Un=n(n-1)/2 Sebagaicontoh,jikapertandingansepakboladengansistemsetengahkompetisidiikuti sebany sebanyak ak 11 kesebe kesebelas lasan, an, maka maka banyak banyak pertan pertandin dingan gan satu satu kesebe kesebelas lasan an adalah adalah 10 kali kali pertandingandanbanyakpertandingansemuakes pertandingandanbanyak pertandingandanbanyakpertandingansemuakesebelasanadalah55kalipertandingan. pertandingansemuakesebelasanadalah55k  ebelasanadalah55k alipertandingan. Banyakkesebelasan  n=11 Pertandingansatukesebelasan  n-1=11-1=10 Pertandinganseluruhkesebelasan  Un=n(n-1)/2  U11=11(11-1)/2=11(5)=55 Kesimpulan: Polabilanganuntukpertandingansepakbolayangdiikutisebanyaknkesebelasandengan

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A B

B  C A  C A B  C

=Peserta =Pesertayang yangtelah telahmenyelesaikan menyelesaikanRPP RPPkelas kelasII IIdan danIII IIIada ada20 20orang orang =Peserta =Pesertayang yangtelah telahmenyelesaikan menyelesaikanRPP RPPkelas kelasIII IIIdan danIV IVada ada25 25orang orang =Peserta =Pesertayang yangtelah telahmenyelesaikan menyelesaikanRPP RPPkelas kelasII IIdan danIV IVada ada15 15orang orang =Pesertayang =Pesertayangtelahselesaimembuat telahselesaimembuatRPPkelasII RPPkelasII,III,danI ,III,danIVada100orang Vada100orang

Langkah2. Menuliskandatayangditanyadanyangbelumdiketahui a. PesertayangbelummenyelesaikansatupunR PesertayangbelummenyelesaikansatupunRPPyangharusdibuat PPyangharusdibuat b. PesertayangtelahmembuatR Pesertay Peser Pesertayang tayang angtelah telahmembuatRPPkelasII,III,dan telahmembu membuatR atRPP PPkelasII,III,danIV PPkelasII,III,danIV IV c. PesertayangmembuatRPPkelasIIsaja Pesertay Pesertayang angmembu membuatR atRPP PPkelas kelas IIsaja d. Pesertay PesertayangmembuatRPPkelasIIIsaja Pesertayang angmembu membuatR atRPP PPkelas kelas IIIsaja e. PesertayangmembuatRPPkelasIVsaja Pesertaya Pesertayangme ngmembuat mbuatRPP RPPkela kelasIV sIVsaj sajaa f. Pesertaya Peser PesertayangtelahmembuatRPPkelasIIdanIII tayangte ngtelahm lahmembua embuatRP tRPPkel PkelasI asIIdan IdanIII III g. Pesertay PesertayangtelahmembuatRPPkelasIIIdanIV Pesertayang angtelah telahmembu membuatR atRPP PPkelasIIIdanIV h. Pesertay PesertayangtelahmembuatRPPkelasIIdanIV Pesertayang angtelah telahmembu membuatR atRPP PPkelasIIdanIV Langkah3. Membuatgambaranilus Membuatgambaranilustrasiawaldiagr trasiawaldiagramvenndaridata-datay amvenndaridata-datayangdiketahui angdiketahui Sebaga Sebagai i langka langkah h awal awal dimisa dimisalka lkan n pesert peserta a yang yang telah telah membua membuat t RPP RPP kelas kelas II, III dan IV adalahx.

S A

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c. PesertayangmembuatRPPkelasIIsajaadalah Pesertay Pesertayangm angmembua embuatRP tRPPkel PkelasI asIIsa Isajaad jaadalah alah  30+x =30+8=38orang d. PesertayangmembuatRPPkelasIIIsajaadalah PesertayangmembuatRPPkelasIII PesertayangmembuatR PPkelasIIIsajaadalah sajaadalah  x =8orang e. PesertayangmembuatRPPkelasIVsajaadalah Pesertay Pesertayangm angmembua embuatRP tRPPkel PkelasI asIVs Vsajaad ajaadalah alah  2+x=2+8=10orang f. Pesertay Peser PesertayangmembuatRPPkelasIIdan PesertayangmembuatR tayangm angmembua embuatRP tRPPkel PPkelasIIdanIIIsajaadalah PkelasI asIIdan IdanIII IIIsajaadalah IIIsaja sajaadal adalah ah  20 x =20 8=12orang g. PesertayangmembuatR PesertayangmembuatRPPkelasIII PPkelasIIIdanIVsajaadalah danIVsajaadalah  25 x=25 8=17orang h. PesertayangmembuatR PesertayangmembuatRPPkelasIIdan PPkelasIIdanIVsajaadalah IVsajaadalah  15 x=15 8=7orang –

–

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Langkah4. Membuatdiagramvenn

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BagianE RancanglahsebuahRPPmatematikapadamater RancanglahsebuahRPPmatematikapadamateriperkalianduabilanganp iperkalianduabilanganpecahan. ecahan. RancanganBagianE

PEMERINTAHANKABUPATENMERAUKE DINASPENDIDIKANDANPENGAJARAN SEKOLAHDASARINPRESMUTING3 Alamat:Kamp.Kafyamke,DistrikUlilin,Kab.Merauke

RENCANAPELAKSANAANPEMBELAJARAN (RPP)

SatuanPendidikan SatuanPendidikan Kelas/Semester Kelas/Semester MataPelajaran MataPelajaran MateriPokok MateriPokok AlokasiWaktu AlokasiWaktu

:SD :SD SDInpres InpresMuting Muting3 3 :V :V V(Lima)/ (Lima)/Genap Genap :Matematika :Matematika Matematika :Perkalian :Perkalian PerkalianBilangan BilanganPecahan Pecahan :2 :2 2x x35 35menit menit(2 (2JP) JP)

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C. Tuju Tu TujuanPembelajaran juan anPe Pemb mbel elaj ajar aran an Adapuntujuanpembelajaranyangdiharapkanyaitu Adapuntujuanpembelaj aranyangdiharapkanyaitusebagaiberikut: sebagaiberikut: 1. 1. Siswa dapat membuat ilustrasi gambar perkalian dua bilangan pecahan biasa menggunakanpitapecahandenganbaikdanbenar. 2. Siswadapatmenentukanhasilperkaliandua Siswadapatmenentukanhasilperkalianduabuahbilanganpecahanbiasa buahbilanganpecahanbiasadenganbenar. denganbenar. 3. Siswa Sisw Sis Siswa wa a dapat dapa dap dapat at t membua memb mem membua buat uat t kreasi krea kre kreasi asi si Mid Mid Mid Mappin Mapp Map Mappin ping ing g perkal perk per perkal kalian alia ian ian n bilang bila bil bilang angan ngan an an pecaha peca pec pecaha ahan han n dari dari dar darii kegiat kegi keg kegiat iatan atan an yangtelahdilakukandengankreatifdaninovatif. D. Mate Ma MateriPembelajaran teri riPe Pemb mbel elaj ajar aran an Berikutinimateripembelajaranyangakandi Berikutinimateripembelajaranyangakandipelajariyaitu:Perkalian pelajariyaitu:PerkalianBilanganPecahan BilanganPecahan PetaKonsepKegiatanBelajar OperasiPerkalian

Pecahan

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c.

d. e. f.

Inti

memulaipembelajaran. Guru Gu Guru ru ru mengec men meng mengec gecek ecek ek ek kehadi keh keha kehadi adiran dira ran ran n siswa sis sisw siswa wa a dan dan dan memint mem memi memint inta nta a siswa sis sisw siswa wa a untuk  unt untu untuk  uk  k  meny menyia iapk pkan an perl perlen engk gkap apan an dan dan pera perala lata tan n yang yang dipe diperl rluk ukan an,, 5 misalnyabukudanalattulis. Menit Guru Guru Guru menyampaikan menyam menyampai paikan kan indikator indika indik indikator ator tor pencapaian pencap pencapaia aian n kompetensi kompet kompe kompetens tensi ensi i yang yang akandicapaisiswamelaluipembelajaran. Guru Guru meny menyam ampa paik ikan an mate materi ri yang yang akan akan dipe dipela laja jari ri hari hari ini ini yaitutentangperkalianbilanganpecahanbiasa Sebaga Seb Sebagai Sebag agai ai i apresi apr apresiasi, apres esiasi iasi, asi, , gurumengajukan guru guru mengaj mengajuka ukan n pertan per pertanyaanyang perta tanyaa nyaanyang yaan n yang yang terkai ter terkait terka kait itt dengan dengan penget pengetahu ahuan an sebelu sebelumny mnya a dengan dengan materi materi yang yang akan akan dipelajari.

Fase1.MenyampaikanTujuandanMemotivasiSiswa a. a. Sebagai langkah awal guru menyampaikan tujuan pembelajaran yanghendak yang hendak hendak dicapaioleh dicapai dicapai olehsiswa, siswa,dan danmemberi memberi taumodelkegiatanbelajarhariini. b. b. Kemudian Kemu Kemud emudia dian ian n gur  gu guru gurr u memberikan memberikan motiva mot motivasi motiv ivasi asi si kepada kepada siswaberupa sisw siswa siswa aberupa  berupa mena menamp mpil ilka kan n gamb gambar ar pada pada powe powerp rpoi oint nt tent tentan ang g bila bilang ngan an pecahan. Fase2.MenyajikanatauMenyampaik Fase2.MenyajikanatauMenyampaikanInformas anInformasii a. Gurumemintasiswamelihat Gurumem Gurumeminta Gurumeminta intasisw siswamelihatmelihatcontoh siswame amelihat lihatmel melihatcontohmengilustrasikan melihat ihatconto contohme hmengilu mengilustrasikan ngilustra strasikan sikan dan menent menentuka ukan n hasil hasil perkal perkalian ian pecaha pecahan n pada pada powerp powerpoin ointt

55 Menit

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d.

e.

f.

g.

kelompoknyamembahasmasalahyangdiberikan. Guru Guru Guru ru berkel berk ber berkel kelili elil iling ilin ing ng g memant mema mem memant antau ntau au au siswa sisw sis siswa wa a bekerj beke bek bekerj erja, rja, a, a, mencer menc men mencer cermat erma mati mati tii dan dan mene menemu muka kan n berb berbag agai ai kesu kesuli lita tan n yang yang dial dialam ami i sisw siswa, a, sert sertaa memberikankesempatankepadasiswauntukbertanyahal-hal yangbelumdipahami. Gurumeng Gurumenghimbaukepadasiswayangmampumenjawabsoal Gurumenghimba himbaukepa ukepadasi dasisway swayangma angmampum mpumenjaw enjawabso absoal al yang telah diberikan untuk membantu teman-teman kelo kelomp mpok okny nya a dala dalam m meny menyel eles esai aika kan n soal soal ters terseb ebut ut (tah (tahap ap mengomunikasikan) Gurumemi Gu Gurumemintaperwakilansetiapkelompokuntukpresentasi rumeminta nta perwa perwakil kilanseti ansetiapkelo apkelompo mpokuntuk kuntuk presen presentas tasii hasil diskusi kelompok mereka di depan kelas sesuai permintaanguru. Kemudi Kemu Kem Kemudi udian dian an an guru guru gur guru u memint memi mem memint inta nta a setiap seti set setiap iap ap kelomp kelo kel kelomp ompok mpok ok ok mengum meng men mengum gumpul umpu pulkan pulk lkan kan an semuahasildiskusikelompo semuahasildiskusikelompokuntukdinilai. kuntukdinilai.

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disiplin. e. Siswa Sisw Siswa a melakukan melaku melakukan kan kan operasi opera operas operasi si i semut semu semut t untuk untuk untuk menjaga menja menjag menjaga ga a kebersiha keber kebers kebersiha sihan ihan n kelas. f. Kelas Kel Kelasditutupdengansalam. asdit ditutu utupd pdeng engan ansal salam. am.

G. Media,Ala Medi Media,Alat,danSumberPembelajaran a,Alat,dan t,danSumb SumberPem erPembela belajara jaran n 1. Media eed diia a :Powerpoint, :Powerpoint, Powerpoint,LKS LKS 2. 2. Alat :Papan :Papan PapanTulis, Tulis,Leptop, Leptop,Proyektor, Proyektor,kertas kertasmanila, manila,kertas kertasorigami origamidan danSpidol Spidol 3. 3. Sumber :  BukuGuruMatematikakelasV BukuGuruMatematikakelasVuntuksekolahdasar untuksekolahdasarkurikulum2013. kurikulum2013. H. Penila Pen PenilaianProsesdanHasilBelajar ilaian ianPro Prose sesda sdanHa nHasil silBel Belaja ajarr 1. TeknikPenilaian Teknik TeknikPe Penil nilaia aian n

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Langkah1. MembuatIlustrasigambaraw MembuatIlustrasigambarawalmasing-mas almasing-masingpecahan ingpecahan

10

Langkah2. MenyatukanIlustrasigambar MenyatukanIlustrasigambarawalmenjadi awalmenjadisatubagian satubagian

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SebagaicontohMidMappingyangdiharapkansebagaiberikut:

80

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10

Langkah 3. Mene Menent ntuk ukan an hasi hasil l perk perkal alia iann nnya ya dari dari ilus ilustr tras asi i gamb gambar ar yait yaitu u daerahyangtergabungarsirannya.

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J. J.

L Lampiran ampiran LEMBARKERJASISWA (LKS)

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LEMBARKERJASISWA (LKS) KelompokNomorGenap :

1.