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  • GETIntPhaseMaths display tagshide tags

    This collection is included inLens: Siyavula: Mathematics (Gr. 4-6)
    By: Siyavula

    Collection Review Status: In Review

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Om probleme in konteks op te los

Module by: Siyavula Uploaders. E-mail the author

WISKUNDE

Gewone Breuke en Desimale Breuke

Gewone Breuke

OPVOEDERS AFDELING

Memorandum

INLEIDING

Daar is 5 modules:

1. Getalbegrip, Optelling en Aftrekking

2. Vermenigvuldiging en Deling

3. Breuke en Desimale Breuke

4. Meting en Tyd

5. Meetkunde; Datahantering en Waarskynlikheid

4 Dit is belangrik dat opvoeders die modules in volgorde (soos hierbo genoem) sal doen, aangesien die leerders die vorige module se kennis en vaardighede benodig vir die daaropvolgende module.

3. GEWONE EN DESIMALE BREUKE (LU 1; 2 EN 5)

LEEREENHEID 1 FOKUS OP GEWONE BREUKE

  • Hierdie module is ‘n voortsetting van die werk wat in graad 5 gedoen is. Daar word uitgebrei op die optelling en aftrekking van breuke, en die berekening van ‘n breuk van ‘n sekere hoeveelheid word ook hersien.
  • Maak seker dat die leerders die korrekte terminologie bemeester het, asook die korrekte strategieë om bogenoemde korrek te bereken.
  • Kritieke Uitkoms 5 (Effektiewe kommunikasie deur visuele, simboliese, en/of taalvaardighede op verskillende maniere te gebruik) is hier van toepassing.
  • 3 weke behoort voldoende te wees om hierdie module te voltooi.
  • ** Aktiwiteit 17 is ‘n taak vir die portefeulje. Hoewel dit ‘n baie eenvoudige opdrag is, moet leerders in staat wees om dit netjies en akkuraat uit te voer. Leerders moet voor die tyd weet hoe opvoeders die taak gaan assesseer.

LEEREENHEID 2 FOKUS OP DESIMALE BREUKE

  • Hierdie module is ‘n uitbreiding op werk wat in graad 5 afgehandel is. Leerders moet nou in staat wees om desimale breuke korrek af te rond tot die naaste tiende, honderdste en duisendste. Beklemtoon weer die korrekte metode om op te tel en af te trek (vertikaal). Gee ook baie aandag aan die vermenigvuldiging en deling van desimale breuke.
  • Aangesien leerders laasgenoemde nogal moeiliker vind, kan 3 - 4 weke aan dié module spandeer word.
  • ** Aktiwiteit 19 is ‘n taak vir die portefeulje. Die opdrag is baie eenvoudig, maar leerders moet in staat wees om dit netjies en akkuraat uit te voer. Leerders moet voor die tyd weet hoe opvoeders die taak gaan assesseer.
  • 5 2+342+34 size 12{ { { size 8{2+3} } over { size 8{4} } } } {} = 5 5454 size 12{ { { size 8{5} } over { size 8{4} } } } {} = 1 1414 size 12{ { { size 8{1} } over { size 8{4} } } } {}

1.2 1 5858 size 12{ { { size 8{5} } over { size 8{8} } } } {} + 2 2323 size 12{ { { size 8{2} } over { size 8{3} } } } {}

3 15+162415+1624 size 12{ { { size 8{"15"+"16"} } over { size 8{"24"} } } } {} = 3 31243124 size 12{ { { size 8{"31"} } over { size 8{"24"} } } } {} = 4 7878 size 12{ { { size 8{7} } over { size 8{8} } } } {}

1.3 3 1414 size 12{ { { size 8{1} } over { size 8{4} } } } {} + 2 1515 size 12{ { { size 8{1} } over { size 8{5} } } } {}

5 5+4205+420 size 12{ { { size 8{5+4} } over { size 8{"20"} } } } {} = 5 920920 size 12{ { { size 8{9} } over { size 8{"20"} } } } {}

2.

  • 4 1212 size 12{ { { size 8{1} } over { size 8{2} } } } {}
  • 5 19201920 size 12{ { { size 8{"19"} } over { size 8{"20"} } } } {}

2.3 5 10211021 size 12{ { { size 8{"10"} } over { size 8{"21"} } } } {}

KOPKRAPPERS

1 + 1212 size 12{ { {1} over {2} } } {} = 11212 size 12{ { {1} over {2} } } {}

1 + 1212 size 12{ { {1} over {2} } } {} + 1414 size 12{ { {1} over {4} } } {} = 1 size 12{ { size 8{3} } wideslash { size 8{4} } } {}

1 + 1212 size 12{ { {1} over {2} } } {} + 1414 size 12{ { {1} over {4} } } {} + 1818 size 12{ { {1} over {8} } } {} = 1 7878 size 12{ { { size 8{7} } over { size 8{8} } } } {}

1 + 1212 size 12{ { {1} over {2} } } {} + 1414 size 12{ { {1} over {4} } } {} + 1818 size 12{ { {1} over {8} } } {}+116116 size 12{ { {1} over {"16"} } } {}= 1 15161516 size 12{ { { size 8{"15"} } over { size 8{"16"} } } } {}

1 + 1212 size 12{ { {1} over {2} } } {} + 1414 size 12{ { {1} over {4} } } {} + 1818 size 12{ { {1} over {8} } } {}+116116 size 12{ { {1} over {"16"} } } {} + 132132 size 12{ { {1} over {"32"} } } {}= 1 31323132 size 12{ { { size 8{"31"} } over { size 8{"32"} } } } {}

Table 1
5 2 5 2 size 12{ { {5} over {2} } } {} 3 1 2 1 2 size 12{ { {1} over {2} } } {}
0 2 4
31212 size 12{ { {1} over {2} } } {} 1 11212 size 12{ { {1} over {2} } } {}

KLASBESPREKING

  • Noemers dieselfde maak
  • Kry kleinste gemene veelvoud
  • Maak alles eers onegte breuke
  • Trek eers heelgetalle van mekaar

LEERDERS AFDELING

Inhoud

AKTIWITEIT: Om probleme in konteks op te los [LU 1.6.2]

Werk saam met ‘n maat en los die volgende probleem op:

1.1 Ma gebruik 212212 size 12{2 { {1} over {2} } } {} koppie suiker vir een resep en 334334 size 12{3 { {3} over {4} } } {} koppies vir ‘n ander. Hoeveel koppies suiker is altesaam gebruik?

.........................................................................................................................

.........................................................................................................................

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1.2 By ‘n verjaarsdagpartytjie eet Rafiek en sy maats een en vyf agstes van die ham-en-salami-pizzas op. Hulle eet ook twee en twee derdes van die ham-en-pynappel-pizzas op. Watter breuk pizza het hul altesaam opgeëet?

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

1.3 Rafiek en sy maats drink ook drie en ‘n kwart liter Coke en twee en ‘n vyfde liter Creamsoda op. Watter breuk koeldrank het hul altesaam opgedrink?

.........................................................................................................................

.........................................................................................................................

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2. Bereken die volgende op jou eie:

2.1 25656 size 12{ { {5} over {6} } } {} + 12323 size 12{ { {2} over {3} } } {}

2.2 334334 size 12{3 { {3} over {4} } } {} + 21515 size 12{ { {1} over {5} } } {}

2.3 41717 size 12{ { {1} over {7} } } {} + 11313 size 12{ { {1} over {3} } } {}

KOPKRAPPERS!

  • Kan jy die breuke-patroon voltooi?

1 + = 11212 size 12{ { {1} over {2} } } {}

1 + 1212 size 12{ { {1} over {2} } } {} + 1414 size 12{ { {1} over {4} } } {} = 13434 size 12{ { {3} over {4} } } {}

1 + 1212 size 12{ { {1} over {2} } } {} + 1414 size 12{ { {1} over {4} } } {} + = 1

1 + 1212 size 12{ { {1} over {2} } } {} + 1414 size 12{ { {1} over {4} } } {} + += 1

1 + 1212 size 12{ { {1} over {2} } } {} + 1414 size 12{ { {1} over {4} } } {} + + + = 1

  • Kan jy hierdie towervierkant voltooi?
Table 2
5 2 5 2 size 12{ { {5} over {2} } } {} 3  
  2 4
  1  

KLASBESPREKING:

  • Wat moet ek eers doen voordat ek breuke van mekaar kan aftrek?

  • Wat doen ek as ek twee breuke waarvan die noemers nie veelvoude van mekaar is nie, bv. 910910 size 12{ { {9} over {"10"} } } {} – 1313 size 12{ { {1} over {3} } } {} , van mekaar wil aftrek?

  • Wat is die maklikste manier om die verskil tussen twee gemengde getalle te bereken?

  • Watter ander manier(e) is daar nog?

ONTHOU!

Wanneer ons ekwivalente breuke aftrek, trek ons net die tellers af.

Die noemer word net so behou.

ONTHOU OOK!

Indien die antwoord ‘n onegte breuk is, moet jy

dit na ‘n gemengde getal herlei.

Assessering

Leeruitkomste 1:Die leerder is in staat om getalle en die verwantskappe daarvan te herken, te beskryf en voor te stel, en om tydens probleemoplossing bevoeg en met selfvertroue te tel, te skat, te bereken en te kontroleer.

Assesseringstandaard 1.6: probleme oplos in konteks, insluitend kontekste wat gebruik kan word om ‘n bewustheid van ander leerareas, asook van menseregte-, sosiale, ekonomiese en omgewingskwessies, te bevorder, soos:

1.6.2 meting in konteks van Natuurwetenskappe en Tegnologie;

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