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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 + 3 4 size 12{ { { size 8{2+3} } over { size 8{4} } } } {} = 5 5 4 size 12{ { { size 8{5} } over { size 8{4} } } } {} = 1 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {}

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

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

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

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

2.

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

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

KOPKRAPPERS

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

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

1 + 1 2 size 12{ { {1} over {2} } } {} + 1 4 size 12{ { {1} over {4} } } {} + 1 8 size 12{ { {1} over {8} } } {} = 1 7 8 size 12{ { { size 8{7} } over { size 8{8} } } } {}

1 + 1 2 size 12{ { {1} over {2} } } {} + 1 4 size 12{ { {1} over {4} } } {} + 1 8 size 12{ { {1} over {8} } } {} + 1 16 size 12{ { {1} over {"16"} } } {} = 1 15 16 size 12{ { { size 8{"15"} } over { size 8{"16"} } } } {}

1 + 1 2 size 12{ { {1} over {2} } } {} + 1 4 size 12{ { {1} over {4} } } {} + 1 8 size 12{ { {1} over {8} } } {} + 1 16 size 12{ { {1} over {"16"} } } {} + 1 32 size 12{ { {1} over {"32"} } } {} = 1 31 32 size 12{ { { size 8{"31"} } over { size 8{"32"} } } } {}

5 2 size 12{ { {5} over {2} } } {} 3 1 2 size 12{ { {1} over {2} } } {}
0 2 4
3 1 2 size 12{ { {1} over {2} } } {} 1 1 1 2 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 2 1 2 size 12{2 { {1} over {2} } } {} koppie suiker vir een resep en 3 3 4 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?

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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 2 5 6 size 12{ { {5} over {6} } } {} + 1 2 3 size 12{ { {2} over {3} } } {}

2.2 3 3 4 size 12{3 { {3} over {4} } } {} + 2 1 5 size 12{ { {1} over {5} } } {}

2.3 4 1 7 size 12{ { {1} over {7} } } {} + 1 1 3 size 12{ { {1} over {3} } } {}

Kopkrappers!

  • Kan jy die breuke-patroon voltooi?

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

1 + 1 2 size 12{ { {1} over {2} } } {} + 1 4 size 12{ { {1} over {4} } } {} = 1 3 4 size 12{ { {3} over {4} } } {}

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

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

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

  • Kan jy hierdie towervierkant voltooi?
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. 9 10 size 12{ { {9} over {"10"} } } {} 1 3 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;

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Wiskunde graad 6. OpenStax CNX. Sep 15, 2009 Download for free at http://cnx.org/content/col11072/1.1
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