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    This module and collection are included inLens: Siyavula: Mathematics (Gr. 7-9)
    By: Siyavula

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Oppervlakte / area van onreëlmatige figure

Module by: Siyavula Uploaders. E-mail the author

WISKUNDE

Omtrek, Oppervlakte en Volume

OPVOEDERS AFDELING

Memorandum

  • Groter as die helfte + kleiner as die helfte maak 1 blokkie, en blokkies wat groter as die helfte is, is reeds getel.

19.

a) 30

b) 40

c) 25

d) 35

e) 4 986

f) 2,51

g) 308

h) 71,2

i) 10

j) 40

k) 120

l) 1,743

m) 186

n) 1 528

o) 8,249

LEERDERS AFDELING

Inhoud

AKTIWITEIT: Oppervlakte / area van onreëlmatige figure [LO 4.2, LO 2.5, LO 2.3]

16. Oppervlakte of area van onreëlmatige figure

16.1 a) Werk saam met ’n maat. Hoe sal julle die oppervlakte van hierdie figuur bepaal? Veronderstel dat elke vierkant 1 cm2 groot is.

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b) Gebruik nou jul metode en bepaal die oppervlakte!

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Figuur 1
Figuur 1 (graphics1.png)

16.2 Het jy geweet?

By onreëlmatige figure kan ons net ’n benaderde oppervlakte bepaal. Ons doen dit deur al die heel vierkante binne die tekening te tel. Ons tel ook die vierkante wat groter as ’n halwe vierkant is, en tel dit by bo­genoemde. Die vierkante wat kleiner is as ’n halwe vierkant word nie getel nie. Kan jy sê hoekom nie?

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So word die benaderde oppervlakte dan in cm² uitgedruk.

Figuur 2
Figuur 2 (graphics2.png)

Bv.

Heel vierkante : 26

Groter as ’n halwe vierkante : 12

Benaderde oppervlakte :38 cm²

16.3 Trek nou jou hand af op die blokkiespapier hieronder. Veronderstel elke vierkant is 1cm².

Figuur 3
Figuur 3 (graphics3.png)

a) Bepaal die benaderde oppervlakte van jou hand. _______________________

b) Watter klasmaat se hand het die grootste oppervlakte? ___________________

c) Wie se hand se oppervlakte is die kleinste? ___________________________

17 Tyd vir selfassessering

Tabel 1
  • Maak ’n regmerkie in die toepaslike kolom:
On­seker Redelik seker Dood­seker
Ek kan die begrip “oppervlakte / area” verduidelik      
Ek kan cm² herlei na mm² en andersom      
Ek kan m² herlei na cm en andersom      
Ek kan km² herlei na m² en andersom      
Ek kan m² herlei na hektaar en andersom      
Ek ken die formules om die oppervlakte van die volgende figure te bepaal:      
  • Vierkant
     
  • Reghoek
     
  • Driehoek
     
Ek kan die oppervlakte van reëlmatige figure bepaal      
Ek kan die benaderde oppervlakte van onreëlmatige figure bepaal      

18.1 Kom ons speel ‘n speletjie!

Jy benodig ’n maat, twee dobbelstene, papier en ’n potlood. Speler A is die “omtrek” en speler B is die “oppervlakte”. Julle is albei “reghoeke” en werk in cm.

Speler A gooi die twee dobbelstene en bereken dan die omtrek van ’n reghoek met die twee getalle, bv. 6 en 2. (6 × 2) + (2 × 2) = 16 cm

Speler B bereken die oppervlakte met dieselfde getalle: 6 × 2 = 12 cm2

Die omtrek is groter, dus kry speler A twee punte. Maak beurte. Die speler wat die meeste punte na 15 rondtes het, is die wenner.

18.2 UITDAGING!

a) Kyk goed na die voorbeeld van die huisplan.

Figuur 4
Figuur 4 (graphics4.png)

b) Teken nou jul eie huisplan so eenvoudig moontlik.

c) Wat is die vloeroppervlakte van jul huis? _____________________________

d) Hoe groot is julle erf? ____________________________________________

e) Wat is die omtrek van jul motorhuis(e)? _____________________________

f) As julle huis vir ’n half miljoen rand sou verkoop, wat sal die koste per vierkante meter dan wees? _____________________________________________________________________

_____________________________________________________________________

g) As jou ouers nog ’n vertrek van 6,1 m by 3,5 m aanbou, wat sal die oppervlakte van jul huis dan wees?

_____________________________________________________________________

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19. Kom ons kyk nou eers of jy op jou vorige hoofrekentoets kan verbeter!Voltooi die volgende so vinnig en akkuraat moontlik:

a) 0,6 of 50 = _______________________

b) 0,8 of 50 = _______________________

c) 50% of 50 = ______________________

d) 70% of 50 = ______________________

e) 4,986 x 1 000 = ___________________

f) 0,251 x 10 = ____________________

g) 3,08 x 100 = ______________________

h) 7,12 x 10 = ____________________

i) 25% x 40 = _______________________

j) 100% x 40 = ______________________

k) 300% x 40 = ______________________

l) 174,3 ÷ 100 = _____________________

m) 18,6 ÷ 0,1 = ______________________

n) 15,28 ÷ 0,01 = ____________________

o) 8 249 ÷ 1 000 = ___________________

Ht jy verbeter? ______________________

Assessering

Leeruitkomste 4:Die leerder is in staat om gepaste meeteenhede, instrumente en formules in ‘n verskeidenheid kontekste te gebruik.

Assesseringstandaard 4.2: Dit is duidelik wanneer die leerder probleme oplos;

Assesseringstandaard 4.5: Dit is duidelik wanneer die leerder berekenings doen deur die geskikte formules te gebruik;

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 1.8: Dit is duidelik wanneer die leerder hoofrekenberekeninge doen wat kwadrate van natuurlike getalle tot minstens 102 en derdemagswaardes van natuurlike getalle tot minstens 53 behels.

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A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

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Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

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