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

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Getallepatrone (Fibonacci-patroon)

Module by: Siyavula Uploaders. E-mail the author

WISKUNDE

Getalpatrone

OPVOEDERS AFDELING

Memorandum

4.

4; 8; 12: 28; 40; 48

5. Ry foutief: moet wees 0; 1; 1; 2; 3; 5; 8; etc.

a) 0 + 1 = 1; 1 + 1 = 2; 2 + 1 = 3; 3 + 2 = 5; 5 + 3 = 8; 8 + 5 = 13; 13 + 8 = 21;

21 + 13 = 34

b) Dit volg die Fibonaccipatroon

c) 55; 89; 144

d) 1 7 - 21 - 35 - 35 - 21 - 7 - 1

1 - 8 - 28 - 56 - 70 - 56 - 28 - 8 - 1

1 - 9 - 36 - 84 - 126v126 - 84 - 36 - 9 - 1

LEERDERS AFDELING

Inhoud

AKTIWITEIT: Getallepatrone (Fibonacci-patroon) [LU 2.2, LU 2.3.3]

Vir die volgende aktiwiteit het jy ’n dosie vuurhoutjies nodig. Pak die vuurhoutjies soos gewys om die figure te vorm:

4.

Figure 1
Figure 1 (graphics1.jpg)
  • Voltooi die tabel. Gebruik jou vuurhoutjies indien nodig.
Table 1
Aantal vierkante 1 2 3 7 10 12
Aantal vuurhoutjies _______ _______ _______ _______ _______ _______

5. Het jy geweet?

’n Italiaanse Wiskundige, Leonardo Fibonacci, het in die 12 de eeu geleef. Hy het ook as Leonardo van Pisa bekend gestaan omdat hy in Pisa gewoon het. Fibonacci het patrone in plante ondersoek en met die baie bekende Fibonacci-ry vorendag gekom:

0 ; 1 ; 1 ; 2 ; 3 ; 5 ; 8 ; 13 ; 21 ; 34

  • Gaan kyk gerus na sonneblomkoppe en die sade in die spiraal van ’n dennebol en jy sal die Fibonacci-patroon daar raakloop!

a) Kan jy die patroon verklaar? ____________________________________

b) Werk in groepe van 4. Kyk in die skool se tuin (of tuis) en tel die kroonblare van die verskillende blomme wat jy sien.

w Wat merk julle op?_______________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

c) Voeg nog 3 getalle by die Fibonacci-getalry:

5 ; 8 ; 13 ; 21 ; 34 ; ________________________________________________

d) Vra jou opvoeder vir grafiekpapier en probeer om die Fibonacci-spiraal te teken.

Assessering

Leeruitkomste 2:Die leerder is in staat om patrone en verwantskappe te herken, te beskryf en voor te stel en probleme op te los deur algebraïese taal en vaardighede te gebruik.

Assesseringstandaard 2.2: Dit is duidelik wanneer die leerder verwantskappe of reëls wat waargeneem is, in eie woorde beskryf, verduidelik en bewys;

Assesseringstandaard 2.3: Dit is duidelik wanneer die leerder voorstellings maak van en verwantskappe tussen veranderlikes gebruik sodat inset- en/of uitsetwaardes op ‘n verskeidenheid maniere bepaal kan word deur die gebruik van:

2.3.3: tabelle.

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