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  • GETSenPhaseMaths display tagshide tags

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

    Module Review Status: In Review
    Collection Review Status: In Review

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Reghoek- en Derdemagsgetalle

Module by: Siyavula Uploaders. E-mail the author

WISKUNDE

Voorspellings, Vergelykings en Veranderlikes

OPVOEDERS AFDELING

Memorandum

1. (b) kwadraatgetalle

2.

(a)

(b) Nee Nie getal se kwadraat

(c) Nee 1 + 2 + 3 + 4 size 12{ div } {} 4 size 12{ div } {} 5 size 12{ <> } {}

3.

(b) 64; 125; 216; 343

(c) 64

(d) 64 000

(e) 274 625

(f) K4: + 64

K5: + 64 + 125 = 225

(g) 1 + 8 + 27 + 64 + 125 + 216 = 441

(h) Almal kwadrate / vierkantgetalle

LEERDERS AFDELING

Inhoud

AKTIWITEIT: Reghoek- en Derdemagsgetalle [LU 1.3.4, LU 1.7.2, LU 1.7.7, LU 2.3.1, LU 2.3.3]

1. Onthou jy nog?

In module 1 het ons geleer van vierkantgetalle en driehoekgetalle.

a) Kan jy gou aan ’n maat verduidelik hoe bogenoemde patrone lyk?

b) Wat is ’n sinoniem vir vierkantgetalle?

2. Kom ons kyk hoe lyk REGHOEKGETALLE.

Het jy geweet?

Elke telgetal groter as 0 is ’n reghoekgetal. Die Grieke het die term reghoekgetalle gebruik slegs vir die produkte van twee opeenvolgende getalle, bv. 42 = 6 × 7.

As ons reghoekgetalle wil teken, sal dit so lyk:

Tabel 1
___ ___ ___ ___ ___ ___     ___ ___ ___  
6 = 1 × 6     ___ ___ ___  
                6 = 2 × 3  

a) Maak nou ’n skets van die reghoekgetal 18 op soveel verskillende maniere as moontlik.

b) Is 18 ’n vierkantgetal? _________________________ Hoekom/hoekom nie?

_____________________________________________________________________

_____________________________________________________________________

c) Is 18 ’n driehoekgetal? _________________________ Hoekom/hoekom nie?

_____________________________________________________________________

_____________________________________________________________________

3. Het jy geweet??

a) Ons kry ook derdemagsgetalle!! Hierdie getalle word ook kubusgetalle genoem. Kyk goed na die voorbeelde:

Figuur 1
Figuur 1 (graphics1.png)

1 = 1 × 1 × 1

Figuur 2
Figuur 2 (graphics2.png)

8 = 2 × 2 × 2

Figuur 3
Figuur 3 (graphics3.png)

27 = 3 × 3 × 3

b) Voorspel nou wat die volgende 4 kubusgetalle sal wees (jy mag jou sakrekenaar gebruik).

___________________________;

___________________________;

___________________________;

___________________________;

c) Watter van die bogenoemde getalle is ook ’n vierkantgetal? ______________

d) Wat sal die 40ste kubusgetal wees? _______________________________

e) Hoeveel is 65³ (tot die mag 3)?___________________________________

f) Kyk goed na die volgende. Kan jy die tabel voltooi?

Tabel 2
Kubus getalle Som van die kubusgetalle
K1 1
K2 1 + 8 = 9
K3 1 + 8 + 27 = 36
K4 1 + 8 + 27 + ........... = 100
K5 1 + 8 + 27 + ........... + ........... = .........................

g) Kan jy voorspel wat die som van die eerste 6 kubusgetalle sal wees?

_____________________________________________________________________

h) Wat merk jy op omtrent die getalle in die tweede kolom?

_____________________________________________________________________

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 1.3: Dit is duidelik wanneer die leerder die volgende getalle herken, klassifiseer en voorstel sodat dit beskryf en vergelyk kan word:

1.3.4: getalle in eksponensiële vorm, insluitend kwadrate van natuurlike getalle tot minstens 12², natuurlike getalle tot die derde mag tot minstens 5³, asook die vierkants- en derdemagswortels van hierdie getalle;

Assesseringstandaard 1.7: Dit is duidelik wanneer die leerder skat en bereken deur geskikte bewerkings vir probleme wat die volgende behels, te kies en te gebruik:

1.7.2: veelvoudige bewerkings met heelgetalle;

1.7.7: eksponente;

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 2.3: 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:

2.3.1: woordelikse beskrywings;

2.3.3: tabelle.

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