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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:

___ ___ ___ ___ ___ ___ ___ ___ ___
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:

1 = 1 × 1 × 1

8 = 2 × 2 × 2

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 65 ³ (tot die mag 3)?___________________________________

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

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 12 ² , natuurlike getalle tot die derde mag tot minstens 5 ³ , 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.

Questions & Answers

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
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
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 7. OpenStax CNX. Oct 21, 2009 Download for free at http://cnx.org/content/col11076/1.2
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