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Wiskunde

Voorspellings, vergelykings en veranderlikes

Opvoeders afdeling

Memorandum

14. (a) 100

(b) 12

(c) 124

(d) 8

15. (a) 10 99 75 5

(c)

______ 8 ______ 21
39 ______ 74 ______

16.2 (a) 5 х + 7 = 22

(b) 8 х - 10 = 46

(c) 5 + 9 х = 59

(d) х - 13 = 6

16.3 (a) 21

(b) 17

(c) 34

18 (a) 72 (j) 30

(b) 12 (k) 5

(c) 7 (l) 57

(d) 141 000 (m) 9

  1. 900 (n) 9 987
  2. 47 (o) 125

(g) 135

(h) 336

(i) 7

20. (a) х >10

(b) y <2 000

(c) ( c +8)>6

(d) y <50

(e) k – ( k ÷ 2)<20

Leerders afdeling

Inhoud

Aktiwiteit: voorspellings, vergelykings en veranderlikes (algebraïese vergelyking) [lu 1.7.2, lu 1.9.1, lu 1.10, lu 2.5]

14. Vervang nou die letters deur die korrekte getalle in die volgende vloeidiagram:

15. Legkaarte!

a) Kan jy die volgende raaisels oplos?

Ek dink aan ’n sekere getal. As ek die getal met 7 vermenigvuldig, dan 6 aftrek en die antwoord wat ek kry deur 8 deel, is die kwosiënt 8. Aan watter getal dink ek?

____________________________________________________________________

Ek het 9. As ek dit met 12 vermenigvuldig, dan 2 bytel en weer 11 aftrek, is die antwoord _____________________________________________________________

Wat sal die antwoord wees as ek met 7 begin? _______________________________

En as ek met 5 begin? __________________________________________________

b) Ons kan ’n tabel opstel om ons met probleme soos dié hierbo te help.

Getalle 9 7 5
Getalle × 12 + 2 – 11 99 75 51

c) Ons kan die woord “getal” deur enige letter van die alfabet vervang. Kan jy die ontbrekende getalle in die volgende tabel inskryf?

k 6 ________ 13 _________
(k × 5) + 9 49 114

d) Verduidelik aan ’n maat hoe jy bogenoemde antwoorde gekry het.

16.1 Het jy geweet?

Ons noem die stelling (k × 5) + 9 = 49 ’n algebraïese vergelyking . “Algebra” beteken “die studie van getallesinne”.

16.2 Skryf nou ’n algebraiëse vergelyking vir die volgende:

a) ’n Sekere getal x 5 + 7 = 22

____________________________________________________________________

b) 8 x ’n getal – 10 = 46 ______________________________________

c) 5 + (9 x ’n getal ) = 59 _______________________________________

d) Wanneer 13 van ’n groter getal afgetrek word, is die verskil 6.

_____________________________________________________________________

16.3 Los die volgende vergelykings op: (Jy mag jou sakrekenaar gebruik).

a) 49 x a – 29 = 1 000

_____________________________________________________________________

b) (b + 15) x 6 = 192

_____________________________________________________________________

c) 16 x c – 15 = 529

_____________________________________________________________________

17. Het jy geweet?

Die letters wat in die plek van enige getal staan, word veranderlikes genoem.

18. Kom ons kyk nou eers hoe vaar jy in jou volgende hoofrekentoets.

a) 9 x 8 = ___________________________

b) ___________________________ x 4 = 48

c) 4 x ___________________________ = 28

d) 6 x 235 x 100 = ______________________

e) 25 x 9 x 4 = _________________________

f) 16 + 17 + 14 = ______________________

g) 104 + 15 + 16 = _____________________

h) Verdriedubbel: 112: = _____________________

i) 42 ÷ 6 = ___________________________

j) ___________________________ ÷ 6 = 5

k) 35 ÷ ___________________________ = 7

l) (7 x 3) + (4 x 9) =_______________________

m) 4 x 9 + ___________________________ = 45

n) 10 000 – 13 = ___________________________

o) 5 tot die krag van 3 = _______________________

15

19. Het jy geweet?

Wanneer ons>en<-tekens in getallesinne gebruik, bv. as ons wil sê ’n getal gedeel deur 4 is kleiner as 5, sal ons dit so skryf:

y ÷ 4<5

As ons bv. wil sê ’n getal vermenigvuldig met 5 is groter as 16, sal ons dit so skryf:

b x 5>16

Ons noem getallesinne soos hierdie wat nie = -tekens het nie, ongelykhede.

20. Skryf die volgende woordsinne as getallesinne deur gebruik te maak van ongelykhede:

a) Die getal lekkers wat ek het, is meer as 10.

_____________________________________________________________________

b) Die getal leerders in ons skool is minder as 2 000.

_____________________________________________________________________

c) ’n Getal, vermeerder met 8, is groter as 6.

_____________________________________________________________________

d) Daar is minder as 50 leerders in ons klas.

_____________________________________________________________________

e) As ek die helfte van my albasters weggee, sal ek minder as 20 hê.

_____________________________________________________________________

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 1.7: 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;

Assesseringstandaard 1.10: Dit is duidelik wanneer die leerder ‘n verskeidenheid strategieë gebruik om oplossings te kontroleer en die redelikheid daarvan te beoordeel.

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 2.1: Dit is duidelik wanneer die leerder ‘numeriese en meetkundige patrone ondersoek en uitbrei op soek na ‘n verwantskap of reëls, insluitend patrone;

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:

2.3.2: vloeidiagramme;

2.3.3: tabelle;

Assesseringstandaard 2.5: Dit is duidelik wanneer die leerder getalsinne oplos of voltooi deur inspeksie of deur ‘n proses van probeer en verbeter, en die oplossings deur vervanging kontroleer (bv. 2 x - 8 = 4).

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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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