|
Think Online versprei leermateriaal gebaseer
op die Suid-Afrikaanse leerplan, opgestel deur ervare opvoeders. Dis
in elektroniese formaat (op CD of per e-pos) met die voordeel van laer
kostes, en teks kan verander word soos nodig. Think
Online distributes learning material designed by experienced teachers and
based on the South African Curriculum. It
is available in electronic format (on CD or by e-mail) with the benefit of
low costs - texts can be adapted as necessary.
|
|
"Water your dreams with optimism
and solutions and you will cultivate success." (Lao Tzu) |
HOOFREKEN
/ MENTAL MATHS
(Kliek hier vir meer inligting oor die Graad 7
Wiskunde-module / Click here for more information on the Grade
7 Math Module)
"Op die eerste dag het my klas 'n
gemiddeld van 68,8% behaal vir hul spoedtoetse.
Teen Dag 10 was die gemiddeld 94% - 'n 25% verbetering - verstommend!
Ek glo dit sal hul Wiskunde-punte die res van die jaar opstoot."
|
Baie Gr4-6 leerders sukkel met moeiliker Wiskunde-bewerkings (soos lang
deling, lang vermenigvuldiging, die optel en aftrek van breuke) omdat tafels
en basiese Wiskunde-kennis nie vasgelê is nie. Hoofreken moet, volgens die leerplan, daagliks in klasse gedoen
word. Intermediêre klasse is egter te
klein vir groepwerk. As dit klassikaal
gedoen word, besef leerders die kans is skraal dat hy/sy die vraag sal moet
beantwoord, en "skakel dan af".
As elke leerder die antwoorde moet neerskryf, gee hul aandag. Ons werkvelle en
aanlynoefeninge spreek hierdie probleem aan, en leerders geniet hierdie
daaglikse oefeninge. Ons bied: §
240 werkvelle met hoofreken geskik vir die intermediêre fase (± Graad
5 tot 6-vlak ) §
Die eerste tien werkvelle word gebruik om vas te stel of leerders hul
tafels en kombinasies ken - ideaal vir
die begin van die jaar. §
Daarna volg werkvelle wat meer ingewikkeld is en toets of begrippe in
die intermediêre fase vasgelê is. §
Werkvelle is gegradeer volgens moeilkheidsvlak - Vlak 1 is makliker,
terwyl Graad 3 moeiliker is. §
Daar is ook remediërende werkvelle op die CD om
spesifieke probleme aan te spreek, bv. leerders wat sukkel met deel; met nul
en een, ens. §
Elke werkvel het 50 vrae elk en kan aan die begin van 'n les gebruik
word - sowat 5 tot 15 minute, of soos deur die opvoeder bepaal. §
Memorandums vir elke werkvel is op die 'flash
disk', asook tabelle met tafels en kombinasies wat leerders kan gaan leer, en
grafieke waarop resultate aangeteken kan word. |
Many Grade 4-6
learners struggle with more difficult Math concepts (e.g. adding of
fractions, long division, long multiplication) simply because they do not
know their bonds and tables. Teachers are expected
to do mental maths daily. However,
there is not enough space in intermediary phase classrooms to split the class
into groups. In a big group, learners
know their chances are poor to answer a question, and stop paying
attention. If everyone writes down the
answers, everyone pays attention. Our worksheets and online tests were
designed to address this problem, and learners love these daily exercises. We offer: §
240 mental
maths worksheets for the intermediary phase (± Grade 5 to
6-level) §
The first
set (ten worksheets) may be used at the beginning of the year to establish
whether learners know their basic times tables and
bonds. §
The
following sets of worksheets are more difficult and test learners' knowledge
of neccessary concepts. §
Worksheets
are graded - Level 1 is easier, and Level 3 more difficult. §
There are
a few remedial worksheets on the CD as well, e.g. to address
specific problems like division, problems with 0 and 1. §
Each
worksheet has 50 questions and they are ideal to use for 5 to 15 minutes at
the beginning of a lesson. §
The flash
disk also contains memorandums for worksheets, fact sheets to
learn as well as graphs for learners to record results. |
Voorbeeld
van werkvel - Example of worksheet
Hoofreken: Gratis voorbeelde om af te laai
/ Mental Maths: Free examples to download
(right-click, save target as...)
Vlak/Level2-diagnosties/diagnostic
Tables-Tafels-Factsheet-Feiteblad
Grafiek/Graph Hoofrekenoefeninge/Mental Math exercises
Vlak/Level2-KortDeling/Short division
Vlak/Level2-Ekwivalente
breuke/Equivalent fractions
Vlak/Level2-Voorbereiding
vir desimale breuke/Preparation for decimal fractions
Alle
werkvelle bevat antwoorde / All worksheets include answers:
Meer inligting oor werkvelle / More information on
worksheets
|
Vlak
/ Level 2 Basic worksheets / Basiese werkvelle (for
all learners / vir alle leerders) Vlak
/ Level 1 Diagnostic & remedial / Diagnosties &
remediërend (jonger leerders of dié wat hulp benodig /
younger learners or those who need help) Vlak
/ Level 3 Advanced / Gevorderd (verrykking
vir sterker leerders / enrichment for stronger learners) |
||
|
A1 Vlak 2 (+-x/) |
5 min |
A1 Level 2 (+-x/) |
|
A2 Vlak 2 (+-x/-) bewerkings met 0 en 1 |
5 min |
A2 Level 2 (+-x/-) calculations with 0 and 1 |
|
A3 Vlak 3 (+-x/) groter getalle |
|
A3 Level 3 (+-x/) bigger numbers |
|
E2 Vlak 2 (+) geen hergroepering <1000 |
10 min |
E2 Level 2 (+) no regrouping <1000 |
|
E3 Vlak 2 (-) geen hergroepering <1000 |
10 min |
E3 Level 2 (-) no regrouping
<1000 |
|
E4 Vlak 3 (-) >20 |
|
E4 Level 3 (-) >20 |
|
F1 Vlak 3 (x) 12-16 |
|
F1 Level 3 (x) 12-16 |
|
F2 Vlak 3 (x) 17-21 |
|
F2 Level 3 (x) 17-21 |
|
F2 Vlak 3 (x) Getalle met nulle |
|
F2 Level 3 (x) Numbers with zeros |
|
G1 Vlak 2 (+-) Inverse (bv.4+a=8) |
|
G1 Level 2 (+-) Inverse (e.g.4+a=8) |
|
G2 Vlak 2 (x÷) Inverse |
|
G2 Level 2 (x÷) Inverse |
|
G3 Vlak 2 (+-x÷) Inverse |
|
G3 Level 2 (+-x÷) Inverse |
|
G4 Vlak 3 (+-x÷) Inverse gemeng |
|
G4 Level 3 (+-x÷) Inverse mixed |
|
G5 Vlak 3 (+-x÷) Inverse mixed /gemeng >20 |
|
G5 Level 3 (+-x÷) Inverse mixed >20 |
|
H1 Vlak 3 Veelvoude |
15 min |
H1 Level 3 Multiples |
|
I1 Vlak 2 Aantel |
|
I1 Level 2 Counting |
|
I2 Vlak 3 Aantel |
|
I2 Level 3 Counting |
|
J1 Vlak 2 Breuk van heelgetal (÷,
dan x) |
|
J1 Level 2 Fraction of number |
|
J2 Vlak 3 Breuke - gemengde oefeninge |
|
J2 Level 2 Fractions - mixed
exercises |
|
K1 Vlak 2 Omtrek en area (+, x:
toepassing) |
|
K1 Level 2 Perimeter and Area (+,
x: application) |
|
K2 Vlak 3 Omtrek en area (+, x -
toepassing) |
|
K2 Level 3 Perimeter and Area (+,
x: application) |
|
L1 Vlak 2 Kort deling (÷) |
15 min |
L1 Level 2 Short division (÷) |
|
L2 Vlak 2 Kort vermenigvuldiging
(x) |
20 min |
L2 Level 2 Short multiplication
(x) |
|
L2 Vlak 2 Kort optel, aftrek,
vermenigvuldig (x) |
20 min |
L2 Level 2 Short add, subtract,
multiply (x) |
|
M1 Vlak 2 Sirkelsomme (+-x÷) |
|
M1 Level 2 Circle sums (+-x÷) |
|
N1 Vlak 2 (x)
x10, x100, x1000 |
|
N1 Level 2 (x)
x10, x100, x1000 |
|
N2 Vlak 2 (x)
x10, x100, x1000 (geld) |
|
N2 Level 2 (x)
x10, x100, x1000 (currency) |
|
N3 Vlak 2 (÷)
÷10, ÷100, ÷1000 |
|
N3 Level 2 (÷)
÷10, ÷100, ÷1000 |
|
O1 Vlak 2 Veelvuldige bewerkings |
15 min |
O1 Level 2
Multiple operations |
|
P6 Vlak 2
Ekwivalente breuke |
|
P6 Level 2
Equivalent Fractions |
|
P1 Vlak 3
Ekwivalente Breuke |
|
P1 Level 3
Equivalent Fractions |
|
P2 Vlak 2
Vereenvoudig Breuke |
|
P2 Level 2
Simplify Fractions |
|
P9 Vlak 2
Voorbereiding vir desimale breuke |
|
P9 Level 2
Preparation for decimal fractions |
|
P3 Vlak 2
Verander gewone na desimale breuke |
|
P3 Level 2
Convert proper to decimal fractions |
|
P4 Vlak 2
Verander desimale na gewone breuke |
|
P4 Level 2
Convert decimal to proper fractions |
|
P5 Vlak 2
Verander gemengde getalle na onegte breuke |
|
P5 Level 2
Convert mixed numbers to improper fractions |
|
P7 Vlak 2 Breuke
- gemengde oefeninge |
|
P7 Level 2
Fractions - mixed exercises |
|
P8 Vlak 2
Optel/aftrek van breuke (noemers is veelvoude) |
|
P8 Level 2
Add/subtract fractions (denominators are multiples) |
|
Q1 Vlak 2
Afronding |
|
Q1 Level 2 Rounding |
|
R1 Vlak 2
Frenzies |
|
R1 Level 2 Frenzies |
|
T1 Vlak 2 Optel
van geld (SA-note en munte) |
|
T1 Level 2 Adding
of money (SA-notea and coins) |
|
U1 Tyd - lees
analoog, digitale & 24-uur tyd |
|
U1 Time - read
analogue, digital & 24-hour time |
Remediërende werkvelle
|
B1 Vlak 1 (x) 0-12 |
|
B1 Level 1 (x) 0-12 |
|
B2 Vlak 1 (x) 0-5 |
|
B2 Level 1 (x) 0-5 |
|
B3 Vlak 1 (x) 6-12 |
|
B3 Level 1 (x) 6-12 |
|
C1 Vlak 1 (÷) 1-12 |
|
C1 Level 1 (÷) 1-12 |
|
C2 Vlak 1 (÷) 1-5 |
|
C2 Level 1 (÷) 1-5 |
|
C3 Vlak 1 (÷) 6-12 |
|
C3 Level 1 (÷) 6-12 |
|
D1 Vlak 1 (x÷) 0-12 |
|
D1 Level 1 (x÷) 0-12 |
|
E1 Vlak 1 (+-) <20 |
|
E1 Level 1 (+-) <20 |
Notas aan opvoeder:
Hoewel u die werkvelle op enige manier kan gebruik of
inkorporeer in u klas, gee ons die volgende voorstelle:
1. Die tabel hierbo dui die
nommers van elke oefening aan en wat elkeen behels.
2. Begin met die diagnostiese
reeks A1 en doen een oefening per
dag met die hele klas.
3. Gee vooraf die volgende
inligting aan leerders:
§ Moenie vashaak by 'n som
nie. As jy nie die antwoord ken nie,
gaan aan met die volgende som en keer terug as jy klaar is.
§ As jy klaar is voor die tyd
om is, gaan weer deur jou antwoorde en maak seker dat alles reg is.
4. Leerders kry 5 minute om 'n
toets te doen (A1-10). Vir ander
oefeninge kan opvoeders die tyd verminder of vermeerder soos nodig.
5. Daarna ruil hul om en elke
leerder merk iemand anders s'n.
6. Die opvoeder lees die vrae
én antwoorde uit (bv. 6 x 5 = 30) - hierdie dien as verdere ouditiewe
vaslegging van tafels.
7. Die leerder wat nasien, tel
die punte op, skryf dit in, teken daaronder en gee terug.
8. Elke leerder teken nou self
sy/haar punte op die grafiek aan (kies self: blok- of lyngrafiek, of gebruik
verskillende tipes - dis goeie vaslegging vir datahantering).
9. Leerders kan ook hul totaal
en/of gemiddelde bereken (hul kan sakrekenaars hiervoor gebruik) - dit verbeter
hul begrip van datahantering.
10. Leerders doen verbeteringe
vir huiswerk, merk dit op hul tafelblad (met 'n 'highlighter' of
kleurpotlood) en gaan leer die somme wat hulle verkeerd gehad het.
11. Nadat die eerste groep
oefeninge (A1) voltooi is, kan u die klas volgens hul resultate hierin verdeel
in twee groepe.
12. Die swakker groep doen die
Vlak 1-oefeninge (intervensie) - u behoort nou duidelik te kan sien waar elkeen
se probleem lê, bv. by deling.
13. Indien 'n assistent of
remediërende opvoeder beskikbaar is, kan hy/sy die swakker groep help, of u kan
dit ook gee as tuisprogram.
14. Die sterk groep, wat reeds
hul tafels en kombinasies goed ken, gaan voort met die ander Vlak 2 en die Vlak
3-oefeninge. Sodoende vorder elke
leerder volgens sy/haar vlak.
15. Swakker leerders kan óók
die Vlak 2 en 3-oefeninge doen - u kan hulle meer tyd gee om dit te voltooi, of
hul kan dit uitwerk op papier.
16. Pryse en kompetisies is
baie motiverend - gee belonings vir volpunte of 'n mooi verbetering, of maak
gee 'n beloning vir die hele klas om 'n sekere gemiddeld te bereik. (Gebruik ons Excel-sigblad om hiermee te
help).
17. Gebruik die reeks
Quia-oefeninge op die internet wat hierby aansluit. Sien http://www.quia.com/profiles/thinkonline
vir die volledige lys. Leerders kan hierdie ook gebruik om na skool of tuis te gaan oefen.
Ons versoek u vriendelik om take aan albei
kante van die blad te druk.
A note to educators:
There are many ways to use and incorporate these worksheets in
your teaching. We are, however, including a few suggestions for inexperienced
educators:
1. The table shows the number
of each exercise and what the exercise entails.
2. Starting with the
diagnostic set A1, do one exercise
per day with the whole class.
3. Ensure that the learners
are aware of the following before commencing:
§ Don’t get stuck on one
sum. If you do not know the answer,
continue with the next sum and return to it once you have completed the rest.
§ If you finish with time to
spare, go through your work again and check that your answers are correct.
4. Learners get exactly 5
minutes to complete a test (A1-A10).
More or less time can be given for other exercises.
5. They then swap tests and
everyone marks someone else’s work.
6. The educator reads out the
questions as well as the answers (e.g. 6 x 5 = 30) – this serves as a further
auditory reinforcement of their tables.
7. The learner marking the
work, counts the marks, fills them in and signs the test before returning it to
the appropriate learner.
8. Each learner then plots
his/her results on the graph. (The choice is yours: bar graph or line graph, or
a variety of types – good consolidation of data handling skills).
9. Learners can also calculate
their totals and/or average marks (calculators may be used for these
calculations).
10. Learners do the corrections
for homework, mark them on the tables worksheet using a highlighter or a
coloured pencil crayon, and then go and learn those that were wrong.
11. After completing the first
group of ten exercises (A1), you can use the results to divide your class into
two groups.
12. The weaker group then does
the Level 1 exercises (intervention) – you should now be able to identify where
each learners struggles (e.g. division).
13. If an assistant or remedial
teacher is available, he/she could assist the weaker group, or you could give
it as part of the homework programme.
14. The strong group, those who
already know their tables and combinations well, continue with the other Level
2 and Level 3 exercises. In this way, each learner is able to progress at
his/her own pace.
15. Weaker learners can also do
the Level 3 exercises – give them extra time or allow them to do their
calculations on paper.
16. Competitions and prizes are
very motivating – reward full marks or a good improvement, or challenge the
whole class to achieve a better average.
(Use our Excel-spreadsheet to record results).
17. Use the set of Quia
internet exercises that we have included. See http://www.thinkonline.co.za/quia.htm
for a complete list. Learners can also use these to practise after school or at
home.
A friendly request: please print on both sides of the page.
Aanbevole boek oor die onderrig van breuke en
ratio / Recommended book for teaching fractions and ratios
Order the E-book (±R384) or the book (±R670) from Kalahari.net
"A groundbreaking book"
"This book addresses the urgent need for curriculum materials that cross
traditional boundaries ... mathematics content, teacher understanding, student
thinking, teaching methods, instructional activities, and assessment.
purposes."
"Extremely well written and illuminating.
Fractions remain one of the key stumbling blocks in math education. I think
think this book is a must read for all teachers of mathematics."
Order the book (±R695) from Kalahari.net
"The Princeton Companion to Mathematics is
not only a beautiful book from an aesthetic standpoint, with its heavy, high
quality pages and sturdy binding, but above all it’s a monumental piece of
work. It rigorously illustrates the (pure) mathematical field while remaining
as accessible as possible to the general reader. There is no mathematician in
the world who, upon reading this book cover to cover, would not have learned a
great deal from it. If you are looking for the perfect gift for people who’re
interested in mathematics, this is the right book. If you are a parent, I
especially encourage you to pick it up for your son or daughter, it could
change their lives."
(Kliek hier vir meer inligting oor die Graad 7 Wiskunde-module / Click here for more information on the
Grade 7 Math Module)
|
Click here for an order form in
MSWord-format. Kliek asseblief hier
vir 'n bestelvorm in MSWord-formaat. Please click here
for an order form in pdf-format. Kliek asseblief hier
vir 'n bestelvorm in pdf-formaat. Namibia and other countries: Please send us
an e-mail. |
MEER INLIGTING / MORE INFORMATION:
Fax/Faks 086 766
2558
Last revised:
2011-11-08
Kernwoorde vir soekenjins:
Afrikaans vir Almal
Afrikaans spelling exercises online speloefeninge aanlyn African languages
teach Afrikaans teacher Dutch English Afrikaans translation
Afrikaans worksheets Exciting Afrikaans tasks
werkvelle taakkaarte Primary Schools
Punktuasie Beeldspraak Vergelykings Intensiewe vorme Idiome Woordsoorte
Selfstandige naamwoorde Werkwoorde Voorsetsels Telwoorde Voegwoorde Byvoeglike
naamwoorde Bywoorde Lidwoorde Voornaamwoorde Meervoude Verkleinwoorde
Afkortings en akronieme Leenwoorde Aanspreekvorme Sinonieme Antonieme Homonieme
Homofone Direkte en indirekte Rede Skryftekens Enkelvoudige en samegestelde
sinne Aktiewe en passiewe vorm Konsonante, vokale en lettergrepe Manlike en
vroulike geslag Trappe van vergelyking Digkuns:
Woordeskat Educational Laerskole
skole opvoedkundig Afrikaans online games Afrikaanse wordsearches Afrikaanse Taalreëls
woordeskat spelling prosa poësie metataal horlosies timers Time timer bestel
order Afrikaans learning games Voorbeelde van Afrikaanse vraestelle
Afrikaanse spelkompetisie spelolimpiade taalolimpiade vir die laerskool
hersieningsoefeninge taallleer oefeninge
Afrikaans language exercises taaloefeninge Afrikaans
Taal Leer Afrikaans aanlyn Learn Afrikaans online Afrikaanse blokkiesraaisels
Afrikaans wordsearches Afrikaans vir
almal klaskamer onderrig vasvra blokkiesraaisels lettergrepe homonieme homofone
dictionary Namibia Namibië inheemse tale Afrika
Afrikaans tuisonderrig tuiswerk huiswerk hersiening
vaslegging homeschooling taalolimpiade leenwoorde leestekens punktuasie
Suid-Afrika Leer Afrikaans Learn
Afrikaans Afrikaans Speltoetse
Alfabetiese spellyste taalreëls anagramme onderwysers opvoeders leerders
leerlinge Afrikaans taalreëls spelreëls learner and teacher support materials
Graad 4 Vier Graad 5 Vyf Graad 6 Ses Afrikaans
metataal Afrikaans Intermediêre fase Leerarea Afrikaans Modules South Africa
meervoude verkleinwoorde punktuasie Sinonieme Antonieme Idiome Woordsoorte
Rededele Senior Primêr Hulp vir Onderwysers Opvoeders Leesbegrip Afrikaans
language taakkaarte leerplanne konsepleerplanne CAP CAPS-dokumente CAPS
documents Gratis tafeltoetse spoedtoetse tafelbladsye Free times tables sheets
Xhosa learn isiXhosa second additional language tweede addisionele taal
Handskrif Writing korrekte skrif vir Suid-Afrikaanse
skole drukskrif kursiewe skrif plakkaat correct handwriting for South African schools
cursive print
