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PART 2 PRACTICE
354
Addendum A to Chapter 9
NATIONAL CURRICULUM OUTCOMES PER GRADE
A. Content area: Numbers, operations and relationships
Gr. R
Gr. 1
Gr. 2
Gr. 3
Gr. 4
Gr. 5
Gr. 6
Coun
ting
(num
-be
r ran
ge)
1–10
1–10
01–
200
1–1
000
1–10
000
1–10
000
Also
in d
ecim
als
Orde
rs a
nd
com
pare
s an
d un
ders
tand
pl
ace
valu
e
1–10
(n
o pl
ace
valu
e)1–
20
(pla
ce v
alue
: 11
–20)
1–10
01–
999
to 4
-dig
it nu
m-
bers
to 6
-dig
it nu
m-
bers
to 9
-dig
it
num
bers
Writ
ten
calc
ula-
tions
and
pro
b-le
m s
olvi
ng
No w
ritte
n ca
lcu-
latio
ns;
info
rmal
ver
bal
prob
lem
sol
ving
.
+ an
d –
and
repe
ated
add
i-tio
n:
up to
20
+ an
d –
up to
10
0;
×: 2
-dig
it by
1-
digi
t < 1
00;
÷: 1
-dig
it by
1-
digi
t num
bers
+ an
d –
up to
99
9;
×: 2
-dig
it by
1-
digi
t num
bers
; ÷:
2-d
igit
num
-be
rs b
y 1-
digi
t nu
mbe
rs
+ an
d –
up to
9
999;
×:
2-d
igit
by
2-di
git n
umbe
rs;
÷: 3
-dig
it by
1-
digi
t num
bers
+ an
d –
up to
99
999
; ×:
3-d
igit
by
2-di
git n
umbe
rs;
÷: 3
-dig
it by
2-
digi
t num
bers
+ an
d –
up to
6-
digi
ts a
nd
mor
e ×:
4-d
igit
by
3-di
git n
umbe
rs;
÷: 4
-dig
it by
3-
digi
t num
bers
Men
tal M
aths
none
+ an
d –:
ans
wer
s in
dom
ain
0–20
(w
ith
conc
rete
app
ara-
tus
if ne
cess
ary)
+, –
and
×:
answ
ers
in
dom
ain
0–20
+, –
and
×
answ
ers
in
dom
ain
0–50
+: a
dd
1-di
git t
o 3-
digi
t nu
mbe
rs
–: s
ubtra
ct
1-di
git f
rom
3-
digi
t num
bers
×:
to 1
0×10
÷:
reci
proc
al re
la-
tions
hip
betw
een
× an
d ÷
+: a
dd
1-di
git t
o 3-
digi
t nu
mbe
rs
–: s
ubtra
ct
2-di
git f
rom
4-
digi
t num
bers
×:
to 1
0×10
; ÷:
reci
proc
al re
la-
tions
hip
betw
een
× an
d ÷
+ an
d –:
as
prev
i-ou
s, b
ut a
lso:
14
7–M
=28
×: to
12×
12;
÷: d
ivis
ibili
ty
rule
s fo
r: 2,
5, 1
0, 1
00 a
nd
1 00
0
1. T
op
ic: W
ho
le n
um
be
rs
SUPPORTING LEARNERS IN ACQUIRING THE SKILL OF MATHEMATISATION
355
92.
To
pic
: Fra
ctio
ns
Gr. R
Gr. 1
Gr. 2
Gr. 3
Gr. 4
Gr. 5
Gr. 6
Com
mon
fra
ctio
nsIn
form
al p
robl
em
solv
ing:
sha
ring
and
grou
ping
up
to 1
0 th
at in
clud
es
rem
aind
ers.
Info
rmal
pro
blem
so
lvin
g:
shar
ing
and
grou
ping
up
to
10 th
at in
clud
es
rem
aind
ers.
Orde
r and
com
-pa
re h
alve
s an
d qu
arte
rs:
Prob
lem
sol
ving
: eq
ual s
harin
g an
d gr
oupi
ng w
ith
who
le n
umbe
rs
that
may
lead
to
unita
ry fr
actio
ns
(up
to 2
0).
Orde
r and
com
pare
ha
lves
, eig
hths
, six
ths,
qu
arte
rs a
nd th
irds
Prob
lem
sol
ving
: eq
ual s
harin
g an
d gr
oupi
ng w
ith w
hole
nu
mbe
rs th
at m
ay
lead
to re
mai
nder
s as
un
itary
frac
tions
(u
p to
50)
.
+ an
d –
(sam
e de
nom
-in
ator
s) u
p to
eig
hts.
Prob
lem
sol
ving
as
equa
l sha
ring
with
re
mai
nder
s ex
pres
sed
as u
nita
ry fr
actio
ns.
+ an
d –
(sam
e de
nom
-in
ator
s) u
p to
twel
fths
(incl
udin
g m
ixed
fra
ctio
n)
Calc
ulat
e fra
ctio
ns
of w
hole
num
bers
(r
esul
ting
in w
hole
nu
mbe
rs).
Prob
lem
sol
ving
with
co
mm
on fr
actio
ns.
+ an
d –
deno
min
ator
s:
mul
tiple
s of
eac
h ot
her:
tent
hs to
hu
ndre
ds
+ an
d –
of m
ixed
frac
-tio
ns. A
lso
in p
robl
em
solv
ing.
Deci
mal
fra
ctio
nsn/
an/
an/
an/
aIn
con
text
of m
ea-
sure
men
t com
pare
an
d de
scrib
e 0,
5; 1
,5;
2,5
etc.
Prob
lem
sol
ving
in
clud
ing
deci
mal
s.
In c
onte
xt o
f mea
-su
rem
ent c
ompa
re
and
desc
ribe
0,5;
1,5
; 2,
5 et
c.
Prob
lem
sol
ving
in
clud
ing
deci
mal
s.
Com
pare
dec
imal
s to
at l
east
2 d
ecim
al
plac
es
+ an
d –
of p
ositi
ve
deci
mal
s w
ith a
t lea
st
two
deci
mal
pla
ces.
Prob
lem
sol
ving
in
clud
ing
deci
mal
s.
Equi
vale
nt fo
rms
n/a
n/a
n/a
n/a
Reco
gnis
ing
and
usin
g eq
uiva
lent
form
s (d
enom
inat
ors
whi
ch
are
mul
tiple
s of
eac
h ot
her)
.
Reco
gnis
ing
and
usin
g eq
uiva
lent
form
of
deci
mal
frac
tion:
0,5
; 1,
5; 2
,5 e
tc.–
in c
on-
text
of m
easu
rem
ent.
Reco
gnis
ing
and
usin
g eq
uiva
lent
form
s (d
enom
inat
ors
whi
ch
are
mul
tiple
s of
eac
h ot
her)
.
Reco
gnis
ing
and
usin
g eq
uiva
lent
form
of
deci
mal
frac
tion:
0,5
; 1,
5; 2
,5 e
tc.–
in c
on-
text
of m
easu
rem
ent.
Reco
gnis
ing
and
usin
g eq
uiva
lent
form
s of
co
mm
on fr
actio
ns
with
1 /2-
digi
t den
omi-
nato
rs.
Equi
vale
nt fo
rms
of
deci
mal
frac
tions
to
at le
ast t
wo
deci
mal
pl
aces
.
Equi
vale
nt fo
rms
of
perc
enta
ges.
PART 2 PRACTICE
356
3. T
op
ic: F
inan
cial
Mat
hs
Gr. R
Gr. 1
Gr. 2
Gr. 3
Gr. 4
Gr. 5
Gr. 6
Fina
ncia
l Mat
hs /
mon
eyNo
form
al o
utco
mes
ID S
A co
ins
and
bank
note
s
Solv
e m
oney
pro
b-le
ms
in n
umbe
r ra
nge
0–20
and
ch
ange
in e
ither
R
or c
.
ID S
A co
ins
and
bank
note
s
Solv
e m
oney
pro
b-le
ms
in n
umbe
r ra
nge
0–10
0 an
d ch
ange
in e
ither
R
or c
.
ID S
A co
ins
and
bank
note
s
Solv
e m
oney
pro
b-le
ms
in n
umbe
r ra
nge
0–99
9 an
d ch
ange
in e
ither
R
or c
. As
wel
l as
conv
ertin
g be
twee
n R
and
c.
Buyi
ng a
nd s
ellin
g in
num
ber r
ange
0–
9 99
9
Sim
ple
budg
ets
Buyi
ng a
nd s
ellin
g in
num
ber r
ange
0–
99 9
99
Sim
ple
budg
ets
Profi
t and
loss
Buyi
ng a
nd s
ellin
g in
num
ber r
ange
to
9-di
gits
Sim
ple
budg
ets
Profi
t and
loss
Read
ing
and
inte
r-pr
etin
g ac
coun
ts
Calc
ulat
ing
disc
ount
4. R
atio
an
d r
ate
5.
Mu
ltip
les
and
fac
tors
6.
Pro
pe
rtie
s o
f ra
tio
nal
nu
mb
ers
Gr. R
Gr. 1
Gr. 2
Gr. 3
Gr. 4
Gr. 5
Gr. 6
Ratio
and
rate
n/a
n/a
n/a
n/a
Com
parin
g tw
o or
mor
e qu
an-
titie
s of
the
sam
e ki
nd (r
atio
)
Com
parin
g tw
o qu
antit
ies
of d
iffer
ent k
inds
(rat
e) in
ab
ove-
men
tione
d nu
mbe
r ra
nge
Com
parin
g tw
o or
mor
e qu
an-
titie
s of
the
sam
e ki
nd (r
atio
)
Com
parin
g tw
o qu
antit
ies
of d
iffer
ent k
inds
(rat
e) in
ab
ove-
men
tione
d nu
mbe
r ra
nge
Com
parin
g tw
o or
mor
e qu
antit
ies
of th
e sa
me
kind
(rat
io)
Com
parin
g tw
o qu
antit
ies
of d
iffer
ent
kind
s (r
ate)
in a
bove
-men
tione
d nu
mbe
r ra
nge
Mul
tiple
s an
d fa
ctor
sn/
an/
an/
an/
aM
ultip
les
of 1
-dig
it nu
mbe
rs to
at
leas
t 100
Mul
tiple
s of
2-d
igit
who
le
num
bers
to a
t lea
st 1
00; f
ac-
tors
of 2
-dig
it w
hole
num
bers
to
at l
east
100
Mul
tiple
s of
2 ⁄ 3-d
igit
who
le n
umbe
rs;
Fact
ors
of 2 ⁄ 3
-dig
it w
hole
num
bers
to a
t le
ast 1
00
Prim
e fa
ctor
s of
num
bers
to a
t lea
st 1
00
Prop
ertie
s of
ra
tiona
l num
-be
rs
n/a
n/a
n/a
n/a
Com
mut
ativ
e, a
ssoc
iativ
e an
d di
strib
utiv
e pr
oper
ties
of w
hole
nu
mbe
rs in
abo
ve-m
entio
ned
num
ber r
ange
Com
mut
ativ
e, a
ssoc
iativ
e an
d di
strib
utiv
e pr
oper
ties
of
who
le n
umbe
rs in
abo
ve-m
en-
tione
d nu
mbe
r ran
ge
Com
mut
ativ
e, a
ssoc
iativ
e an
d di
strib
utiv
e pr
oper
ties
of w
hole
num
bers
in a
bove
- m
entio
ned
num
ber r
ange
pr
oper
ties
of 0
and
1
SUPPORTING LEARNERS IN ACQUIRING THE SKILL OF MATHEMATISATION
357
9B
. Co
nte
nt
area
: Pat
tern
s, f
un
ctio
ns
and
alg
ebra
Top
ics:
1.
Nu
me
ric
and
ge
om
etr
ic p
atte
rns
Top
ics:
2.
Inp
ut
and
ou
tpu
t va
lue
s
Top
ics:
3.
Nu
mb
er
sen
ten
ces
Gr. R
Gr. 1
Gr. 2
Gr. 3
Gr. 4
Gr. 5
Gr. 6
Num
eric
and
ge
omet
ric
patte
rns
Copy
and
ext
end
sim
ple
patte
rns
usin
g ph
ysic
al
obje
cts
and
draw
-in
gs.
Crea
te n
ew p
at-
tern
s.
Copy
and
ext
end
sim
ple
patte
rns
usin
g ph
ysic
al
obje
cts
and
draw
-in
gs.
Copy
and
ext
end
sim
ple
num
ber
sequ
ence
s to
100
.
Crea
te n
ew p
at-
tern
s.
Desc
ribe
obse
rved
pa
ttern
s.
Copy
and
ext
end
sim
ple
patte
rns
usin
g ph
ysic
al o
bjec
ts a
nd
draw
ings
.
Copy
and
ext
end
sim
-pl
e nu
mbe
r seq
uenc
es
to 2
00.
Crea
te n
ew p
atte
rns.
Desc
ribe
obse
rved
pa
ttern
s ID
, des
crib
e an
d co
py g
eom
etric
pa
ttern
s in
nat
ural
and
cu
ltura
l arte
fact
s.
Copy
and
ext
end
sim
ple
patte
rns
usin
g ph
ysic
al o
bjec
ts a
nd
draw
ings
.
Copy
and
ext
end
sim
-pl
e nu
mbe
r seq
uenc
-es
to 1
000
.
Crea
te n
ew p
atte
rns.
Desc
ribe
obse
rved
pa
ttern
s ID
, des
crib
e an
d co
py g
eom
etric
pa
ttern
s in
nat
ural
and
cu
ltura
l arte
fact
s.
Now
als
o lo
ok fo
r re
latio
nshi
ps o
r ru
les
of p
atte
rns
and
desc
ribe
obse
rved
re
latio
nshi
ps o
r rul
es
in o
wn
wor
ds.
Obse
rved
rela
tion-
ship
s or
rule
s of
pa
ttern
s de
scrib
ed in
ow
n w
ords
.
Obse
rved
rela
tions
hips
or
rule
s of
pat
tern
s de
scrib
ed in
ow
n w
ords
.
Desc
ribe
gene
rate
d ru
les.
Inpu
t and
out
-pu
t val
ues
n/a
n/a
n/a
n/a
Dete
rmin
e ou
tput
va
lues
for g
iven
in
put v
alue
s us
ing
verb
al d
escr
iptio
n an
d flo
w d
iagr
ams.
Dete
rmin
e ou
tput
va
lues
for g
iven
in
put v
alue
s us
ing
verb
al d
escr
iptio
n an
d flo
w d
iagr
ams.
Dete
rmin
e ou
tput
val
ues
for g
iven
inpu
t val
ues,
or
inpu
t val
ues
for g
iven
ou
tput
val
ues
usin
g ve
rbal
des
crip
tion,
flow
di
agra
ms
and
tabl
es.
Num
ber s
en-
tenc
esn/
an/
an/
an/
aW
rite
num
ber s
en-
tenc
es to
des
crib
e pr
oble
m s
ituat
ions
. So
lve
and
com
plet
e nu
mbe
r sen
tenc
es
by:
Writ
e nu
mbe
r sen
-te
nces
to d
escr
ibe
prob
lem
situ
atio
ns.
Solv
e an
d co
mpl
ete
num
ber s
ente
nces
by
:
Writ
e nu
mbe
r sen
tenc
es
to d
escr
ibe
prob
lem
si
tuat
ions
. So
lve
and
com
plet
e nu
mbe
r sen
tenc
es b
y:
{
PART 2 PRACTICE
358
Gr. R
Gr. 1
Gr. 2
Gr. 3
Gr. 4
Gr. 5
Gr. 6
• in
spec
tion
• tri
al a
nd im
prov
emen
t•
subs
titut
ion.
Dete
rmin
e eq
uiva
lent
s of
di
ffere
nt d
escr
iptio
ns o
f sa
me
rela
tions
hip
or ru
le
pres
ente
d:•
verb
ally
• in
flow
dia
gram
s•
by n
umbe
r sen
tenc
e.
• in
spec
tion
• tri
al a
nd im
prov
emen
t•
subs
titut
ion.
Dete
rmin
e eq
uiva
lent
s of
di
ffere
nt d
escr
iptio
ns o
f sa
me
rela
tions
hip
or ru
le
pres
ente
d:•
verb
ally
• in
flow
dia
gram
s•
by n
umbe
r sen
tenc
e.
• in
spec
tion
• tri
al a
nd im
prov
emen
t•
subs
titut
ion.
Dete
rmin
e eq
uiva
lent
s of
di
ffere
nt d
escr
iptio
ns o
f sam
e re
latio
nshi
p or
rule
pre
sent
ed:
• ve
rbal
ly•
in fl
ow d
iagr
ams
• by
num
ber s
ente
nce
• ta
bles
.
SUPPORTING LEARNERS IN ACQUIRING THE SKILL OF MATHEMATISATION
359
9C.
Co
nte
nt
area
: Sp
ace
and
sh
ape
(geo
met
ry)
Top
ics:
1.
2-D
sh
ape
s an
d 3
-D o
bje
cts
Top
ics:
2.
Tran
sfo
rmat
ion
s (I
nte
rme
dia
te P
has
e o
nly
)
Gr. R
Gr. 1
Gr. 2
Gr. 3
Gr. 4
Gr. 5
Gr. 6
2-D
shap
es a
nd
3-D
obje
cts
Reco
gnis
es a
nd
nam
es 3
-D o
bjec
ts
in c
lass
room
and
on
pict
ures
(box
es a
nd
balls
).
Desc
ribes
, sor
ts a
nd
com
pare
s ph
ysic
al
3-D
obje
cts
acco
rd-
ing
to:
• si
ze•
obje
cts
that
roll
• ob
ject
s th
at s
lide.
Build
s 3-
D ob
ject
s us
ing
conc
rete
mat
e-ria
ls.
Reco
gnis
es a
nd
nam
es 2
-D s
hape
s an
d 3-
D ob
ject
s in
cl
assr
oom
and
on
pict
ures
:•
trian
gles
, rec
tan-
gles
, and
circ
les
• pr
ism
s an
d sp
here
s.
Desc
ribes
, sor
ts a
nd
com
pare
s ph
ysic
al
2-D
shap
es a
nd 3
-D
obje
cts
acco
rdin
g to
:•
size
• ob
ject
s th
at ro
ll/sl
ide
• sh
apes
that
hav
e st
raig
ht o
r rou
nd
edge
s.
Obse
rves
and
bui
lds
give
n 3-
D ob
ject
s us
ing
conc
rete
mat
e-ria
ls.
Reco
gnis
es a
nd
nam
es 2
-D s
hape
s an
d 3-
D ob
ject
s in
cl
assr
oom
and
on
pict
ures
:•
trian
gles
, rec
tan-
gles
, squ
ares
and
ci
rcle
s•
pris
ms,
cyl
inde
rs
and
sphe
res.
Desc
ribes
, sor
ts a
nd
com
pare
s ph
ysic
al
2-D
shap
es a
nd 3
-D
obje
cts
(pic
ture
s an
d en
viro
nmen
t) ac
cord
ing
to:
• si
ze
• ob
ject
s th
at ro
ll/sl
ide
• sh
apes
that
hav
e st
raig
ht o
r rou
nd
edge
s.
Obse
rves
and
bui
lds
give
n 2-
D sh
apes
an
d 3-
D ob
ject
s us
ing
conc
rete
mat
e-ria
ls.
Reco
gnis
es a
nd
nam
es 2
-D s
hape
s an
d 3-
D ob
ject
s in
cl
assr
oom
and
on
pict
ures
:•
trian
gles
, rec
tan-
gles
, squ
ares
and
ci
rcle
s•
pris
ms,
cyl
inde
rs,
cone
s, p
yram
ids
and
sphe
res.
Desc
ribes
, sor
ts a
nd
com
pare
s ph
ysic
al
2-D
shap
es a
nd 3
-D
obje
cts
(pic
ture
s an
d en
viro
nmen
t):•
2-D
shap
es in
th
e fa
ces
of 3
-D
obje
cts
• fla
t/stra
ight
and
ro
und/
curv
ed s
ur-
face
s an
d ed
ges.
Obse
rves
and
cr
eate
s gi
ven
and
desc
ribed
2-D
sh
apes
and
3-D
ob
ject
s us
ing
con-
cret
e m
ater
ials
.
Reco
gnis
es n
ames
, vi
sual
ises
2-D
sh
apes
and
3-D
ob
ject
s in
the
envi
-ro
nmen
t:•
rect
angu
lar p
rism
• sp
here
s•
cylin
ders
• py
ram
ids
• ci
rcle
s•
(pol
ygon
s)
(up
to 6
-sid
ed
figur
es).
Draw
2-D
sha
pes
on
grid
pap
er.
Desc
ribes
, sor
ts
and
com
pare
s 2-
D sh
apes
and
3-D
ob
ject
s in
term
s of
: •
shap
es o
f fac
es•
flat a
nd c
urve
d su
rface
s•
stra
ight
and
cu
rved
sid
es•
num
ber o
f sid
es•
leng
th o
f sid
es.
Mak
es 3
-D m
odel
s us
ing
cut-o
ut p
oly -
gons
.
Reco
gnis
es a
nd
nam
es 2
-D s
hape
s an
d 3-
D ob
ject
s in
na
tura
l and
cul
tura
l fo
rms
and
geom
etric
se
tting
:•
sim
ilarit
ies/
dif-
fere
nces
bet
wee
n cu
bes
and
rect
an-
gula
r pris
ms
• si
mila
ritie
s/di
f-fe
renc
es b
etw
een
squa
res
and
rect
-an
gles
• (p
olyg
ons)
(u
p to
7-s
ided
fig
ures
).
Draw
2-D
sha
pes
on
grid
pap
er.
Desc
ribes
, sor
ts
and
com
pare
s 2-
D sh
apes
and
3-D
ob
ject
s in
term
s of
:•
shap
es o
f fac
es•
num
ber o
f fac
es•
num
ber o
f sid
es•
leng
th o
f sid
es.
Reco
gnis
es a
nd
nam
es 2
-D s
hape
s an
d 3-
D ob
ject
s in
na
tura
l and
cul
tura
l fo
rms
and
geom
etric
se
tting
:•
sim
ilarit
ies/
dif-
fere
nces
bet
wee
n te
trahe
dron
s, a
nd
othe
r pyr
amid
s si
mila
ritie
s/di
f-fe
renc
es b
etw
een
para
lello
gram
s an
d re
ctan
gles
• (p
olyg
ons)
(u
p to
8-s
ided
fig
ures
).
Desc
ribes
, sor
ts
and
com
pare
s 2-
D sh
apes
and
3-D
ob
ject
s in
term
s of
: •
face
s •
verti
ces
• ed
ges
• le
ngth
of s
ides
•
size
of a
ngle
s.
{
Top
ics:
3.
Vie
win
g o
f o
bje
cts
(In
term
ed
iate
Ph
ase
on
ly)
Top
ics:
4.
Po
siti
on
an
d m
ove
me
nt
(In
term
ed
iate
Ph
ase
on
ly)
PART 2 PRACTICE
360
Gr. R
Gr. 1
Gr. 2
Gr. 3
Gr. 4
Gr. 5
Gr. 6
Mak
es 3
-D m
odel
s us
ing
cut o
ut p
oly-
gons
.
Mak
es 3
-D m
odel
s us
ing:
• dr
inki
ng s
traw
s to
m
ake
a sk
elet
on•
nets
.
Draw
sha
pes
on g
rid
pape
r.
Draw
s ci
rcle
s, p
at-
tern
s in
circ
les
and
patte
rns
with
circ
les
usin
g a
pair
of c
om-
pass
es.
Tran
sfor
mat
ions
Reco
gnis
es s
ym-
met
ry in
ow
n bo
dy
and
envi
ronm
enta
l ob
ject
s –
focu
s on
fro
nt a
nd b
ack.
Reco
gnis
es s
ym-
met
ry in
ow
n bo
dy
and
envi
ronm
enta
l ob
ject
s –
focu
s on
fro
nt a
nd b
ack;
left
and
right
.
Reco
gnis
es
sym
met
ry in
2-D
sh
apes
and
3-D
ob
ject
s.
Dete
rmin
es li
nes
of
sym
met
ry in
2-D
sh
apes
and
use
s pa
per f
oldi
ng a
nd
refle
ctio
n.
Reco
gnis
es, d
raw
s an
d de
scrib
es li
ne
of s
ymm
etry
in 2
-D
shap
es.
Mak
ing
2-D
shap
es.
3-D
obje
cts
and
pat-
tern
s us
ing:
• te
ssel
atio
ns•
line
sym
met
ry.
Reco
gnis
es, d
raw
s an
d de
scrib
es li
ne
of s
ymm
etry
in 2
-D
shap
es.
Use
geom
etric
fig-
ures
and
sol
ids
to
perfo
rm:
• ro
tatio
ns (t
urns
)•
refle
ctio
ns (fl
ips)
• tra
nsla
tions
(s
lides
).
Mak
ing
2-D
shap
es.
3-D
obje
cts
and
pat-
tern
s us
ing:
• te
ssel
atio
ns
• lin
e sy
mm
etry
•
rota
tiona
l sym
-m
etry
• ro
tatio
ns
• re
flect
ions
•
trans
latio
n.
Reco
gnis
es, d
raw
s an
d de
scrib
es li
ne
of s
ymm
etry
in 2
-D
shap
es.
Draw
enl
arge
men
t an
d re
duct
ions
of
2-D
sha
pes
to
com
pare
size
and
sh
ape
of:
• tri
angl
es•
quad
rilat
eral
s.
{
SUPPORTING LEARNERS IN ACQUIRING THE SKILL OF MATHEMATISATION
361
9
Gr. R
Gr. 1
Gr. 2
Gr. 3
Gr. 4
Gr. 5
Gr. 6
View
ing
of
obje
cts
Desc
ribe
one
3-D
obje
ct in
rela
tion
to
anot
her (
e.g.
fron
t or
behi
nd).
Desc
ribe
one
3-D
obje
ct in
rela
tion
to
anot
her (
e.g.
fron
t or
behi
nd; t
o th
e le
ft/rig
ht).
Reco
gnis
es 3
-D
obje
cts
from
diff
er-
ent p
ositi
ons.
Reco
gnis
es 3
-D
obje
cts
from
diff
er-
ent p
ositi
ons.
View
ing
of o
bjec
ts in
di
ffere
nt p
ositi
ons.
View
ing
of o
bjec
ts in
di
ffere
nt p
ositi
ons.
View
ing
of o
bjec
ts in
di
ffere
nt p
ositi
ons.
Posi
tion
and
mov
emen
tFo
llow
s di
rect
ions
to
mov
e/pl
ace
self
with
in th
e cl
ass-
room
.
Follo
ws
dire
ctio
ns
to m
ove/
plac
e se
lf w
ithin
the
clas
s-ro
om; o
r pla
ce/m
ove
3-D
obje
cts
in re
la-
tion
to e
ach
othe
r.
Posi
tions
sel
f with
in
the
clas
sroo
m; o
r pl
ace/
mov
e 3-
D ob
ject
s in
rela
tion
to
each
oth
er.
Desc
ribes
pos
i-tio
nal r
elat
ions
hips
be
twee
n se
lf, p
eer
and
3-D
obje
cts.
Read
s, in
terp
rets
an
d dr
aws
info
rmal
m
aps
of th
e sc
hool
en
viro
nmen
t or o
f an
arra
ngem
ent o
f 3-D
ob
ject
s an
d lo
cate
s ob
ject
s on
the
map
.
Desc
ribes
pos
i-tio
nal r
elat
ions
hips
be
twee
n se
lf, p
eer
and
3-D
obje
cts.
Loca
te p
ositi
on o
n•
labe
lled
(cod
ed)
grid
• co
lum
n an
d ro
w•
map
s.
Loca
te p
ositi
on o
n•
labe
lled
(cod
ed)
grid
• m
aps.
Trac
ing
a pa
th
betw
een
posi
tion.
Loca
te p
ositi
on o
n•
labe
lled
(cod
ed)
grid
• m
aps.
Desc
ribe
how
to
mov
e be
twee
n th
e po
sitio
ns o
n th
e gr
id.
PART 2 PRACTICE
362
D.
Con
ten
t ar
ea: M
easu
rem
ent
Top
ics:
1.
Len
gth
, mas
s an
d c
apac
ity
Top
ics:
2.
Tim
e
Top
ics:
3.
Tem
pe
ratu
re
Gr. R
Gr. 1
Gr. 2
Gr. 3
Gr. 4
Gr. 5
Gr. 6
Leng
thDe
scrib
es o
bjec
ts
in te
rms
of:
long
er, s
horte
r, w
ider
, tal
l, sh
ort,
etc.
Estim
ates
, com
-pa
res,
ord
ers,
mea
-su
res
3-D
obje
cts
(non
-sta
ndar
d m
ea-
sure
s: h
and
span
s,
foot
step
s).
Estim
ates
, com
-pa
res,
ord
ers,
mea
-su
res
3-D
obje
cts
(non
-sta
ndar
d m
ea-
sure
s: h
and
span
s,
foot
step
s).
Estim
ates
, com
pare
s,
orde
rs, m
easu
res
3-D
obje
cts
(non
-sta
ndar
d an
d st
anda
rd m
easu
res:
de
sk le
ngth
s, m
etre
s).
Appr
oxim
ate
dist
ance
be
twee
n 2-
D sh
apes
us
ing
strin
g; a
rea
of 2
-D
shap
es u
sing
tilin
g.
Units
: mm
, cm
, m
and
km.
Usin
g ru
lers
, met
re
stic
ks, t
ape
,mea
-su
res
and
trund
le
whe
els.
Conv
ersi
on b
etw
een
mm
, cm
, m a
nd k
m.
Units
: mm
, cm
, m
and
km.
Usin
g ru
lers
, met
re
stic
ks, t
ape
,mea
-su
res
and
trund
le
whe
els.
Conv
ersi
on b
etw
een
mm
, cm
, m a
nd k
m.
As b
efor
e.
Estim
ates
, mea
-su
res,
reco
rds
and
orde
rs 2
-D s
hape
s an
d 3-
D ob
ject
s us
ing
SI-u
nits
(mm
, cm
, m a
nd k
m) t
o pr
ecis
ion.
Mas
sDe
scrib
es o
bjec
ts
in te
rms
of:
light
, hea
vy, h
eavi
-er
, etc
.
Estim
ates
, com
-pa
res,
ord
ers,
mea
-su
res
3-D
obje
cts
(non
-sta
ndar
d m
easu
res:
bric
k,
sand
bags
, etc
.).
Estim
ates
, com
-pa
res,
ord
ers,
mea
-su
res
3-D
obje
cts
(non
-sta
ndar
d m
easu
res:
bric
k,
sand
bags
, etc
.).
Estim
ates
, com
pare
s,
orde
rs, m
easu
res
3-D
obje
cts
(non
-sta
ndar
d an
d st
anda
rd m
easu
res:
kg
pac
kets
).
Units
: g a
nd k
g.
Mea
surin
g in
stru
-m
ents
: mea
surin
g ju
gs, k
itche
n sc
ales
an
d ba
lanc
es.
Conv
ersi
ons
betw
een
g an
d kg
.
Units
: g a
nd k
g.
Mea
surin
g in
stru
-m
ents
: mea
surin
g ju
gs, k
itche
n sc
ales
an
d ba
lanc
es.
Conv
ersi
ons
betw
een
g an
d kg
.
Estim
ates
, mea
-su
res,
reco
rds
and
orde
rs 3
-D o
bjec
ts
usin
g SI
-uni
ts, u
sing
g
and
kg (c
onve
r-si
on a
s w
ell).
Capa
city
Desc
ribe
obje
cts
in te
rms
of:
empt
y, fu
ll, le
ss
than
, mor
e th
an,
etc.
Estim
ates
, com
-pa
res,
ord
ers
capa
c-ity
, mea
sure
s ca
pac-
ity o
f 3-D
obj
ects
(n
on-s
tand
ard
mea
sure
s: s
poon
s,
cups
, etc
.).
Estim
ates
, com
-pa
res,
ord
ers
capa
c-ity
, mea
sure
s ca
pac-
ity o
f 3-D
obj
ects
(n
on-s
tand
ard
mea
sure
s: s
poon
s,
cups
, etc
.).
Estim
ates
, com
pare
s,
orde
rs a
ccor
ding
to
capa
city
.
Mea
sure
s ca
paci
ty o
f 3-D
ob
ject
s (n
on-s
tand
ard
and
stan
dard
mea
sure
s:
litre
s, b
ottle
s, e
tc.).
Usin
g m
l and
l (a
s w
ell a
s co
nver
sion
s).
Mea
surin
g in
stru
-m
ents
: mea
surin
g ju
gs.
Usin
g m
l and
l (a
s w
ell a
s co
nver
sion
s).
Mea
surin
g in
stru
-m
ents
: mea
surin
g ju
gs.
Usin
g m
l and
l (a
s w
ell a
s co
nver
sion
s).
{
Top
ics:
4.
Pe
rim
ete
r, s
urf
ace
are
a an
d v
olu
me
Top
ics:
5.
Cla
ssifi
cati
on
of
ang
les
SUPPORTING LEARNERS IN ACQUIRING THE SKILL OF MATHEMATISATION
363
9
Gr. R
Gr. 1
Gr. 2
Gr. 3
Gr. 4
Gr. 5
Gr. 6
Tim
eDe
scrib
es ti
me
i.t.o
. da
y/ni
ght.
Orde
rs re
curr
ing
even
ts in
ow
n da
ily
life.
Sequ
ence
s ev
ents
w
ithin
one
day
.
Desc
ribes
tim
e of
da
y, u
sing
voc
ab.
such
as
early
, lat
e, m
orni
ng,
afte
rnoo
n, n
ight
.
Com
pare
s ev
ents
i.t
.o. d
urat
ion:
lo
nger
, sho
rter,
fast
-er
, slo
wer
.
Sequ
ence
s ev
ents
us
ing
lang
uage
suc
h as
yes
terd
ay, t
oday
an
d to
mor
row
.
Plac
es b
irthd
ays
on
cale
ndar
.
Read
s an
alog
ue
time
in h
ours
and
m
inut
es.
Nam
es in
ord
er:
days
of w
eek
and
mon
ths
of th
e ye
ar.
Calc
ulat
es e
laps
ed
time
in:
• Ho
urs
and
min
-ut
es u
sing
clo
cks
• Da
ys, w
eeks
and
m
onth
s us
ing
cal-
enda
rs.
Sequ
ence
s ev
ents
ac
cord
ing
to d
ays,
w
eeks
, mon
ths
and
year
s.
ID im
porta
nt d
ates
on
cal
enda
rs, i
nclu
d-in
g da
tes
of:
lear
ner b
irthd
ays,
re
ligio
us fe
stiv
als,
hi
stor
ical
eve
nts.
Read
s an
d w
rites
ana
-lo
gue
and
digi
tal t
ime
in te
rms
of h
ours
, hal
f ho
urs,
qua
rters
of h
ours
an
d m
inut
es.
Solv
es p
robl
ems
invo
lv-
ing
calc
ulat
ion
with
and
co
nver
sion
bet
wee
n:
• m
inut
es
ho
urs
• ho
urs
d
ays
• da
ys
m
onth
s.
ID im
porta
nt d
ates
on
cale
ndar
s, in
clud
ing
date
s of
: re
ligio
us fe
stiv
als,
his
-to
rical
eve
nts.
Reco
gnis
es a
nd
desc
ribes
diff
eren
t cal
-en
dars
use
d in
diff
eren
t cu
lture
s.
Read
s, te
lls a
nd
writ
es a
nalo
gue,
di
gita
l and
24-
h tim
e in
term
s of
•
seco
nds
• m
inut
es
• ho
urs.
Mea
surin
g in
stru
-m
ents
: wat
ches
and
cl
ocks
.
Conv
ersi
ons
betw
een
time
units
: se
cond
s, m
inut
es,
hour
s, d
ays,
wee
ks,
mon
ths,
yea
rs.
Solv
es p
robl
ems
invo
lvin
g tim
e.
Read
s, te
lls a
nd
writ
es a
nalo
gue,
di
gita
l and
24-
h tim
e in
term
s of
•
seco
nds
• m
inut
es
• ho
urs.
Mea
surin
g in
stru
-m
ents
: wat
ches
and
st
op w
atch
es.
Conv
ersi
ons
betw
een
time
units
: as
pre
viou
s pl
us
deca
des,
cen
turie
s an
d m
illen
nia.
Solv
es p
robl
ems
invo
lvin
g tim
e.
Read
s, te
lls a
nd
writ
es a
nalo
gue,
di
gita
l and
24-
h tim
e in
term
s of
•
seco
nds
• m
inut
es
• ho
urs.
Conv
ersi
ons
betw
een
time
units
: as
pre
viou
s pl
us
time
zone
s.
Tem
pera
ture
n/a
n/a
n/a
n/a
n/a
Units
: °C
Mea
surin
g in
stru
-m
ents
: th
erm
omet
ers.
Solv
e re
al-li
fe
prob
lem
s in
volv
ing
tem
pera
ture
.
Units
: °C
Mea
surin
g in
stru
-m
ents
: th
erm
omet
ers.
Solv
e re
al-li
fe
prob
lem
s in
volv
ing
tem
pera
ture
.
←
→←
→ ←
→
{
PART 2 PRACTICE
364
Gr. R
Gr. 1
Gr. 2
Gr. 3
Gr. 4
Gr. 5
Gr. 6
Perim
eter
, sur
-fa
ce a
rea
and
volu
me
n/a
n/a
n/a
n/a
Inve
stig
ates
per
imet
er
usin
g ru
lers
or m
easu
r-in
g ta
pes:
• Ar
eas
of p
olyg
ons
usin
g sq
uare
grid
s an
d til
ing
to d
evel
op
the
conc
ept o
f squ
are
units
• V
olum
e an
d ca
paci
ty o
f 3-
D ob
ject
s to
dev
elop
th
e co
ncep
t of c
ubic
un
its
• So
lves
real
-life
pro
b-le
ms
invo
lvin
g pe
rim-
eter
, sur
face
are
a an
d vo
lum
e.
Inve
stig
ates
per
imet
er
usin
g ru
lers
or m
easu
r-in
g ta
pes:
• Ar
eas
of p
olyg
ons
usin
g sq
uare
grid
s an
d til
ing
to d
evel
op
the
conc
ept o
f squ
are
units
• V
olum
e an
d ca
paci
ty o
f 3-
D ob
ject
s to
dev
elop
th
e co
ncep
t of c
ubic
un
its
• So
lves
real
-life
pro
b-le
ms
invo
lvin
g pe
rim-
eter
, sur
face
are
a an
d vo
lum
e.
Inve
stig
ates
per
imet
er u
sing
ru
lers
or m
easu
ring
tape
s:
• A
reas
of p
olyg
ons
usin
g sq
uare
grid
s to
dev
elop
th
e ru
les
for c
alcu
latin
g th
e ar
ea o
f squ
ares
and
rect
an-
gles
• V
olum
e an
d ca
paci
ty o
f 3-D
ob
ject
s to
dev
elop
the
rule
s fo
r cal
cula
ting
the
area
of
squa
res
and
rect
angl
es.
Rela
tions
hip
betw
een
perim
e-te
r and
are
a of
rect
angl
es a
nd
squa
res.
Rela
tions
hip
betw
een
surfa
ce
area
, vol
ume
and
dim
ensi
ons
of re
ctan
gula
r pris
ms.
Solv
es re
al-li
fe p
robl
ems
invo
lvin
g pe
rimet
er, s
urfa
ce
area
and
vol
ume.
Clas
sific
atio
n of
an
gles
n/a
n/a
n/a
n/a
n/a
Reco
gnis
es a
nd
desc
ribes
righ
t ang
les
in
2-D
shap
es, 3
-D o
bjec
ts
and
the
envi
ronm
ent.
Reco
gnis
es a
nd d
escr
ibes
rig
ht a
ngle
s in
2-D
sha
pes,
3-
D ob
ject
s an
d th
e en
viro
n-m
ent i
n te
rms
of:
• Ri
ght a
ngle
s •
Angl
es <
90°
•
Angl
es >
90°
SUPPORTING LEARNERS IN ACQUIRING THE SKILL OF MATHEMATISATION
365
9E.
Co
nte
nt
area
: Dat
a h
and
ling
Top
ics:
1.
Co
llect
ing
dat
a
Top
ics:
2.
Org
anis
ing
, re
cord
ing
an
d s
um
mar
isin
g d
ata
Top
ics:
3.
Dis
pla
yin
g d
ata
Gr. R
Gr. 1
Gr. 2
Gr. 3
Gr. 4
Gr. 5
Gr. 6
Colle
ctin
g da
taCo
llect
s ph
ysic
al
obje
cts
in e
nviro
n-m
ent a
ccor
ding
to
stat
ed fe
atur
es.
Colle
cts
phys
ical
ob
ject
s in
env
iron-
men
t acc
ordi
ng to
st
ated
feat
ures
.
Colle
cts
phys
ical
ob
ject
s in
env
i-ro
n-m
ent a
ccor
ding
to
sta
ted
feat
ures
.
Colle
cts
phys
ical
ob
ject
s in
env
iron-
men
t acc
ordi
ng to
st
ated
feat
ures
.
Pose
s qu
estio
ns
abou
t ow
n an
d fa
mily
and
sch
ool
envi
ronm
ent.
Iden
tifies
app
ropr
i-at
e da
ta s
ourc
es.
Colle
cts
data
to
answ
er q
uest
ions
.
Pose
s qu
estio
ns a
bout
ow
n an
d fa
mily
and
sc
hool
env
ironm
ent.
Iden
tifies
app
ropr
iate
da
ta s
ourc
es.
Mak
es a
nd u
ses
sim
ple
data
col
lect
ion
shee
ts
that
invo
lve
coun
ting
obje
cts
to a
nsw
er
ques
tions
.
Colle
cts
data
to a
nsw
er
ques
tions
.
Pose
s qu
estio
ns a
bout
ow
n an
d fa
mily
and
sc
hool
env
ironm
ent.
Iden
tifies
app
ropr
iate
dat
a so
urce
s. U
ses
sim
ple
data
co
llect
ion
shee
ts (r
equi
r-in
g ta
lly m
arks
) and
sim
-pl
e qu
estio
nnai
res
(yes
/no
resp
onse
s) to
ans
wer
qu
estio
ns.
Colle
cts
data
to a
nsw
er
ques
tions
.
Orga
nisi
ng,
reco
rdin
g an
d su
mm
aris
ing
data
Sorts
phy
sica
l ob
ject
s ac
cord
ing
to a
sin
gle
prop
-er
ty.
Sorts
phy
sica
l ob
ject
s ac
cord
ing
to a
sin
gle
prop
-er
ty, c
hose
n fo
r a
reas
on.
Give
s re
ason
s fo
r co
llect
ions
bei
ng
grou
ped
in p
artic
u-la
r way
s.
Sorts
phy
sica
l ob
ject
s ac
cord
ing
to a
sin
gle
prop
erty
, ch
osen
by
teac
her.
Give
s re
ason
s fo
r co
llect
ions
bei
ng
grou
ped
in p
artic
u-la
r way
s.
Sorts
, ord
ers
and
orga
nise
s ow
n an
d su
pplie
d da
ta b
y ½
pr
oper
ties
for a
par
-tic
ular
reas
on.
Reco
rds
data
usi
ng
• ta
lly m
arks
.Or
gani
ses
and
reco
rds
data
usi
ng
• ta
lly m
arks
• ta
bles
.
Exam
ines
ung
roup
ed
num
eric
al d
ata
to
dete
rmin
e th
e m
ode.
Orga
nise
s an
d re
cord
s da
ta u
sing
• ta
lly m
arks
• ta
bles
.
Dist
ingu
ishe
s be
twee
n sa
mpl
es a
nd p
opul
atio
n.
Exam
ines
ung
roup
ed
num
eric
al d
ata
to d
eter
-m
ine
the
mod
e an
d th
e m
edia
n.
{
Top
ics:
4.
Inte
rpre
tin
g d
ata
Top
ics:
5.
Pro
bab
ility
PART 2 PRACTICE
366
Gr. R
Gr. 1
Gr. 2
Gr. 3
Gr. 4
Gr. 5
Gr. 6
Disp
layi
ng
data
Draw
s a
pict
ure
as
reco
rd o
f col
-le
cted
obj
ect.
Draw
s a
pict
ure
as
reco
rd o
f col
lect
ed
obje
ct.
Cons
truct
s pi
cto-
grap
hs w
here
stic
kers
/st
amps
repr
esen
t ind
i-vi
dual
ele
men
ts in
a
colle
ctio
n of
obj
ects
.
Draw
s pi
ctur
es
and
cons
truct
s pi
ctog
raph
s th
at
have
a 1
-1
corr
espo
nden
ce
betw
een
own
data
and
repr
e-se
ntat
ions
.
Draw
s pi
ctur
es
and
cons
truct
s pi
ctog
raph
s an
d ba
r gra
phs
that
hav
e a
1-1
corr
espo
nden
ce
betw
een
own
data
an
d re
pres
enta
-tio
ns.
Draw
s a
varie
ty o
f gr
aphs
to d
ispl
ay
and
inte
rpre
t dat
a in
clud
ing
• pi
ctog
raph
s (1
-1 c
orre
spon
-de
nce)
• ba
r gra
phs.
Draw
s a
varie
ty o
f gra
phs
to d
ispl
ay a
nd in
terp
ret d
ata
incl
udin
g•
pict
ogra
phs
(man
y-to
-one
cor
resp
on-
denc
e)•
bar g
raph
s.
Draw
s a
varie
ty o
f gra
phs
to d
is-
play
and
inte
rpre
t dat
a in
clud
ing
• pi
ctog
raph
s (m
any-
to-o
ne c
orre
spon
-de
nce)
• ba
r gra
phs.
Inte
rpre
ting
data
Answ
ers
ques
tions
ba
sed
on
own-
pict
ure
or o
wn-
sort-
ed o
bjec
ts.
Desc
ribes
ow
n co
l-le
ctio
n of
obj
ects
, ex
plai
ns h
ow it
was
so
rted
and
answ
ers
ques
tions
abo
ut it
.
Desc
ribes
ow
n or
pee
rs’ c
olle
c-tio
n of
obj
ects
, ex
plai
ns h
ow it
w
as s
orte
d an
d an
swer
s qu
es-
tions
abo
ut it
.
Read
s, in
terp
rets
an
d re
ports
on
info
in o
wn
and
peer
s’ re
pres
enta
-tio
ns o
f dat
a.
Read
s an
d in
ter-
pret
s da
ta p
re-
sent
ed in
sim
ple
tabl
es a
nd li
sts.
Criti
cally
read
s an
d in
terp
rets
dat
a pr
e-se
nted
in a
var
iety
of
way
s to
dra
w c
on-
clus
ions
and
mak
e pr
edic
tions
sen
sitiv
e to
the
role
of:
• Co
ntex
t•
Othe
r hum
an ri
ghts
is
sues
Criti
cally
read
s an
d in
ter-
pret
s da
ta p
rese
nted
in a
va
riety
of w
ays
to d
raw
co
nclu
sion
s an
d m
ake
pred
ictio
ns s
ensi
tive
to th
e ro
le o
f:•
Cont
ext
• Ca
tego
ries
with
in th
e da
ta•
Othe
r hum
an ri
ghts
is
sues
Criti
cally
read
s an
d in
terp
rets
da
ta p
rese
nted
in a
var
iety
of
way
s to
dra
w c
oncl
usio
ns a
nd
mak
e pr
edic
tions
sen
sitiv
e to
th
e ro
le o
f:•
Cont
ext
• Ca
tego
ries
with
in th
e da
ta•
Othe
r hum
an ri
ghts
issu
es
Prob
abili
tyCo
mpa
res
and
clas
si-
fies
even
ts a
s •
certa
in th
at th
ey
will
hap
pen
• ce
rtain
that
they
w
ill N
OT h
appe
n•
unce
rtain
.
Coun
ting
the
num
ber
of p
ossi
ble
outc
omes
fo
r sim
ple
trial
s.
Com
pare
s an
d cl
assi
fies
even
ts o
n sc
ale
from
: •
certa
in th
at th
ey w
ill
happ
ento •
certa
in th
at th
ey w
ill N
OT
happ
en.
List
pos
sibl
e ou
tcom
es fo
r si
mpl
e ex
perim
ents
:•
Toss
ing
a co
in•
Rolli
ng a
die
• Sp
inni
ng a
spi
nner
Coun
ting
the
frequ
ency
of
actu
al o
utco
mes
for a
ser
ies
of tr
ials
.
Pred
icts
the
likel
ihoo
d of
eve
nts
base
d on
obs
erva
tion
and
plac
-es
them
on
a sc
ale
from
: •
impo
ssib
le
to • ce
rtain
.
List
pos
sibl
e ou
tcom
es fo
r sim
-pl
e ex
perim
ents
: •
Toss
ing
a co
in•
Rolli
ng a
die
• Sp
inni
ng a
spi
nner
Coun
ting
the
frequ
ency
of a
ctua
l ou
tcom
es fo
r a s
erie
s of
tria
ls.
Sour
ce: A
dapt
ed fr
om D
BE (2
011)
, Jan
uary
. Cur
ricul
um a
nd A
sses
smen
t Pol
icy
Stat
emen
t (CA
PS).
Mat
hem
atic
s (In
term
edia
te P
hase
).
SUPPORTING LEARNERS IN ACQUIRING THE SKILL OF MATHEMATISATION
367
9
Addendum B to Chapter 9
AN EXAMPLE OF A GRADE 5 MULTILEVEL MATHEMATICS LESSON
Multilevel lesson for formal assessment purposes
PL
AN
NIN
G
Content:Maths
Numbers, Operations andRelationships: Doubling &
halving of 1, 2, 3-digitnumbers
Mass and capacity:g, kg; l and ml
(convertingbetween units)
Selectcore content:
doublingand halving
Selectteaching
material e.g.d/h in thekitchen
Recipe foruncookedfudgeIngredients:mass usingg and kgcapacityusingml and l
• 3 × 200g packets Marie biscuits• 1 packet (500g) icing sugar• 1 block (500g) melted margarine• 1 tin (300g) caramel treat• 2 teaspoons (10ml) vanilla essence
Planning theprocess:Planninglearner
activities/assessment
tasks
Reviseability
grouping(Ab gr)
Designdifferentiatedassessment
tasks/assignments
for eachgroup
Ab gr 1: no modificationIngredients in ml and l, g and kg.Double and halve the recipe. Check answers by× 2 and ÷ 2
Ab gr 2: unwinding with ASSIngredients only in g and ml.Double and halve the recipe.
Ab gr 3: straddling to gr 3 numbers, operations and relationships: doubling and halving of 1 and 2-digitnumbers.Measurement: Estimate measure, compare and order 3-D objects using non-standard and standardmeasures: a) Mass, e.g. packets b) Capacity, e.g. bottles. Learners use non-standard units only and by using drawings or contrete objects, they also double and halvethe ingredients. Also attempt continuous doubling.
Planning theassessment
process:Planningformal
assessment
Teach thecore content(concept of
doublingand halving)
to the whole class.
Design Rubric – keeping the focus of the
differentiated assignmentsin mind. Assess valuesand attitudes as well.
Refer to example andexplanation of Rubric on
following page.
40%
Split
into
abi
lity
grou
ping
s.
TE
AC
HIN
G
Discuss possiblemethod by which
fudge will bemade.
Receives assessmenttask. If necessary
learner from group 1explains the assignment.
Teacher support:In order to master
concept ofdoubling/halving.
20%
Give feedbackto teacher.
Teacher explainsassessment task.
Carry on withassessment task.
Assessment task.
20%
Completesassessment
task.
Completesassessment.
Teacher supportto individual
learners.
Completesassessment
task.
20%
PART 2 PRACTICE
368
AS
SE
SS
ME
NT
OF
LE
AR
NIN
G O
UT
CO
ME
S
ASSESSPRODUCT
ACCORDINGTO THE
ASSESSMENTCRITERIA ASSTATED IN
RUBRIC
RE
CO
RD
ING
Record assessmentoutcomes in the format
as prescribed inNational Protocol for
Assessment:Grades R–12
RE
PO
RT
ING Formal reporting at least once a term.
• Suggested format to be found in National Protocol for Assessment: Grades R–12• Schools may use own format• Not advisable to use LOs and Assessment Standards in reports to parents – rather use core curriculum as headings.
Refer to next section for examplesof report cards.
MATHEMATICS ASSESSMENT TASK 3 GRADE 5
Name of learner: Date:
Numbers, Operations and Relationships: doubling and halving Topic:in the kitchenMeasurement: mass and capacity
Assessment criteria
• Learner is able to differentiate between capacity and mass by describing when to use appropriate units
All a
bilit
y gr
oups
Abili
ty g
roup
27
• Learner can master appropriate doubling operations• Learner can master appropriate halving operations only with g and ml, no conversion yet
Abili
ty g
roup
1 • Learner can master appropriate doubling operations• Learner can master appropriate halving operations• Learner is able to convert between SI units g and kg• Learner is able to check answers by doing appropriate alternataive operations
Ability group 3: Mastering of doubling and halving,capacityand mass units – l, ml, g and kgDoubling & halving of 1 & 2-digit numbers.Measurement: mass & capacity: non-standard units
Grade3
level
• Learner demonstrates the ability to use l instead of ml for larger capacities
• Learner demonstrates the ability to use kg instead of g for bigger masses
• Learner masters the concept of halving
• Learner masters the concept of doubling
6 5 4 3 2 1
Ratingcode
7
6
5
4
3
2
1
Marks%
80–100
70–79
60–69
50–59
40–49
30–39
0–29
Achievement description
Outstanding Achievement
Meritorious Achievement
Substantial Achievement
Adequate Achievement
Moderate Achievement
Elementary Achievement
Not Achieved
SUPPORTING LEARNERS IN ACQUIRING THE SKILL OF MATHEMATISATION
369
9
? m kg g l ml
? c kg
Double flowers _________
Double flowers _________
Double ALL flowers _________
Halve flowers _________
Halve flowers _________
Halve ALL flowers _________
Double all petals _________
Halve all petals _________
g l ml
? m kg g l ml
? c kg g l ml
? m kg g l ml
? m kg g l ml
kg g l ml
kg g l ml
kg g l ml
kg g l ml
kg g l ml
m = massc = capacity
Circle themost suitable
unit.
PART 2 PRACTICE
370
Uncooked fudgeIngredients for 100 squares
• 600g (_____ kg) Marie biscuits• 500g (_____ kg) icing sugar• 500g (_____ kg) melted margarine• 300g (_____ kg) caramel treat• 10ml (_____ l) vanilla essence
Uncooked fudgeIngredients for 100 squares
• 600g Marie biscuits• 500g icing sugar• 500g melted margarine• 300g caramel treat• 10ml vanilla essence
Uncooked fudgeIngredients for 100 squares
• 3 packets of Marie biscuits• 1 packet of icing sugar• 1 block of melted margarine• 1 tin of caramel treat• 2 teaspoons of vanilla essence
Unmodified curriculum
Unwinding of Assessment Standards
Straddling down to Grade 3 Assessment Standards
EXSTRATA PrimaryGrade4–6
Nameoflearner:_________________________________Grade:_________
Dateofbirth:–––––––––––––
Subject Term 1
Grade level Level of achievement
Language:
Homelanguage
Firstadditionallanguage
LifeOrientation
Mathematics 5 3:Alloutcomeswereachievedsatisfactorily
NaturalSciences
UN
MO
DIFIED
CU
RR
ICU
LUM
Example extracts from report cards
SNAPSHOTS OF REPORT CARDS
Example of differentiated learner tasks
SUPPORTING LEARNERS IN ACQUIRING THE SKILL OF MATHEMATISATION
371
9
Subject Term 1
Grade level Level of achievement
Language:
Homelanguage
Firstadditionallanguage
LifeOrientation
Mathematics 5 2:Inordertopromotenumberconceptandskills,ithadnotbeenexpectedfromthelearnertoachieveassess-mentstandardsinfullyet.
NaturalSciences
etc.
Subject Term 1
Grade level Level of achievement
Language:
Homelanguage
Firstadditionallanguage
LifeOrientation
Mathematics 3 3:Learnerhadbeentaughtaccordingtohisownlevelsofcompetence.Heiscurrentlydisplayinggoodprogressandallappropriateassessmentstan-dardswereachievedsatisfactorily.
NaturalSciences
UN
WIN
DIN
G O
F ASSESSM
ENT STA
ND
AR
DS
STRA
DD
LING
GR
OU
P
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