APP in mathematics at Key Stage 3: Assessment...
Transcript of APP in mathematics at Key Stage 3: Assessment...
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Assessing pupils' progress in mathematics at Key Stage 3: Assessment guidelines
Assessing pupils’ progress in mathematics at Key Stage 3: Assessment guidelines
Assessing pupils’ progress in mathematics at Key Stage 3: Assessment guidelines
First published in 2008 Ref: 00730-2008BKT-EN
1The National Strategies | Secondary Assessing Pupil Progress at Key Stage 3: Assessment guidelines
© Crown copyright 2008 00730-2008BKT-EN
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1The National Strategies | Secondary Assessing Pupil Progress at Key Stage 3: Assessment guidelines
© Crown copyright 2008 00730-2008BKT-EN
Mat
hem
atic
s ass
essm
ent g
uide
lines
: lev
els 2
and
3
Pupi
l nam
e……
……
……
….C
lass
/gro
up…
……
……
……
..Dat
e……
……
Usi
ng a
nd a
pply
ing
mat
hem
atic
sN
umbe
rs a
nd th
e nu
mbe
r sy
stem
Calc
ulat
ing
Alg
ebra
Shap
e, s
pace
and
mea
sure
Han
dlin
g da
ta
Leve
l 3•s
elec
t the
m
athe
mat
ics t
hey
use
in a
wid
er ra
nge
of
clas
sroo
m a
ctiv
ities
•try
diff
eren
t ap
proa
ches
and
find
w
ays o
f ove
rcom
ing
diff
icul
ties t
hat a
rise
whe
n th
ey a
re so
lvin
g pr
oble
ms
•beg
in to
org
anis
e th
eir
wor
k an
d ch
eck
resu
lts
•use
and
inte
rpre
t m
athe
mat
ical
sym
bols
an
d di
agra
ms
•und
erst
and
a ge
nera
l st
atem
ent b
y fin
ding
pa
rtic
ular
exa
mpl
es
that
mat
ch it
•rev
iew
thei
r wor
k an
d re
ason
ing
•und
erst
and
plac
e va
lue
in
num
bers
to 1
000
•use
pla
ce v
alue
to m
ake
appr
oxim
atio
ns
•rec
ogni
se n
egat
ive
num
bers
in
cont
exts
such
as t
empe
ratu
re
•use
sim
ple
frac
tions
that
are
se
vera
l par
ts o
f a w
hole
and
re
cogn
ise
whe
n tw
o si
mpl
e fr
actio
ns a
re e
quiv
alen
t
•beg
in to
use
dec
imal
not
atio
n in
co
ntex
ts su
ch a
s mon
ey
•der
ive
asso
ciat
ed d
ivis
ion
fact
s fr
om k
now
n m
ultip
licat
ion
fact
s
•add
and
subt
ract
two-
digi
t nu
mbe
rs m
enta
lly
•add
and
subt
ract
thre
e di
git
num
bers
usi
ng w
ritte
n m
etho
d
•mul
tiply
and
div
ide
two
digi
t nu
mbe
rs b
y 2,
3, 4
or 5
as w
ell a
s 10
with
who
le n
umbe
r ans
wer
s an
d re
mai
nder
s
•use
men
tal r
ecal
l of a
dditi
on
and
subt
ract
ion
fact
s to
20 in
so
lvin
g pr
oble
ms i
nvol
ving
larg
er
num
bers
•sol
ve w
hole
num
ber p
robl
ems
incl
udin
g th
ose
invo
lvin
g m
ultip
licat
ion
or d
ivis
ion
that
may
gi
ve ri
se to
rem
aind
ers
•rec
ogni
se a
wid
er
rang
e of
sequ
ence
s
•beg
in to
und
erst
and
the
role
of ‘
=’ (t
he
‘equ
als’
sign
)
•cla
ssify
3-D
and
2-D
shap
es in
var
ious
w
ays u
sing
mat
hem
atic
al p
rope
rtie
s suc
h as
refle
ctiv
e sy
mm
etry
for 2
-D sh
apes
•beg
in to
reco
gnis
e ne
ts o
f fam
iliar
3-D
sh
apes
, e.g
. cub
e, c
uboi
d, tr
iang
ular
pris
m,
squa
re-b
ased
pyr
amid
•rec
ogni
se sh
apes
in d
iffer
ent o
rient
atio
ns
and
refle
ct sh
apes
, pre
sent
ed o
n a
grid
, in
a ve
rtic
al o
r hor
izon
tal m
irror
line
•des
crib
e po
sitio
n an
d m
ovem
ent
•use
a w
ider
rang
e of
mea
sure
s inc
ludi
ng
non-
stan
dard
uni
ts a
nd st
anda
rd m
etric
un
its o
f len
gth,
cap
acity
and
mas
s in
a ra
nge
of c
onte
xts
•use
stan
dard
uni
ts o
f tim
e
•gat
her i
nfor
mat
ion
•con
stru
ct b
ar c
hart
s and
pi
ctog
ram
s, w
here
the
sym
bol
repr
esen
ts a
gro
up o
f uni
ts
•use
Ven
n an
d Ca
rrol
l dia
gram
s to
reco
rd th
eir s
ortin
g an
d cl
assi
fyin
g of
info
rmat
ion
•ext
ract
and
inte
rpre
t in
form
atio
n pr
esen
ted
in si
mpl
e ta
bles
, lis
ts, b
ar c
hart
s and
pi
ctog
ram
s
Leve
l 2•s
elec
t the
m
athe
mat
ics t
hey
use
in so
me
clas
sroo
m
activ
ities
•dis
cuss
thei
r wor
k us
ing
mat
hem
atic
al
lang
uage
•beg
in to
repr
esen
t th
eir w
ork
usin
g sy
mbo
ls a
nd si
mpl
e di
agra
ms
•pre
dict
wha
t com
es
next
in a
sim
ple
num
ber,
shap
e or
sp
atia
l pat
tern
or
sequ
ence
and
giv
e re
ason
s for
thei
r op
inio
ns
•exp
lain
why
an
answ
er is
cor
rect
•cou
nt se
ts o
f obj
ects
relia
bly
•beg
in to
und
erst
and
the
plac
e va
lue
of e
ach
digi
t; us
e th
is to
or
der n
umbe
rs u
p to
100
•beg
in to
use
hal
ves a
nd
quar
ters
and
rela
te th
e co
ncep
t of
hal
f of a
smal
l qua
ntity
to th
e co
ncep
t of h
alf o
f a sh
ape
•use
the
know
ledg
e th
at
subt
ract
ion
is th
e in
vers
e of
ad
ditio
n an
d un
ders
tand
hal
ving
as
a w
ay o
f ‘un
doin
g’ d
oubl
ing
and
vice
ver
sa
•use
men
tal r
ecal
l of a
dditi
on a
nd
subt
ract
ion
fact
s to
10
•use
men
tal c
alcu
latio
n st
rate
gies
to
solv
e nu
mbe
r pro
blem
s in
clud
ing
thos
e in
volv
ing
mon
ey
and
mea
sure
s
•rec
ord
thei
r wor
k in
writ
ing
•cho
ose
the
appr
opria
te
oper
atio
n w
hen
solv
ing
addi
tion
and
subt
ract
ion
prob
lem
s
•rec
ogni
se
sequ
ence
s of
num
bers
, inc
ludi
ng
odd
and
even
nu
mbe
rs
•use
mat
hem
atic
al n
ames
for c
omm
on
3-D
and
2-D
shap
es
•des
crib
e th
eir p
rope
rtie
s, in
clud
ing
num
bers
of s
ides
and
cor
ners
•des
crib
e th
e po
sitio
n of
obj
ects
•dis
tingu
ish
betw
een
stra
ight
and
turn
ing
mov
emen
ts, r
ecog
nise
righ
t ang
les
in tu
rns a
nd u
nder
stan
d an
gle
as a
m
easu
rem
ent o
f tur
n
•beg
in to
use
a w
ider
rang
e of
mea
sure
s in
clud
ing
to u
se e
very
day
non-
stan
dard
an
d st
anda
rd u
nits
to m
easu
re le
ngth
an
d m
ass
•beg
in to
und
erst
and
that
num
bers
ca
n be
use
d no
t onl
y to
cou
nt d
iscr
ete
obje
cts b
ut a
lso
to d
escr
ibe
cont
inuo
us
mea
sure
s
•sor
t obj
ects
and
cla
ssify
them
us
ing
mor
e th
an o
ne c
riter
ion
•und
erst
and
voca
bula
ry re
latin
g to
han
dlin
g da
ta
•col
lect
and
sort
dat
a to
test
a
sim
ple
hypo
thes
is
•rec
ord
resu
lts in
sim
ple
lists
, ta
bles
, pic
togr
ams a
nd b
lock
gr
aphs
•com
mun
icat
e th
eir f
indi
ngs,
usin
g th
e si
mpl
e lis
ts, t
able
s, pi
ctog
ram
s and
blo
ck g
raph
s th
ey h
ave
reco
rded
BL
IE
Key:
BL-B
elow
Lev
el
IE-In
suff
icie
nt E
vide
nce
Ove
rall
asse
ssm
ent (
tick
one
box
only
)Lo
w 2
S
ecur
e 2
Hig
h 2
Low
3
Sec
ure
3
Hig
h 3
2 The National Strategies | Secondary Assessing Pupil Progress at Key Stage 3: Assessment guidelines
00730-2008BKT-EN © Crown copyright 2008
3The National Strategies | Secondary Assessing Pupil Progress at Key Stage 3: Assessment guidelines
© Crown copyright 2008 00730-2008BKT-EN
Mat
hem
atic
s ass
essm
ent g
uide
lines
: lev
els 3
and
4
Pupi
l nam
e……
……
……
….C
lass
/gro
up…
……
……
……
..Dat
e……
……
Usi
ng a
nd a
pply
ing
mat
hem
atic
sN
umbe
rs a
nd th
e nu
mbe
r sy
stem
Calc
ulat
ing
Alg
ebra
Shap
e, s
pace
and
mea
sure
sH
andl
ing
data
Leve
l 4•d
evel
op o
wn
stra
tegi
es
for s
olvi
ng p
robl
ems
•use
thei
r ow
n st
rate
gies
w
ithin
mat
hem
atic
s and
in
app
lyin
g m
athe
mat
ics
to p
ract
ical
con
text
s
•pre
sent
info
rmat
ion
and
resu
lts in
a c
lear
and
or
gani
sed
way
•sea
rch
for a
solu
tion
by
tryi
ng o
ut id
eas o
f the
ir ow
n
•rec
ogni
se a
nd d
escr
ibe
num
ber p
atte
rns
•rec
ogni
se a
nd d
escr
ibe
num
ber r
elat
ions
hips
in
clud
ing
mul
tiple
, fac
tor
and
squa
re
•use
pla
ce v
alue
to
mul
tiply
and
div
ide
who
le
num
bers
by
10 o
r 100
•rec
ogni
se a
ppro
xim
ate
prop
ortio
ns o
f a w
hole
an
d us
e si
mpl
e fr
actio
ns
and
perc
enta
ges t
o de
scrib
e th
ese
•ord
er d
ecim
als t
o th
ree
deci
mal
pla
ces
•beg
in to
und
erst
and
sim
ple
ratio
•use
a ra
nge
of m
enta
l met
hods
of
com
puta
tion
with
all
oper
atio
ns
•rec
all m
ultip
licat
ion
fact
s up
to 1
0 ×
10 a
nd q
uick
ly d
eriv
e co
rres
pond
ing
divi
sion
fact
s
•use
eff
icie
nt w
ritte
n m
etho
ds o
f ad
ditio
n an
d su
btra
ctio
n an
d of
sh
ort m
ultip
licat
ion
and
divi
sion
•mul
tiply
a si
mpl
e de
cim
al b
y a
sing
le d
igit
•sol
ve p
robl
ems w
ith o
r with
out
a ca
lcul
ator
•che
ck th
e re
ason
able
ness
of
resu
lts w
ith re
fere
nce
to th
e co
ntex
t or s
ize
of n
umbe
rs
•beg
in to
use
sim
ple
form
ulae
exp
ress
ed in
w
ords
•use
and
inte
rpre
t co
ordi
nate
s in
the
first
qu
adra
nt
•use
the
prop
ertie
s of 2
-D a
nd 3
-D
shap
es
•mak
e 3-
D m
odel
s by
linki
ng g
iven
fa
ces o
r edg
es a
nd d
raw
com
mon
2-
D sh
apes
in d
iffer
ent o
rient
atio
ns
on g
rids
•ref
lect
sim
ple
shap
es in
a m
irror
lin
e, tr
ansl
ate
shap
es h
oriz
onta
lly o
r ve
rtic
ally
and
beg
in to
rota
te a
sim
ple
shap
e or
obj
ect a
bout
its c
entr
e or
a
vert
ex
•cho
ose
and
use
appr
opria
te u
nits
and
in
stru
men
ts
•int
erpr
et, w
ith a
ppro
pria
te a
ccur
acy,
nu
mbe
rs o
n a
rang
e of
mea
surin
g in
stru
men
ts
•fin
d pe
rimet
ers o
f sim
ple
shap
es a
nd
find
area
s by
coun
ting
squa
res
•col
lect
and
reco
rd d
iscr
ete
data
•gro
up d
ata,
whe
re a
ppro
pria
te,
in e
qual
cla
ss in
terv
als
•con
tinue
to u
se V
enn
and
Carr
oll d
iagr
ams t
o re
cord
th
eir s
ortin
g an
d cl
assi
fyin
g of
in
form
atio
n
•con
stru
ct a
nd in
terp
ret
freq
uenc
y di
agra
ms a
nd si
mpl
e lin
e gr
aphs
•und
erst
and
and
use
the
mod
e an
d ra
nge
to d
escr
ibe
sets
of
data
Leve
l 3•s
elec
t the
mat
hem
atic
s th
ey u
se in
a w
ider
rang
e of
cla
ssro
om a
ctiv
ities
•try
diff
eren
t app
roac
hes
and
find
way
s of
over
com
ing
diff
icul
ties
that
aris
e w
hen
they
are
so
lvin
g pr
oble
ms
•beg
in to
org
anis
e th
eir
wor
k an
d ch
eck
resu
lts
•use
and
inte
rpre
t m
athe
mat
ical
sym
bols
an
d di
agra
ms
•und
erst
and
a ge
nera
l st
atem
ent b
y fin
ding
pa
rtic
ular
exa
mpl
es th
at
mat
ch it
•rev
iew
thei
r wor
k an
d re
ason
ing
•und
erst
and
plac
e va
lue
in
num
bers
to 1
000
•use
pla
ce v
alue
to m
ake
appr
oxim
atio
ns
•rec
ogni
se n
egat
ive
num
bers
in c
onte
xts s
uch
as te
mpe
ratu
re
•use
sim
ple
frac
tions
th
at a
re se
vera
l par
ts o
f a
who
le a
nd re
cogn
ise
whe
n tw
o si
mpl
e fr
actio
ns a
re e
quiv
alen
t
•beg
in to
use
dec
imal
no
tatio
n in
con
text
s suc
h as
mon
ey
•der
ive
asso
ciat
ed d
ivis
ion
fact
s fr
om k
now
n m
ultip
licat
ion
fact
s
•add
and
subt
ract
two-
digi
t nu
mbe
rs m
enta
lly
•add
and
subt
ract
thre
e-di
git
num
bers
usi
ng w
ritte
n m
etho
d
•mul
tiply
and
div
ide
two-
digi
t nu
mbe
rs b
y 2,
3, 4
or 5
as w
ell a
s 10
with
who
le n
umbe
r ans
wer
s an
d re
mai
nder
s
•use
men
tal r
ecal
l of a
dditi
on a
nd
subt
ract
ion
fact
s to
20 in
solv
ing
prob
lem
s inv
olvi
ng la
rger
nu
mbe
rs
•sol
ve w
hole
num
ber p
robl
ems
incl
udin
g th
ose
invo
lvin
g m
ultip
licat
ion
or d
ivis
ion
that
m
ay g
ive
rise
to re
mai
nder
s
•rec
ogni
se a
wid
er ra
nge
of
sequ
ence
s
•beg
in to
und
erst
and
the
role
of ‘
=’ (t
he ‘e
qual
s’ si
gn)
•cla
ssify
3-D
and
2-D
shap
es in
var
ious
w
ays u
sing
mat
hem
atic
al p
rope
rtie
s su
ch a
s ref
lect
ive
sym
met
ry fo
r 2-D
sh
apes
•beg
in to
reco
gnis
e ne
ts o
f fam
iliar
3-D
sh
apes
, e.g
. cub
e, c
uboi
d, tr
iang
ular
pr
ism
, squ
are-
base
d py
ram
id
•rec
ogni
se sh
apes
in d
iffer
ent
orie
ntat
ions
and
refle
ct sh
apes
, pr
esen
ted
on a
grid
, in
a ve
rtic
al o
r ho
rizon
tal m
irror
line
•des
crib
e po
sitio
n an
d m
ovem
ent
•use
a w
ider
rang
e of
mea
sure
s in
clud
ing
non-
stan
dard
uni
ts a
nd
stan
dard
met
ric u
nits
of l
engt
h,
capa
city
and
mas
s in
a ra
nge
of
cont
exts
•use
stan
dard
uni
ts o
f tim
e
•gat
her i
nfor
mat
ion
•con
stru
ct b
ar c
hart
s and
pi
ctog
ram
s, w
here
the
sym
bol
repr
esen
ts a
gro
up o
f uni
ts
•use
Ven
n an
d Ca
rrol
l dia
gram
s to
reco
rd th
eir s
ortin
g an
d cl
assi
fyin
g of
info
rmat
ion
•ext
ract
and
inte
rpre
t in
form
atio
n pr
esen
ted
in
sim
ple
tabl
es, l
ists
, bar
cha
rts
and
pict
ogra
ms
BL
IE
Key:
BL-B
elow
Lev
el
IE-In
suff
icie
nt E
vide
nce
Ove
rall
asse
ssm
ent (
tick
one
box
only
)Lo
w 3
S
ecur
e 3
Hig
h 3
Low
4
Sec
ure
4
Hig
h 4
2 The National Strategies | Secondary Assessing Pupil Progress at Key Stage 3: Assessment guidelines
00730-2008BKT-EN © Crown copyright 2008
3The National Strategies | Secondary Assessing Pupil Progress at Key Stage 3: Assessment guidelines
© Crown copyright 2008 00730-2008BKT-EN
Mat
hem
atic
s ass
essm
ent g
uide
lines
: lev
els 4
and
5
Pupi
l nam
e……
……
……
….C
lass
/gro
up…
……
……
……
..Dat
e……
……
Usi
ng a
nd a
pply
ing
mat
hem
atic
sN
umbe
rs a
nd th
e nu
mbe
r sys
tem
Calc
ulat
ing
Alg
ebra
Shap
e, s
pace
and
mea
sure
Han
dlin
g da
ta
Leve
l 5•i
dent
ify a
nd
obta
in n
eces
sary
in
form
atio
n to
car
ry
thro
ugh
a ta
sk a
nd
solv
e m
athe
mat
ical
pr
oble
ms
•che
ck re
sults
, co
nsid
erin
g w
heth
er
thes
e ar
e re
ason
able
•sol
ve w
ord
prob
lem
s an
d in
vest
igat
ions
fr
om a
rang
e of
co
ntex
ts
•sho
w u
nder
stan
ding
of
situ
atio
ns b
y de
scrib
ing
them
m
athe
mat
ical
ly u
sing
sy
mbo
ls, w
ords
and
di
agra
ms
•dra
w si
mpl
e co
nclu
sion
s of t
heir
own
and
give
an
expl
anat
ion
of th
eir
reas
onin
g
•use
und
erst
andi
ng o
f pla
ce v
alue
to
mul
tiply
and
div
ide
who
le
num
bers
and
dec
imal
s by
10, 1
00
and
1000
and
exp
lain
the
effe
ct
•rou
nd d
ecim
als t
o th
e ne
ares
t de
cim
al p
lace
and
ord
er n
egat
ive
num
bers
in c
onte
xt
•rec
ogni
se a
nd u
se n
umbe
r pa
tter
ns a
nd re
latio
nshi
ps
•use
equ
ival
ence
bet
wee
n fr
actio
ns a
nd o
rder
frac
tions
and
de
cim
als
•red
uce
a fr
actio
n to
its s
impl
est
form
by
canc
ellin
g co
mm
on
fact
ors
•und
erst
and
sim
ple
ratio
•use
kno
wn
fact
s, pl
ace
valu
e,
know
ledg
e of
ope
ratio
ns a
nd
brac
kets
to c
alcu
late
incl
udin
g us
ing
all f
our o
pera
tions
with
dec
imal
s to
two
plac
es
•use
a c
alcu
lato
r whe
re a
ppro
pria
te
to c
alcu
late
frac
tions
/per
cent
ages
of
quan
titie
s/m
easu
rem
ents
•und
erst
and
and
use
an a
ppro
pria
te
non-
calc
ulat
or m
etho
d fo
r sol
ving
pr
oble
ms t
hat i
nvol
ve m
ultip
lyin
g an
d di
vidi
ng a
ny th
ree-
digi
t num
ber
by a
ny tw
o-di
git n
umbe
r
•sol
ve si
mpl
e pr
oble
ms i
nvol
ving
or
derin
g, a
ddin
g, su
btra
ctin
g ne
gativ
e nu
mbe
rs in
con
text
•sol
ve si
mpl
e pr
oble
ms i
nvol
ving
ra
tio a
nd d
irect
pro
port
ion
•app
ly in
vers
e op
erat
ions
and
ap
prox
imat
e to
che
ck a
nsw
ers
to p
robl
ems a
re o
f the
cor
rect
m
agni
tude
•con
stru
ct, e
xpre
ss
in sy
mbo
lic
form
, and
use
si
mpl
e fo
rmul
ae
invo
lvin
g on
e or
tw
o op
erat
ions
•use
and
inte
rpre
t co
ordi
nate
s in
all
four
qua
dran
ts
•use
a w
ider
rang
e of
pro
pert
ies o
f 2-D
and
3-
D sh
apes
and
iden
tify
all t
he sy
mm
etrie
s of
2-D
shap
es
•use
lang
uage
ass
ocia
ted
with
ang
le a
nd
know
and
use
the
angl
e su
m o
f a tr
iang
le
and
that
of a
ngle
s at a
poi
nt
•rea
son
abou
t pos
ition
and
mov
emen
t and
tr
ansf
orm
shap
es
•mea
sure
and
dra
w a
ngle
s to
the
near
est
degr
ee, w
hen
cons
truc
ting
mod
els a
nd
draw
ing
or u
sing
shap
es
•rea
d an
d in
terp
ret s
cale
s on
a ra
nge
of
mea
surin
g in
stru
men
ts, e
xpla
inin
g w
hat
each
labe
lled
divi
sion
repr
esen
ts
•sol
ve p
robl
ems i
nvol
ving
the
conv
ersi
on
of u
nits
and
mak
e se
nsib
le e
stim
ates
of a
ra
nge
of m
easu
res i
n re
latio
n to
eve
ryda
y si
tuat
ions
•und
erst
and
and
use
the
form
ula
for t
he
area
of a
rect
angl
e an
d di
stin
guis
h ar
ea
from
per
imet
er
•ask
que
stio
ns, p
lan
how
to
answ
er th
em a
nd c
olle
ct th
e da
ta re
quire
d
•in
prob
abili
ty, s
elec
t met
hods
ba
sed
on e
qual
ly li
kely
ou
tcom
es a
nd e
xper
imen
tal
evid
ence
, as a
ppro
pria
te
•und
erst
and
and
use
the
prob
abili
ty sc
ale
from
0 to
1
•und
erst
and
and
use
the
mea
n of
dis
cret
e da
ta a
nd c
ompa
re
two
sim
ple
dist
ribut
ions
, usi
ng
the
rang
e an
d on
e of
mod
e,
med
ian
or m
ean
•und
erst
and
that
diff
eren
t ou
tcom
es m
ay re
sult
from
re
peat
ing
an e
xper
imen
t
•int
erpr
et g
raph
s and
dia
gram
s, in
clud
ing
pie
char
ts, a
nd d
raw
co
nclu
sion
s
•cre
ate
and
inte
rpre
t lin
e gr
aphs
w
here
the
inte
rmed
iate
val
ues
have
mea
ning
Leve
l 4•d
evel
op o
wn
stra
tegi
es fo
r sol
ving
pr
oble
ms
•use
thei
r ow
n st
rate
gies
with
in
mat
hem
atic
s and
in
appl
ying
mat
hem
atic
s to
pra
ctic
al c
onte
xts
•pre
sent
info
rmat
ion
and
resu
lts in
a c
lear
an
d or
gani
sed
way
•sea
rch
for a
solu
tion
by tr
ying
out
idea
s of
thei
r ow
n
•rec
ogni
se a
nd d
escr
ibe
num
ber
patt
erns
•rec
ogni
se a
nd d
escr
ibe
num
ber
rela
tions
hips
incl
udin
g m
ultip
le,
fact
or a
nd sq
uare
•use
pla
ce v
alue
to m
ultip
ly a
nd
divi
de w
hole
num
bers
by
10 o
r 10
0
•rec
ogni
se a
ppro
xim
ate
prop
ortio
ns o
f a w
hole
and
use
si
mpl
e fr
actio
ns a
nd p
erce
ntag
es
to d
escr
ibe
thes
e
•ord
er d
ecim
als t
o th
ree
deci
mal
pl
aces
•beg
in to
und
erst
and
sim
ple
ratio
•use
a ra
nge
of m
enta
l met
hods
of
com
puta
tion
with
all
oper
atio
ns
•rec
all m
ultip
licat
ion
fact
s up
to 1
0 ×
10 a
nd q
uick
ly d
eriv
e co
rres
pond
ing
divi
sion
fact
s
•use
eff
icie
nt w
ritte
n m
etho
ds o
f ad
ditio
n an
d su
btra
ctio
n an
d of
sh
ort m
ultip
licat
ion
and
divi
sion
•mul
tiply
a si
mpl
e de
cim
al b
y a
sing
le
digi
t
•sol
ve p
robl
ems w
ith o
r with
out a
ca
lcul
ator
•che
ck th
e re
ason
able
ness
of r
esul
ts
with
refe
renc
e to
the
cont
ext o
r siz
e of
num
bers
•beg
in to
use
si
mpl
e fo
rmul
ae
expr
esse
d in
w
ords
•use
and
inte
rpre
t co
ordi
nate
s in
the
first
qua
dran
t
•use
the
prop
ertie
s of 2
-D a
nd 3
-D sh
apes
•mak
e 3-
D m
odel
s by
linki
ng g
iven
face
s or
edg
es a
nd d
raw
com
mon
2-D
shap
es in
di
ffer
ent o
rient
atio
ns o
n gr
ids
•ref
lect
sim
ple
shap
es in
a m
irror
line
, tr
ansl
ate
shap
es h
oriz
onta
lly o
r ver
tical
ly
and
begi
n to
rota
te a
sim
ple
shap
e or
ob
ject
abo
ut it
s cen
tre
or a
ver
tex
•cho
ose
and
use
appr
opria
te u
nits
and
in
stru
men
ts
•int
erpr
et, w
ith a
ppro
pria
te a
ccur
acy,
nu
mbe
rs o
n a
rang
e of
mea
surin
g in
stru
men
ts
•fin
d pe
rimet
ers o
f sim
ple
shap
es a
nd fi
nd
area
s by
coun
ting
squa
res
•col
lect
and
reco
rd d
iscr
ete
data
•gro
up d
ata,
whe
re a
ppro
pria
te,
in e
qual
cla
ss in
terv
als
•con
tinue
to u
se V
enn
and
Carr
oll d
iagr
ams t
o re
cord
th
eir s
ortin
g an
d cl
assi
fyin
g of
in
form
atio
n
•con
stru
ct a
nd in
terp
ret
freq
uenc
y di
agra
ms a
nd si
mpl
e lin
e gr
aphs
•und
erst
and
and
use
the
mod
e an
d ra
nge
to d
escr
ibe
sets
of
data
BL
IE
Key:
BL-B
elow
Lev
el
IE-In
suff
icie
nt E
vide
nce
Ove
rall
asse
ssm
ent (
tick
one
box
only
)Lo
w 4
S
ecur
e 4
Hig
h 4
Low
5
Sec
ure
5
Hig
h 5
4 The National Strategies | Secondary Assessing Pupil Progress at Key Stage 3: Assessment guidelines
00730-2008BKT-EN © Crown copyright 2008
5The National Strategies | Secondary Assessing Pupil Progress at Key Stage 3: Assessment guidelines
© Crown copyright 2008 00730-2008BKT-EN
Mat
hem
atic
s ass
essm
ent g
uide
lines
: lev
els 5
and
6
leve
ls 5
and
6
P
upil
nam
e……
……
……
….C
lass
/gro
up…
……
……
……
..Dat
e……
……
Usi
ng a
nd a
pply
ing
mat
hem
atic
sN
umbe
rs a
nd th
e nu
mbe
r sy
stem
Calc
ulat
ing
Alg
ebra
Shap
e, s
pace
and
mea
sure
Han
dlin
g da
ta
Leve
l 6•s
olve
pro
blem
s an
d ca
rry
thro
ugh
subs
tant
ial t
asks
by
bre
akin
g th
em
into
smal
ler,
mor
e m
anag
eabl
e ta
sks,
usin
g a
rang
e of
ef
ficie
nt te
chni
ques
, m
etho
ds a
nd
reso
urce
s, in
clud
ing
ICT;
giv
e so
lutio
ns to
an
appr
opria
te d
egre
e of
ac
cura
cy
•int
erpr
et, d
iscu
ss a
nd
synt
hesi
se in
form
atio
n pr
esen
ted
in a
var
iety
of
mat
hem
atic
al fo
rms
•pre
sent
a c
onci
se,
reas
oned
arg
umen
t, us
ing
sym
bols
, di
agra
ms,
grap
hs a
nd
rela
ted
expl
anat
ory
text
s
•use
logi
cal a
rgum
ent t
o es
tabl
ish
the
trut
h of
a
stat
emen
t
•use
the
equi
vale
nce
of
frac
tions
, dec
imal
s and
pe
rcen
tage
s to
com
pare
pr
opor
tions
•cal
cula
te p
erce
ntag
es a
nd fi
nd th
e ou
tcom
e of
a g
iven
per
cent
age
incr
ease
or d
ecre
ase
•div
ide
a qu
antit
y in
to tw
o or
mor
e pa
rts i
n a
give
n ra
tio a
nd so
lve
prob
lem
s inv
olvi
ng ra
tio a
nd d
irect
pr
opor
tion
•use
pro
port
iona
l rea
soni
ng to
solv
e a
prob
lem
, cho
osin
g th
e co
rrec
t nu
mbe
rs to
take
as 1
00%
, or a
s a
who
le
•add
and
subt
ract
frac
tions
by
writ
ing
them
with
a c
omm
on d
enom
inat
or,
calc
ulat
e fr
actio
ns o
f qua
ntiti
es
(frac
tion
answ
ers)
, mul
tiply
and
div
ide
an in
tege
r by
a fr
actio
n
•use
syst
emat
ic tr
ial a
nd
impr
ovem
ent m
etho
ds a
nd
ICT
tool
s to
find
appr
oxim
ate
solu
tions
to e
quat
ions
such
as
x³ +
x =
20
•con
stru
ct a
nd so
lve
linea
r eq
uatio
ns w
ith in
tege
r co
effic
ient
s, us
ing
an
appr
opria
te m
etho
d
•gen
erat
e te
rms o
f a se
quen
ce
usin
g te
rm-t
o-te
rm a
nd
posi
tion-
to-t
erm
def
initi
ons
of th
e se
quen
ce, o
n pa
per a
nd
usin
g IC
T; w
rite
an e
xpre
ssio
n to
des
crib
e th
e nt
h te
rm o
f an
arith
met
ic se
quen
ce.
•plo
t the
gra
phs o
f lin
ear
func
tions
, whe
re y
is g
iven
ex
plic
itly
in te
rms o
f x;
reco
gnis
e th
at e
quat
ions
of
the
form
y =
mx
+ c
corr
espo
nd to
stra
ight
-line
gr
aphs
•con
stru
ct fu
nctio
ns a
risin
g fr
om re
al-li
fe p
robl
ems a
nd
plot
thei
r cor
resp
ondi
ng
grap
hs;
•int
erpr
et g
raph
s aris
ing
from
re
al si
tuat
ions
•cla
ssify
qua
drila
tera
ls b
y th
eir g
eom
etric
pr
oper
ties
•sol
ve g
eom
etric
al p
robl
ems u
sing
pr
oper
ties o
f ang
les,
of p
aral
lel a
nd
inte
rsec
ting
lines
, and
of t
riang
les a
nd
othe
r pol
ygon
s
•ide
ntify
alte
rnat
e an
d co
rres
pond
ing
angl
es; u
nder
stan
d a
proo
f tha
t the
sum
of
the
angl
es o
f a tr
iang
le is
180
° and
of a
qu
adril
ater
al is
360
°
•dev
ise
inst
ruct
ions
for a
com
pute
r to
gene
rate
and
tran
sfor
m sh
apes
and
pat
hs
•vis
ualis
e an
d us
e 2-
D re
pres
enta
tions
of
3-D
obj
ects
•enl
arge
2-D
shap
es, g
iven
a c
entr
e of
en
larg
emen
t and
a p
ositi
ve w
hole
-nu
mbe
r sca
le fa
ctor
•kno
w th
at tr
ansl
atio
ns, r
otat
ions
and
re
flect
ions
pre
serv
e le
ngth
and
ang
le a
nd
map
obj
ects
ont
o co
ngru
ent i
mag
es
•use
stra
ight
edg
e an
d co
mpa
sses
to d
o st
anda
rd c
onst
ruct
ions
•ded
uce
and
use
form
ulae
for t
he a
rea
of a
tria
ngle
and
par
alle
logr
am, a
nd th
e vo
lum
e of
a c
uboi
d; c
alcu
late
vol
umes
an
d su
rfac
e ar
eas o
f cub
oids
•kno
w a
nd u
se th
e fo
rmul
ae fo
r the
ci
rcum
fere
nce
and
area
of a
circ
le
•des
ign
a su
rvey
or e
xper
imen
t to
capt
ure
the
nece
ssar
y da
ta fr
om o
ne
or m
ore
sour
ces;
desi
gn, t
rial a
nd, i
f ne
cess
ary,
refin
e da
ta c
olle
ctio
n sh
eets
; co
nstr
uct t
able
s for
larg
e di
scre
te a
nd
cont
inuo
us se
ts o
f raw
dat
a, c
hoos
ing
suita
ble
clas
s int
erva
ls; d
esig
n an
d us
e tw
o-w
ay ta
bles
•sel
ect,
cons
truc
t and
mod
ify, o
n pa
per
and
usin
g IC
T:
-pie
char
ts fo
r cat
egor
ical
dat
a
-bar c
hart
s and
freq
uenc
y di
agra
ms
for d
iscr
ete
and
cont
inuo
us d
ata
-sim
ple
time
grap
hs fo
r tim
e se
ries
-scat
ter g
raph
s•
and
iden
tify
whi
ch a
re m
ost u
sefu
l in
the
cont
ext o
f the
pro
blem
•fin
d an
d re
cord
all
poss
ible
mut
ually
ex
clus
ive
outc
omes
for s
ingl
e ev
ents
an
d tw
o su
cces
sive
eve
nts i
n a
syst
emat
ic w
ay
•kno
w th
at th
e su
m o
f pro
babi
litie
s of a
ll m
utua
lly e
xclu
sive
out
com
es is
1 a
nd
use
this
whe
n so
lvin
g pr
oble
ms
•com
mun
icat
e in
terp
reta
tions
and
re
sults
of a
stat
istic
al su
rvey
usi
ng
sele
cted
tabl
es, g
raph
s and
dia
gram
s in
supp
ort
Leve
l 5•i
dent
ify a
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cess
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rmat
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arry
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ugh
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sk
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e m
athe
mat
ical
pr
oble
ms
•che
ck re
sults
, co
nsid
erin
g w
heth
er
thes
e ar
e re
ason
able
•sol
ve w
ord
prob
lem
s an
d in
vest
igat
ions
from
a
rang
e of
con
text
s
•sho
w u
nder
stan
ding
of
situ
atio
ns b
y de
scrib
ing
them
mat
hem
atic
ally
us
ing
sym
bols
, wor
ds
and
diag
ram
s
•dra
w si
mpl
e co
nclu
sion
s of t
heir
own
and
give
an
expl
anat
ion
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eir
reas
onin
g
•use
und
erst
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ng o
f pl
ace
valu
e to
mul
tiply
an
d di
vide
who
le
num
bers
and
dec
imal
s by
10,
100
and
100
0 an
d ex
plai
n th
e ef
fect
•rou
nd d
ecim
als t
o th
e ne
ares
t dec
imal
pla
ce a
nd
orde
r neg
ativ
e nu
mbe
rs
in c
onte
xt
•rec
ogni
se a
nd u
se
num
ber p
atte
rns a
nd
rela
tions
hips
•use
equ
ival
ence
bet
wee
n fr
actio
ns a
nd o
rder
fr
actio
ns a
nd d
ecim
als
•red
uce
a fr
actio
n to
its
sim
ples
t for
m b
y ca
ncel
ling
com
mon
fa
ctor
s
•und
erst
and
sim
ple
ratio
•use
kno
wn
fact
s, pl
ace
valu
e,
know
ledg
e of
ope
ratio
ns a
nd b
rack
ets
to c
alcu
late
incl
udin
g us
ing
all f
our
oper
atio
ns w
ith d
ecim
als t
o tw
o pl
aces
•use
a c
alcu
lato
r whe
re a
ppro
pria
te
to c
alcu
late
frac
tions
/per
cent
ages
of
quan
titie
s/m
easu
rem
ents
•und
erst
and
and
use
an a
ppro
pria
te
non-
calc
ulat
or m
etho
d fo
r sol
ving
pr
oble
ms t
hat i
nvol
ve m
ultip
lyin
g an
d di
vidi
ng a
ny th
ree-
digi
t num
ber b
y an
y tw
o-di
git n
umbe
r
•sol
ve si
mpl
e pr
oble
ms i
nvol
ving
or
derin
g, a
ddin
g, su
btra
ctin
g ne
gativ
e nu
mbe
rs in
con
text
•sol
ve si
mpl
e pr
oble
ms i
nvol
ving
ratio
an
d di
rect
pro
port
ion
•app
ly in
vers
e op
erat
ions
and
ap
prox
imat
e to
che
ck a
nsw
ers t
o pr
oble
ms a
re o
f the
cor
rect
mag
nitu
de
•con
stru
ct, e
xpre
ss in
sym
bolic
fo
rm, a
nd u
se si
mpl
e fo
rmul
ae in
volv
ing
one
or tw
o op
erat
ions
•use
and
inte
rpre
t coo
rdin
ates
in
all
four
qua
dran
ts
•use
a w
ider
rang
e of
pro
pert
ies o
f 2-D
an
d 3-
D sh
apes
and
iden
tify
all t
he
sym
met
ries o
f 2-D
shap
es
•use
lang
uage
ass
ocia
ted
with
ang
le a
nd
know
and
use
the
angl
e su
m o
f a tr
iang
le
and
that
of a
ngle
s at a
poi
nt
•rea
son
abou
t pos
ition
and
mov
emen
t and
tr
ansf
orm
shap
es
•mea
sure
and
dra
w a
ngle
s to
the
near
est
degr
ee, w
hen
cons
truc
ting
mod
els a
nd
draw
ing
or u
sing
shap
es
•rea
d an
d in
terp
ret s
cale
s on
a ra
nge
of
mea
surin
g in
stru
men
ts, e
xpla
inin
g w
hat
each
labe
lled
divi
sion
repr
esen
ts
•sol
ve p
robl
ems i
nvol
ving
the
conv
ersi
on
of u
nits
and
mak
e se
nsib
le e
stim
ates
of a
ra
nge
of m
easu
res i
n re
latio
n to
eve
ryda
y si
tuat
ions
•und
erst
and
and
use
the
form
ula
for t
he
area
of a
rect
angl
e an
d di
stin
guis
h ar
ea
from
per
imet
er
•ask
que
stio
ns, p
lan
how
to a
nsw
er th
em
and
colle
ct th
e da
ta re
quire
d
•in
prob
abili
ty, s
elec
t met
hods
bas
ed
on e
qual
ly li
kely
out
com
es a
nd
expe
rimen
tal e
vide
nce,
as a
ppro
pria
te
•und
erst
and
and
use
the
prob
abili
ty
scal
e fr
om 0
to 1
•und
erst
and
and
use
the
mea
n of
di
scre
te d
ata
and
com
pare
two
sim
ple
dist
ribut
ions
, usi
ng th
e ra
nge
and
one
of m
ode,
med
ian
or m
ean
•und
erst
and
that
diff
eren
t out
com
es
may
resu
lt fr
om re
peat
ing
an
expe
rimen
t
•int
erpr
et g
raph
s and
dia
gram
s, in
clud
ing
pie
char
ts, a
nd d
raw
co
nclu
sion
s
•cre
ate
and
inte
rpre
t lin
e gr
aphs
whe
re
the
inte
rmed
iate
val
ues h
ave
mea
ning
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suff
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S
ecur
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Hig
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Low
6
Sec
ure
6
Hig
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4 The National Strategies | Secondary Assessing Pupil Progress at Key Stage 3: Assessment guidelines
00730-2008BKT-EN © Crown copyright 2008
5The National Strategies | Secondary Assessing Pupil Progress at Key Stage 3: Assessment guidelines
© Crown copyright 2008 00730-2008BKT-EN
Mat
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leve
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hem
atic
sN
umbe
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nd th
e nu
mbe
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stem
Calc
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pace
and
mea
sure
Han
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ta
Leve
l 6•s
olve
pro
blem
s an
d ca
rry
thro
ugh
subs
tant
ial t
asks
by
bre
akin
g th
em
into
smal
ler,
mor
e m
anag
eabl
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usin
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rang
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ef
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chni
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, m
etho
ds a
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reso
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s, in
clud
ing
ICT;
giv
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lutio
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an
appr
opria
te d
egre
e of
ac
cura
cy
•int
erpr
et, d
iscu
ss a
nd
synt
hesi
se in
form
atio
n pr
esen
ted
in a
var
iety
of
mat
hem
atic
al fo
rms
•pre
sent
a c
onci
se,
reas
oned
arg
umen
t, us
ing
sym
bols
, di
agra
ms,
grap
hs a
nd
rela
ted
expl
anat
ory
text
s
•use
logi
cal a
rgum
ent t
o es
tabl
ish
the
trut
h of
a
stat
emen
t
•use
the
equi
vale
nce
of
frac
tions
, dec
imal
s and
pe
rcen
tage
s to
com
pare
pr
opor
tions
•cal
cula
te p
erce
ntag
es a
nd fi
nd th
e ou
tcom
e of
a g
iven
per
cent
age
incr
ease
or d
ecre
ase
•div
ide
a qu
antit
y in
to tw
o or
mor
e pa
rts i
n a
give
n ra
tio a
nd so
lve
prob
lem
s inv
olvi
ng ra
tio a
nd d
irect
pr
opor
tion
•use
pro
port
iona
l rea
soni
ng to
solv
e a
prob
lem
, cho
osin
g th
e co
rrec
t nu
mbe
rs to
take
as 1
00%
, or a
s a
who
le
•add
and
subt
ract
frac
tions
by
writ
ing
them
with
a c
omm
on d
enom
inat
or,
calc
ulat
e fr
actio
ns o
f qua
ntiti
es
(frac
tion
answ
ers)
, mul
tiply
and
div
ide
an in
tege
r by
a fr
actio
n
•use
syst
emat
ic tr
ial a
nd
impr
ovem
ent m
etho
ds a
nd
ICT
tool
s to
find
appr
oxim
ate
solu
tions
to e
quat
ions
such
as
x³ +
x =
20
•con
stru
ct a
nd so
lve
linea
r eq
uatio
ns w
ith in
tege
r co
effic
ient
s, us
ing
an
appr
opria
te m
etho
d
•gen
erat
e te
rms o
f a se
quen
ce
usin
g te
rm-t
o-te
rm a
nd
posi
tion-
to-t
erm
def
initi
ons
of th
e se
quen
ce, o
n pa
per a
nd
usin
g IC
T; w
rite
an e
xpre
ssio
n to
des
crib
e th
e nt
h te
rm o
f an
arith
met
ic se
quen
ce.
•plo
t the
gra
phs o
f lin
ear
func
tions
, whe
re y
is g
iven
ex
plic
itly
in te
rms o
f x;
reco
gnis
e th
at e
quat
ions
of
the
form
y =
mx
+ c
corr
espo
nd to
stra
ight
-line
gr
aphs
•con
stru
ct fu
nctio
ns a
risin
g fr
om re
al-li
fe p
robl
ems a
nd
plot
thei
r cor
resp
ondi
ng
grap
hs;
•int
erpr
et g
raph
s aris
ing
from
re
al si
tuat
ions
•cla
ssify
qua
drila
tera
ls b
y th
eir g
eom
etric
pr
oper
ties
•sol
ve g
eom
etric
al p
robl
ems u
sing
pr
oper
ties o
f ang
les,
of p
aral
lel a
nd
inte
rsec
ting
lines
, and
of t
riang
les a
nd
othe
r pol
ygon
s
•ide
ntify
alte
rnat
e an
d co
rres
pond
ing
angl
es; u
nder
stan
d a
proo
f tha
t the
sum
of
the
angl
es o
f a tr
iang
le is
180
° and
of a
qu
adril
ater
al is
360
°
•dev
ise
inst
ruct
ions
for a
com
pute
r to
gene
rate
and
tran
sfor
m sh
apes
and
pat
hs
•vis
ualis
e an
d us
e 2-
D re
pres
enta
tions
of
3-D
obj
ects
•enl
arge
2-D
shap
es, g
iven
a c
entr
e of
en
larg
emen
t and
a p
ositi
ve w
hole
-nu
mbe
r sca
le fa
ctor
•kno
w th
at tr
ansl
atio
ns, r
otat
ions
and
re
flect
ions
pre
serv
e le
ngth
and
ang
le a
nd
map
obj
ects
ont
o co
ngru
ent i
mag
es
•use
stra
ight
edg
e an
d co
mpa
sses
to d
o st
anda
rd c
onst
ruct
ions
•ded
uce
and
use
form
ulae
for t
he a
rea
of a
tria
ngle
and
par
alle
logr
am, a
nd th
e vo
lum
e of
a c
uboi
d; c
alcu
late
vol
umes
an
d su
rfac
e ar
eas o
f cub
oids
•kno
w a
nd u
se th
e fo
rmul
ae fo
r the
ci
rcum
fere
nce
and
area
of a
circ
le
•des
ign
a su
rvey
or e
xper
imen
t to
capt
ure
the
nece
ssar
y da
ta fr
om o
ne
or m
ore
sour
ces;
desi
gn, t
rial a
nd, i
f ne
cess
ary,
refin
e da
ta c
olle
ctio
n sh
eets
; co
nstr
uct t
able
s for
larg
e di
scre
te a
nd
cont
inuo
us se
ts o
f raw
dat
a, c
hoos
ing
suita
ble
clas
s int
erva
ls; d
esig
n an
d us
e tw
o-w
ay ta
bles
•sel
ect,
cons
truc
t and
mod
ify, o
n pa
per
and
usin
g IC
T:
-pie
char
ts fo
r cat
egor
ical
dat
a
-bar c
hart
s and
freq
uenc
y di
agra
ms
for d
iscr
ete
and
cont
inuo
us d
ata
-sim
ple
time
grap
hs fo
r tim
e se
ries
-scat
ter g
raph
s•
and
iden
tify
whi
ch a
re m
ost u
sefu
l in
the
cont
ext o
f the
pro
blem
•fin
d an
d re
cord
all
poss
ible
mut
ually
ex
clus
ive
outc
omes
for s
ingl
e ev
ents
an
d tw
o su
cces
sive
eve
nts i
n a
syst
emat
ic w
ay
•kno
w th
at th
e su
m o
f pro
babi
litie
s of a
ll m
utua
lly e
xclu
sive
out
com
es is
1 a
nd
use
this
whe
n so
lvin
g pr
oble
ms
•com
mun
icat
e in
terp
reta
tions
and
re
sults
of a
stat
istic
al su
rvey
usi
ng
sele
cted
tabl
es, g
raph
s and
dia
gram
s in
supp
ort
Leve
l 5•i
dent
ify a
nd o
btai
n ne
cess
ary
info
rmat
ion
to c
arry
thro
ugh
a ta
sk
and
solv
e m
athe
mat
ical
pr
oble
ms
•che
ck re
sults
, co
nsid
erin
g w
heth
er
thes
e ar
e re
ason
able
•sol
ve w
ord
prob
lem
s an
d in
vest
igat
ions
from
a
rang
e of
con
text
s
•sho
w u
nder
stan
ding
of
situ
atio
ns b
y de
scrib
ing
them
mat
hem
atic
ally
us
ing
sym
bols
, wor
ds
and
diag
ram
s
•dra
w si
mpl
e co
nclu
sion
s of t
heir
own
and
give
an
expl
anat
ion
of th
eir
reas
onin
g
•use
und
erst
andi
ng o
f pl
ace
valu
e to
mul
tiply
an
d di
vide
who
le
num
bers
and
dec
imal
s by
10,
100
and
100
0 an
d ex
plai
n th
e ef
fect
•rou
nd d
ecim
als t
o th
e ne
ares
t dec
imal
pla
ce a
nd
orde
r neg
ativ
e nu
mbe
rs
in c
onte
xt
•rec
ogni
se a
nd u
se
num
ber p
atte
rns a
nd
rela
tions
hips
•use
equ
ival
ence
bet
wee
n fr
actio
ns a
nd o
rder
fr
actio
ns a
nd d
ecim
als
•red
uce
a fr
actio
n to
its
sim
ples
t for
m b
y ca
ncel
ling
com
mon
fa
ctor
s
•und
erst
and
sim
ple
ratio
•use
kno
wn
fact
s, pl
ace
valu
e,
know
ledg
e of
ope
ratio
ns a
nd b
rack
ets
to c
alcu
late
incl
udin
g us
ing
all f
our
oper
atio
ns w
ith d
ecim
als t
o tw
o pl
aces
•use
a c
alcu
lato
r whe
re a
ppro
pria
te
to c
alcu
late
frac
tions
/per
cent
ages
of
quan
titie
s/m
easu
rem
ents
•und
erst
and
and
use
an a
ppro
pria
te
non-
calc
ulat
or m
etho
d fo
r sol
ving
pr
oble
ms t
hat i
nvol
ve m
ultip
lyin
g an
d di
vidi
ng a
ny th
ree-
digi
t num
ber b
y an
y tw
o-di
git n
umbe
r
•sol
ve si
mpl
e pr
oble
ms i
nvol
ving
or
derin
g, a
ddin
g, su
btra
ctin
g ne
gativ
e nu
mbe
rs in
con
text
•sol
ve si
mpl
e pr
oble
ms i
nvol
ving
ratio
an
d di
rect
pro
port
ion
•app
ly in
vers
e op
erat
ions
and
ap
prox
imat
e to
che
ck a
nsw
ers t
o pr
oble
ms a
re o
f the
cor
rect
mag
nitu
de
•con
stru
ct, e
xpre
ss in
sym
bolic
fo
rm, a
nd u
se si
mpl
e fo
rmul
ae in
volv
ing
one
or tw
o op
erat
ions
•use
and
inte
rpre
t coo
rdin
ates
in
all
four
qua
dran
ts
•use
a w
ider
rang
e of
pro
pert
ies o
f 2-D
an
d 3-
D sh
apes
and
iden
tify
all t
he
sym
met
ries o
f 2-D
shap
es
•use
lang
uage
ass
ocia
ted
with
ang
le a
nd
know
and
use
the
angl
e su
m o
f a tr
iang
le
and
that
of a
ngle
s at a
poi
nt
•rea
son
abou
t pos
ition
and
mov
emen
t and
tr
ansf
orm
shap
es
•mea
sure
and
dra
w a
ngle
s to
the
near
est
degr
ee, w
hen
cons
truc
ting
mod
els a
nd
draw
ing
or u
sing
shap
es
•rea
d an
d in
terp
ret s
cale
s on
a ra
nge
of
mea
surin
g in
stru
men
ts, e
xpla
inin
g w
hat
each
labe
lled
divi
sion
repr
esen
ts
•sol
ve p
robl
ems i
nvol
ving
the
conv
ersi
on
of u
nits
and
mak
e se
nsib
le e
stim
ates
of a
ra
nge
of m
easu
res i
n re
latio
n to
eve
ryda
y si
tuat
ions
•und
erst
and
and
use
the
form
ula
for t
he
area
of a
rect
angl
e an
d di
stin
guis
h ar
ea
from
per
imet
er
•ask
que
stio
ns, p
lan
how
to a
nsw
er th
em
and
colle
ct th
e da
ta re
quire
d
•in
prob
abili
ty, s
elec
t met
hods
bas
ed
on e
qual
ly li
kely
out
com
es a
nd
expe
rimen
tal e
vide
nce,
as a
ppro
pria
te
•und
erst
and
and
use
the
prob
abili
ty
scal
e fr
om 0
to 1
•und
erst
and
and
use
the
mea
n of
di
scre
te d
ata
and
com
pare
two
sim
ple
dist
ribut
ions
, usi
ng th
e ra
nge
and
one
of m
ode,
med
ian
or m
ean
•und
erst
and
that
diff
eren
t out
com
es
may
resu
lt fr
om re
peat
ing
an
expe
rimen
t
•int
erpr
et g
raph
s and
dia
gram
s, in
clud
ing
pie
char
ts, a
nd d
raw
co
nclu
sion
s
•cre
ate
and
inte
rpre
t lin
e gr
aphs
whe
re
the
inte
rmed
iate
val
ues h
ave
mea
ning
BL
IE
Key:
BL-B
elow
Lev
el
IE-In
suff
icie
nt E
vide
nce
Ove
rall
asse
ssm
ent (
tick
one
box
only
)Lo
w 5
S
ecur
e 5
Hig
h 5
Low
6
Sec
ure
6
Hig
h 6
Mat
hem
atic
s ass
essm
ent g
uide
lines
: lev
els 6
and
7
leve
ls 6
and
7
Pup
il na
me…
……
……
……
.Cla
ss/g
roup
……
……
……
…..D
ate…
……
…
Usi
ng a
nd a
pply
ing
mat
hem
atic
sN
umbe
rs a
nd
the
num
ber
syst
em
Calc
ulat
ing
Alg
ebra
Shap
e, s
pace
and
mea
sure
Han
dlin
g da
ta
Leve
l 7•s
olve
incr
easi
ngly
de
man
ding
pro
blem
s an
d ev
alua
te so
lutio
ns;
expl
ore
conn
ectio
ns
in m
athe
mat
ics a
cros
s a
rang
e of
con
text
s: nu
mbe
r, al
gebr
a, sh
ape,
sp
ace
and
mea
sure
s, an
d ha
ndlin
g da
ta; r
efin
e or
ex
tend
the
mat
hem
atic
s us
ed to
gen
erat
e fu
ller
solu
tions
•giv
e re
ason
s for
cho
ice
of
pres
enta
tion,
exp
lain
ing
sele
cted
feat
ures
and
sh
owin
g in
sigh
t int
o th
e pr
oble
ms s
truc
ture
•jus
tify
gene
ralis
atio
ns,
argu
men
ts o
r sol
utio
ns
•app
reci
ate
the
diff
eren
ce
betw
een
mat
hem
atic
al
expl
anat
ion
and
expe
rimen
tal e
vide
nce
•und
erst
and
and
use
prop
ortio
nalit
y
•cal
cula
te th
e re
sult
of a
ny
prop
ortio
nal c
hang
e us
ing
mul
tiplic
ativ
e m
etho
ds
•und
erst
and
the
effe
cts o
f m
ultip
lyin
g an
d di
vidi
ng
by n
umbe
rs b
etw
een
0 an
d 1,
add
, sub
trac
t, m
ultip
ly a
nd d
ivid
e fr
actio
ns
•mak
e an
d ju
stify
est
imat
es
and
appr
oxim
atio
ns o
f ca
lcul
atio
ns; e
stim
ate
calc
ulat
ions
by
roun
ding
nu
mbe
rs to
one
sign
ifica
nt
figur
e an
d m
ultip
lyin
g an
d di
vidi
ng m
enta
lly
•use
a c
alcu
lato
r eff
icie
ntly
an
d ap
prop
riate
ly
to p
erfo
rm c
ompl
ex
calc
ulat
ions
with
num
bers
of
any
size
, kno
win
g no
t to
roun
d du
ring
inte
rmed
iate
st
eps o
f a c
alcu
latio
n
•squ
are
a lin
ear e
xpre
ssio
n, a
nd
expa
nd a
nd si
mpl
ify th
e pr
oduc
t of
two
linea
r exp
ress
ions
of t
he fo
rm (x
±
n) a
nd si
mpl
ify th
e co
rres
pond
ing
quad
ratic
exp
ress
ion
•use
alg
ebra
ic a
nd g
raph
ical
m
etho
ds to
solv
e si
mul
tane
ous
linea
r equ
atio
ns in
two
varia
bles
•sol
ve in
equa
litie
s in
one
varia
ble
and
repr
esen
t the
solu
tion
set o
n a
num
ber l
ine
•use
form
ulae
from
mat
hem
atic
s and
ot
her s
ubje
cts;
subs
titut
e nu
mbe
rs
into
exp
ress
ions
and
form
ulae
; de
rive
a fo
rmul
a an
d, in
sim
ple
case
s, ch
ange
its s
ubje
ct
•fin
d th
e ne
xt te
rm a
nd n
th te
rm o
f qu
adra
tic se
quen
ces a
nd fu
nctio
ns
and
expl
ore
thei
r pro
pert
ies
•plo
t gra
phs o
f sim
ple
quad
ratic
and
cu
bic
func
tions
, e.g
. y =
x²,
y =
3x²
+ 4,
y =
x³
•und
erst
and
and
appl
y Py
thag
oras
’ the
orem
whe
n so
lvin
g pr
oble
ms i
n 2-
D
•cal
cula
te le
ngth
s, ar
eas a
nd v
olum
es in
pla
ne
shap
es a
nd ri
ght p
rism
s
•enl
arge
2-D
shap
es, g
iven
a c
entr
e of
enl
arge
men
t an
d a
frac
tiona
l sca
le fa
ctor
, on
pape
r and
usi
ng
ICT;
reco
gnis
e th
e si
mila
rity
of th
e re
sulti
ng
shap
es
•fin
d th
e lo
cus o
f a p
oint
that
mov
es a
ccor
ding
to a
gi
ven
rule
, bot
h by
reas
onin
g an
d us
ing
ICT
•rec
ogni
se th
at m
easu
rem
ents
giv
en to
the
near
est
who
le u
nit m
ay b
e in
accu
rate
by
up to
one
-hal
f of
the
unit
in e
ither
dire
ctio
n
•und
erst
and
and
use
mea
sure
s of s
peed
(and
oth
er
com
poun
d m
easu
res s
uch
as d
ensi
ty o
r pre
ssur
e)
to so
lve
prob
lem
s
•sug
gest
a p
robl
em to
exp
lore
usi
ng st
atis
tical
m
etho
ds, f
ram
e qu
estio
ns a
nd ra
ise
conj
ectu
res;
iden
tify
poss
ible
sour
ces o
f bia
s and
pla
n ho
w to
m
inim
ise
it
•sel
ect,
cons
truc
t and
mod
ify, o
n pa
per a
nd u
sing
IC
T su
itabl
e gr
aphi
cal r
epre
sent
atio
n to
pro
gres
s an
enq
uiry
incl
udin
g fr
eque
ncy
poly
gons
and
lin
es o
f bes
t fit
on sc
atte
r gra
phs
•est
imat
e th
e m
ean,
med
ian
and
rang
e of
a se
t of
gro
uped
dat
a an
d de
term
ine
the
mod
al c
lass
, se
lect
ing
the
stat
istic
mos
t app
ropr
iate
to th
e lin
e of
enq
uiry
•com
pare
two
or m
ore
dist
ribut
ions
and
mak
e in
fere
nces
, usi
ng th
e sh
ape
of th
e di
strib
utio
ns
and
mea
sure
s of a
vera
ge a
nd ra
nge
•und
erst
and
rela
tive
freq
uenc
y as
an
estim
ate
of
prob
abili
ty a
nd u
se th
is to
com
pare
out
com
es o
f an
exp
erim
ent
•exa
min
e cr
itica
lly th
e re
sults
of a
stat
istic
al
enqu
iry, a
nd ju
stify
the
choi
ce o
f sta
tistic
al
repr
esen
tatio
n in
writ
ten
pres
enta
tion
Leve
l 6•s
olve
pro
blem
s and
car
ry
thro
ugh
subs
tant
ial
task
s by
brea
king
them
in
to sm
alle
r, m
ore
man
agea
ble
task
s, us
ing
a ra
nge
of e
ffic
ient
te
chni
ques
, met
hods
an
d re
sour
ces,
incl
udin
g IC
T; g
ive
solu
tions
to a
n ap
prop
riate
deg
ree
of
accu
racy
•int
erpr
et, d
iscu
ss a
nd
synt
hesi
se in
form
atio
n pr
esen
ted
in a
var
iety
of
mat
hem
atic
al fo
rms
•pre
sent
a c
onci
se,
reas
oned
arg
umen
t, us
ing
sym
bols
, dia
gram
s, gr
aphs
and
rela
ted
expl
anat
ory
text
s
•use
logi
cal a
rgum
ent t
o es
tabl
ish
the
trut
h of
a
stat
emen
t
•use
the
equi
vale
nce
of fr
actio
ns,
deci
mal
s and
pe
rcen
tage
s to
com
pare
pr
opor
tions
•cal
cula
te p
erce
ntag
es
and
find
the
outc
ome
of a
gi
ven
perc
enta
ge in
crea
se
or d
ecre
ase
•div
ide
a qu
antit
y in
to tw
o or
mor
e pa
rts i
n a
give
n ra
tio a
nd so
lve
prob
lem
s in
volv
ing
ratio
and
dire
ct
prop
ortio
n
•use
pro
port
iona
l re
ason
ing
to so
lve
a pr
oble
m, c
hoos
ing
the
corr
ect n
umbe
rs to
take
as
100%
, or a
s a w
hole
•add
and
subt
ract
frac
tions
by
writ
ing
them
with
a
com
mon
den
omin
ator
, ca
lcul
ate
frac
tions
of
quan
titie
s (fr
actio
n an
swer
s), m
ultip
ly a
nd
divi
de a
n in
tege
r by
a fr
actio
n
•use
syst
emat
ic tr
ial a
nd
impr
ovem
ent m
etho
ds a
nd IC
T to
ols t
o fin
d ap
prox
imat
e so
lutio
ns
to e
quat
ions
such
as x
³ + x
= 2
0
•con
stru
ct a
nd so
lve
linea
r equ
atio
ns
with
inte
ger c
oeff
icie
nts,
usin
g an
ap
prop
riate
met
hod
•gen
erat
e te
rms o
f a se
quen
ce u
sing
te
rm-t
o-te
rm a
nd p
ositi
on-t
o-te
rm d
efin
ition
s of t
he se
quen
ce,
on p
aper
and
usi
ng IC
T; w
rite
an
expr
essi
on to
des
crib
e th
e nt
h te
rm
of a
n ar
ithm
etic
sequ
ence
.
•plo
t the
gra
phs o
f lin
ear f
unct
ions
, w
here
y is
giv
en e
xplic
itly
in te
rms
of x
; rec
ogni
se th
at e
quat
ions
of
the
form
y =
mx
+ c
corr
espo
nd to
st
raig
ht-li
ne g
raph
s
•con
stru
ct fu
nctio
ns a
risin
g fr
om
real
-life
pro
blem
s and
plo
t the
ir co
rres
pond
ing
grap
hs;
•int
erpr
et g
raph
s aris
ing
from
real
si
tuat
ions
•cla
ssify
qua
drila
tera
ls b
y th
eir g
eom
etric
pr
oper
ties
•sol
ve g
eom
etric
al p
robl
ems u
sing
pro
pert
ies o
f an
gles
, of p
aral
lel a
nd in
ters
ectin
g lin
es, a
nd o
f tr
iang
les a
nd o
ther
pol
ygon
s
•ide
ntify
alte
rnat
e an
d co
rres
pond
ing
angl
es;
unde
rsta
nd a
pro
of th
at th
e su
m o
f the
ang
les o
f a
tria
ngle
is 1
80° a
nd o
f a q
uadr
ilate
ral i
s 360
°
•dev
ise
inst
ruct
ions
for a
com
pute
r to
gene
rate
an
d tr
ansf
orm
shap
es a
nd p
aths
•vis
ualis
e an
d us
e 2-
D re
pres
enta
tions
of 3
-D
obje
cts
•enl
arge
2-D
shap
es, g
iven
a c
entr
e of
enl
arge
men
t an
d a
posi
tive
who
le-n
umbe
r sca
le fa
ctor
•kno
w th
at tr
ansl
atio
ns, r
otat
ions
and
refle
ctio
ns
pres
erve
leng
th a
nd a
ngle
and
map
obj
ects
ont
o co
ngru
ent i
mag
es
•use
stra
ight
edg
e an
d co
mpa
sses
to d
o st
anda
rd
cons
truc
tions
•ded
uce
and
use
form
ulae
for t
he a
rea
of a
tria
ngle
an
d pa
ralle
logr
am, a
nd th
e vo
lum
e of
a c
uboi
d;
calc
ulat
e vo
lum
es a
nd su
rfac
e ar
eas o
f cub
oids
•kno
w a
nd u
se th
e fo
rmul
ae fo
r the
circ
umfe
renc
e an
d ar
ea o
f a c
ircle
•des
ign
a su
rvey
or e
xper
imen
t to
capt
ure
the
nece
ssar
y da
ta fr
om o
ne o
r mor
e so
urce
s; de
sign
, tr
ial a
nd, i
f nec
essa
ry, r
efin
e da
ta c
olle
ctio
n sh
eets
; co
nstr
uct t
able
s for
larg
e di
scre
te a
nd c
ontin
uous
se
ts o
f raw
dat
a, c
hoos
ing
suita
ble
clas
s int
erva
ls;
desi
gn a
nd u
se tw
o-w
ay ta
bles
•sel
ect,
cons
truc
t and
mod
ify, o
n pa
per a
nd u
sing
IC
T: -pie
char
ts fo
r cat
egor
ical
dat
a
-bar c
hart
s and
freq
uenc
y di
agra
ms f
or
disc
rete
and
con
tinuo
us d
ata
-sim
ple
time
grap
hs fo
r tim
e se
ries
-scat
ter g
raph
s•
and
iden
tify
whi
ch a
re m
ost u
sefu
l in
the
cont
ext
of th
e pr
oble
m
•fin
d an
d re
cord
all
poss
ible
mut
ually
exc
lusi
ve
outc
omes
for s
ingl
e ev
ents
and
two
succ
essi
ve
even
ts in
a sy
stem
atic
way
•kno
w th
at th
e su
m o
f pro
babi
litie
s of a
ll m
utua
lly
excl
usiv
e ou
tcom
es is
1 a
nd u
se th
is w
hen
solv
ing
prob
lem
s
•com
mun
icat
e in
terp
reta
tions
and
resu
lts o
f a
stat
istic
al su
rvey
usi
ng se
lect
ed ta
bles
, gra
phs a
nd
diag
ram
s in
supp
ort
BL
IE
Key:
BL-B
elow
leve
l IE
-Insu
ffic
ient
evi
denc
e
Ove
rall
asse
ssm
ent (
tick
one
box
only
) L
ow 6
S
ecur
e 6
Hig
h 6
Low
7
Sec
ure
7
Hig
h 7
6 The National Strategies | Secondary Assessing Pupil Progress at Key Stage 3: Assessment guidelines
00730-2008BKT-EN © Crown copyright 2008
Mat
hem
atic
s ass
essm
ent g
uide
lines
: lev
els 7
and
8
Pupi
l nam
e……
……
……
….C
lass
/gro
up…
……
……
……
..Dat
e……
……
Usi
ng a
nd a
pply
ing
mat
hem
atic
sN
umbe
rs a
nd th
e nu
mbe
r sys
tem
Calc
ulat
ing
Alg
ebra
Shap
e, s
pace
and
mea
sure
Han
dlin
g da
ta
Leve
l 8•d
evel
op a
nd fo
llow
alte
rnat
ive
met
hods
and
app
roac
hes
•ref
lect
on
lines
of e
nqui
ry w
hen
expl
orin
g m
athe
mat
ical
task
s
•sel
ect a
nd c
ombi
ne k
now
n fa
cts
and
prob
lem
-sol
ving
stra
tegi
es
to so
lve
prob
lem
s of i
ncre
asin
g co
mpl
exity
•con
vey
mat
hem
atic
al m
eani
ng
thro
ugh
prec
ise
and
cons
iste
nt
use
of sy
mbo
ls
•exa
min
e ge
nera
lisat
ions
or
solu
tions
reac
hed
in a
n ac
tivity
, co
mm
entin
g co
nstr
uctiv
ely
on th
e re
ason
ing
and
logi
c or
the
proc
ess
empl
oyed
, or t
he re
sults
obt
aine
d
•dis
tingu
ish
betw
een
prac
tical
de
mon
stra
tion
and
proo
f; kn
ow u
nder
lyin
g as
sum
ptio
ns,
reco
gnis
ing
thei
r im
port
ance
an
d lim
itatio
ns, a
nd th
e ef
fect
of
vary
ing
them
•und
erst
and
the
equi
vale
nce
betw
een
recu
rrin
g de
cim
als a
nd
frac
tions
•use
frac
tions
or
perc
enta
ges t
o so
lve
prob
lem
s inv
olvi
ng
repe
ated
pro
port
iona
l ch
ange
s or t
he c
alcu
latio
n of
the
orig
inal
qua
ntity
gi
ven
the
resu
lt of
a
prop
ortio
nal c
hang
e
•sol
ve p
robl
ems i
nvol
ving
ca
lcul
atin
g w
ith p
ower
s, ro
ots a
nd n
umbe
rs
expr
esse
d in
stan
dard
form
, ch
ecki
ng fo
r cor
rect
ord
er
of m
agni
tude
and
usi
ng a
ca
lcul
ator
as a
ppro
pria
te
•fac
toris
e qu
adra
tic e
xpre
ssio
ns
incl
udin
g th
e di
ffer
ence
of t
wo
squa
res,
e.g.
: x² –
9 =
(x +
3) (
x –
3)
•man
ipul
ate
alge
brai
c fo
rmul
ae,
equa
tions
and
exp
ress
ions
, fin
ding
co
mm
on fa
ctor
s and
mul
tiply
ing
two
linea
r exp
ress
ions
•der
ive
and
use
mor
e co
mpl
ex fo
rmul
ae
and
chan
ge th
e su
bjec
t of a
form
ula
•eva
luat
e al
gebr
aic
form
ulae
, su
bstit
utin
g fr
actio
ns, d
ecim
als a
nd
nega
tive
num
bers
•sol
ve in
equa
litie
s in
two
varia
bles
and
fin
d th
e so
lutio
n se
t
•ske
tch,
inte
rpre
t and
iden
tify
grap
hs o
f lin
ear,
quad
ratic
, cub
ic a
nd re
cipr
ocal
fu
nctio
ns, a
nd g
raph
s tha
t mod
el re
al
situ
atio
ns
•und
erst
and
the
effe
ct o
n a
grap
h of
ad
ditio
n of
(or m
ultip
licat
ion
by)
a co
nsta
nt
•und
erst
and
and
use
cong
ruen
ce
and
mat
hem
atic
al si
mila
rity
•und
erst
and
and
use
trig
onom
etric
al re
latio
nshi
ps
in ri
ght-
angl
ed tr
iang
les,
and
use
thes
e to
solv
e pr
oble
ms,
incl
udin
g th
ose
invo
lvin
g be
arin
gs
•und
erst
and
the
diff
eren
ce
betw
een
form
ulae
for p
erim
eter
, ar
ea a
nd v
olum
e in
sim
ple
cont
exts
by
cons
ider
ing
dim
ensi
ons
•est
imat
e an
d fin
d th
e m
edia
n, q
uart
iles
and
inte
rqua
rtile
rang
e fo
r lar
ge d
ata
sets
, in
clud
ing
usin
g a
cum
ulat
ive
freq
uenc
y di
agra
m
•com
pare
two
or m
ore
dist
ribut
ions
and
m
ake
infe
renc
es, u
sing
the
shap
e of
the
dist
ribut
ions
and
mea
sure
s of a
vera
ge a
nd
spre
ad in
clud
ing
med
ian
and
quar
tiles
•kno
w w
hen
to a
dd o
r mul
tiply
two
prob
abili
ties
•use
tree
dia
gram
s to
calc
ulat
e pr
obab
ilitie
s of
com
bina
tions
of i
ndep
ende
nt e
vent
s
Leve
l 7•s
olve
incr
easi
ngly
dem
andi
ng
prob
lem
s and
eva
luat
e so
lutio
ns; e
xplo
re c
onne
ctio
ns
in m
athe
mat
ics a
cros
s a ra
nge
of c
onte
xts:
num
ber,
alge
bra,
sh
ape,
spac
e an
d m
easu
res,
and
hand
ling
data
; ref
ine
or e
xten
d th
e m
athe
mat
ics u
sed
to g
ener
ate
fulle
r sol
utio
ns
•giv
e re
ason
s for
cho
ice
of
pres
enta
tion,
exp
lain
ing
sele
cted
fe
atur
es a
nd sh
owin
g in
sigh
t int
o th
e pr
oble
ms s
truc
ture
•jus
tify
gene
ralis
atio
ns, a
rgum
ents
or
solu
tions
•app
reci
ate
the
diff
eren
ce b
etw
een
mat
hem
atic
al e
xpla
natio
n an
d ex
perim
enta
l evi
denc
e
•und
erst
and
and
use
prop
ortio
nalit
y
•cal
cula
te th
e re
sult
of a
ny
prop
ortio
nal c
hang
e us
ing
mul
tiplic
ativ
e m
etho
ds
•und
erst
and
the
effe
cts o
f m
ultip
lyin
g an
d di
vidi
ng b
y nu
mbe
rs b
etw
een
0 an
d 1,
ad
d, su
btra
ct, m
ultip
ly a
nd
divi
de fr
actio
ns
•mak
e an
d ju
stify
est
imat
es
and
appr
oxim
atio
ns o
f ca
lcul
atio
ns; e
stim
ate
calc
ulat
ions
by
roun
ding
nu
mbe
rs to
one
sign
ifica
nt
figur
e an
d m
ultip
lyin
g an
d di
vidi
ng m
enta
lly
•use
a c
alcu
lato
r eff
icie
ntly
an
d ap
prop
riate
ly
to p
erfo
rm c
ompl
ex
calc
ulat
ions
with
num
bers
of
any
size
, kno
win
g no
t to
roun
d du
ring
inte
rmed
iate
st
eps o
f a c
alcu
latio
n
•squ
are
a lin
ear e
xpre
ssio
n, a
nd e
xpan
d an
d si
mpl
ify th
e pr
oduc
t of t
wo
linea
r ex
pres
sion
s of t
he fo
rm (x
± n
) and
si
mpl
ify th
e co
rres
pond
ing
quad
ratic
ex
pres
sion
•use
alg
ebra
ic a
nd g
raph
ical
met
hods
to
solv
e si
mul
tane
ous l
inea
r equ
atio
ns
in tw
o va
riabl
es
•sol
ve in
equa
litie
s in
one
varia
ble
and
repr
esen
t the
solu
tion
set o
n a
num
ber
line
•use
form
ulae
from
mat
hem
atic
s and
ot
her s
ubje
cts;
subs
titut
e nu
mbe
rs
into
exp
ress
ions
and
form
ulae
; der
ive
a fo
rmul
a an
d, in
sim
ple
case
s, ch
ange
its
subj
ect
•fin
d th
e ne
xt te
rm a
nd n
th te
rm o
f qu
adra
tic se
quen
ces a
nd fu
nctio
ns
and
expl
ore
thei
r pro
pert
ies
•plo
t gra
phs o
f sim
ple
quad
ratic
and
cu
bic
func
tions
, e.g
. y =
x²,
y =
3x² +
4,
y =
x³
•und
erst
and
and
appl
y Py
thag
oras
’ the
orem
whe
n so
lvin
g pr
oble
ms i
n 2-
D
•cal
cula
te le
ngth
s, ar
eas a
nd
volu
mes
in p
lane
shap
es a
nd
right
pris
ms
•enl
arge
2-D
shap
es, g
iven
a
cent
re o
f enl
arge
men
t and
a
frac
tiona
l sca
le fa
ctor
, on
pape
r an
d us
ing
ICT;
reco
gnis
e th
e si
mila
rity
of th
e re
sulti
ng sh
apes
•fin
d th
e lo
cus o
f a p
oint
that
m
oves
acc
ordi
ng to
a g
iven
rule
, bo
th b
y re
ason
ing
and
usin
g IC
T
•rec
ogni
se th
at m
easu
rem
ents
gi
ven
to th
e ne
ares
t who
le u
nit
may
be
inac
cura
te b
y up
to o
ne-
half
of th
e un
it in
eith
er d
irect
ion
•und
erst
and
and
use
mea
sure
s of
spee
d (a
nd o
ther
com
poun
d m
easu
res s
uch
as d
ensi
ty o
r pr
essu
re) t
o so
lve
prob
lem
s
•sug
gest
a p
robl
em to
exp
lore
usi
ng
stat
istic
al m
etho
ds, f
ram
e qu
estio
ns a
nd
rais
e co
njec
ture
s; id
entif
y po
ssib
le so
urce
s of
bia
s and
pla
n ho
w to
min
imis
e it
•sel
ect,
cons
truc
t and
mod
ify, o
n pa
per a
nd
usin
g IC
T su
itabl
e gr
aphi
cal r
epre
sent
atio
n to
pro
gres
s an
enqu
iry in
clud
ing
freq
uenc
y po
lygo
ns a
nd li
nes o
f bes
t fit
on sc
atte
r gr
aphs
•est
imat
e th
e m
ean,
med
ian
and
rang
e of
a
set o
f gro
uped
dat
a an
d de
term
ine
the
mod
al c
lass
, sel
ectin
g th
e st
atis
tic m
ost
appr
opria
te to
the
line
of e
nqui
ry
•com
pare
two
or m
ore
dist
ribut
ions
and
m
ake
infe
renc
es, u
sing
the
shap
e of
the
dist
ribut
ions
and
mea
sure
s of a
vera
ge a
nd
rang
e
•und
erst
and
rela
tive
freq
uenc
y as
an
estim
ate
of p
roba
bilit
y an
d us
e th
is to
co
mpa
re o
utco
mes
of a
n ex
perim
ent
•exa
min
e cr
itica
lly th
e re
sults
of a
stat
istic
al
enqu
iry, a
nd ju
stify
the
choi
ce o
f sta
tistic
al
repr
esen
tatio
n in
writ
ten
pres
enta
tion
BL
IE
Key:
BL-B
elow
Lev
el
IE-In
suff
icie
nt E
vide
nce
Ove
rall
asse
ssm
ent (
tick
one
box
only
)Lo
w 7
S
ecur
e 7
Hig
h 7
Low
8
Sec
ure
8
Hig
h 8
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