No
rfolk
an
d S
uffo
lk P
rima
ry A
ss
es
sm
en
t Wo
rkin
g P
arty
Th
is p
roje
ct w
as
led
by th
e E
du
ca
tor S
olu
tion
s M
ath
em
atic
s T
ea
m
an
d fu
nd
ed
by th
e N
orfo
lk a
nd
Su
ffolk
Ma
ths
Hu
b.
Gu
ida
nc
e o
n fo
rma
tive
as
se
ss
me
nt m
ate
rials
to e
xe
mp
lify flu
en
cy, re
as
on
ing
an
d p
rob
lem
so
lvin
g
Ye
ar 4
For m
ore
info
rmatio
n a
nd to
mak
e a
bo
okin
g
ww
w.e
du
ca
tors
olu
tion
s.o
rg.u
k o
r ca
ll 01
60
3 3
077
10
De
ar C
olle
agu
e
Ple
ase
find
atta
ch
ed
gu
ida
nce
writte
n b
y N
orfo
lk a
nd
Suffo
lk P
rima
ry te
ach
ers
to h
elp
un
pic
k
wh
at flu
en
cy, re
ason
ing a
nd
pro
ble
m s
olv
ing lo
oks lik
e in
ye
ar g
rou
ps 1
-6.
Ra
tion
ale
The
se
mate
rials
we
re p
rod
uce
d b
ecau
se
teach
ers
hig
hlig
hte
d a
ga
p o
n h
ow
to te
ach a
nd
asse
ss th
e P
urp
ose
of S
tud
y a
nd
the
thre
e a
ims o
f the
Prim
ary
ma
the
ma
tics c
urric
ulu
m (D
fE,
20
13
). Pre
vio
us in
ca
rna
tion
s o
f the
Prim
ary
Ma
them
atic
s N
atio
na
l Cu
rricu
lum
ha
ve
alw
ays
inclu
de
d g
uid
an
ce
(and
usua
lly o
bje
ctiv
es) o
n th
is a
rea
, alth
ou
gh
the
y h
ave
be
en k
no
wn
un
de
r
ma
ny d
iffere
nt n
am
es s
uch
as u
sin
g a
nd
ap
ply
ing, w
ork
ing m
ath
em
atic
ally
, pro
ble
m s
olv
ing o
r
inve
stig
atio
ns.
Alth
ou
gh
ea
ch
ye
ar g
rou
p c
on
tain
s o
bje
ctiv
es fo
r the
con
ten
t of th
e n
ew
cu
rricu
lum
(DfE
, 20
13
),
the
re a
re fe
w re
fere
nce
s in
the
bo
dy o
f the N
atio
na
l Cu
rricu
lum
tha
t exe
mp
lify flu
en
cy,
rea
so
nin
g o
r pro
ble
m s
olv
ing, a
nd
ye
t the
se
thre
e a
ims w
ill be
ob
se
rve
d, e
xa
min
ed
an
d te
ste
d.
In a
dd
ition to
the
se
mea
su
res th
ere
are
ma
ny (e
.g. N
RIC
H) w
ho
be
lieve
the
se a
ims a
re
pa
rticu
larly
imp
orta
nt w
ithin
the
lea
rnin
g o
f ma
them
atic
s fo
r all c
hild
ren
.
Org
an
isa
tion
of m
ate
rial
The
ma
teria
ls h
ave
bee
n p
rod
uce
d in
sin
gle
age
ye
ar g
rou
ps.
Tea
ch
ers
loo
ked
at a
nd
iden
tified
the b
ig id
ea
s in
ma
them
atic
s. T
en
big
ide
as w
ere
iden
tified
acro
ss e
ve
ry y
ea
r gro
up
. Th
ese
we
re in
form
ed
by th
e N
atio
na
l Cu
rricu
lum
ob
jectiv
es, th
e N
AH
T
KP
I’s (k
ey p
erfo
rma
nce
ind
icato
rs) a
nd
oth
er s
ou
rce
s s
uch
as N
CE
TM
an
d N
RIC
H. T
he
se
big
ide
as a
re o
nly
su
gge
stio
ns a
nd
co
uld
be
ch
ange
d, d
ele
ted o
r ad
ded
to d
ep
en
din
g o
n s
cho
ol
sp
ecific
crite
ria a
nd
foci.
Un
de
r ea
ch
big
ide
a a
re th
ree
bo
xe
s fo
r fluency, re
aso
nin
g a
nd
pro
ble
m s
olv
ing. T
he
first p
art o
f
ea
ch
bo
x in
clu
de
s s
om
e e
xe
mp
lificatio
n fo
r ea
ch
aim
. Th
ese s
tate
me
nts
are
inte
nde
d to
help
su
ppo
rt the
un
de
rsta
nd
ing o
f ea
ch
aim
with
in th
e b
ig id
ea
. Ho
we
ve
r, as a
bo
ve
, the
y a
re n
ot a
defin
itive
or c
om
ple
te lis
t and
tea
che
rs s
hou
ld c
ha
nge
an
d a
lter th
em
acco
rdin
gly
.
The
se
co
nd p
art o
f the b
ox in
clu
de
s s
om
e p
ossib
le a
ctiv
ities th
at c
ou
ld h
elp
sup
po
rt the
exe
mp
lifica
tion
of e
ach a
im. T
he
se
activ
ities h
ave
be
en s
ele
cte
d b
y th
e te
ache
rs a
nd
are
the
re
to s
up
po
rt the te
ach
ing a
nd le
arn
ing o
f ea
ch
aim
, bu
t are
no
t me
an
t to b
eco
me
a c
he
cklis
t.
Ma
ny o
f the a
ctiv
ities a
re th
e te
ach
er’s
ow
n, b
ut if th
ey b
elo
ng to
a s
ou
rce
this
ha
s b
ee
n
ackn
ow
led
ge
d u
nd
ern
ea
th th
e a
ctiv
ity. H
ow
eve
r, wh
ile th
is s
ectio
n is
usefu
l, the
bo
x w
hic
h
offe
rs p
ossib
le e
xe
mp
lificatio
n fo
r ea
ch
aim
is m
ore
impo
rtan
t in u
nde
rsta
nd
ing th
e p
urp
ose o
f
stu
dy o
f the
ma
them
atic
s c
urric
ulu
m.
For m
ore
info
rmatio
n a
nd to
mak
e a
bo
okin
g
ww
w.e
du
ca
tors
olu
tion
s.o
rg.u
k o
r ca
ll 01
60
3 3
077
10
Wo
rkin
g P
arty
Th
is p
roje
ct w
as le
d b
y th
e E
du
ca
tor S
olu
tions M
ath
em
atic
s T
eam
(Alis
on
Bo
rthw
ick) a
nd
fun
de
d b
y th
e N
orfo
lk a
nd
Suffo
lk M
ath
s H
ub .
Pe
op
le w
ho c
ontrib
ute
d to
the m
ate
rials
Co
pyrig
ht a
nd
us
ag
e o
f the
ma
teria
ls
Re
pro
du
ce
d w
ith k
ind
pe
rmis
sio
n o
f NR
ICH
, Un
ive
rsity
of C
am
brid
ge
.
Exa
mp
les fro
m T
ea
ch
ing
for M
aste
ry m
ate
rials
, text ©
Cro
wn
Co
pyrig
ht 2
015
, illustra
tion
an
d
de
sig
n ©
Oxfo
rd U
niv
ers
ity P
ress 2
01
5, a
re re
pro
du
ce
d w
ith th
e k
ind
pe
rmis
sio
n o
f the
NC
ET
M
an
d O
xfo
rd U
niv
ers
ity P
ress. T
he T
ea
ch
ing
for M
aste
ry m
ate
rials
ca
n b
e fo
und
in fu
ll on th
e
NC
ET
M w
eb
site
ww
w.n
ce
tm.o
rg.u
k/re
so
urc
es/4
668
9 a
nd
the
Oxfo
rd O
wl w
eb
site
http
s://
ww
w.o
xfo
rdo
wl.c
o.u
k/fo
r-s
ch
oo
l/18
16
With
in th
e p
ossib
le a
ctiv
ities to
exe
mp
lify flu
en
cy, re
aso
nin
g a
nd
pro
ble
m s
olv
ing, te
ach
er’s
ch
ose
activ
ities fro
m a
va
riety
of s
ou
rce
s, in
clu
din
g th
eir o
wn
wh
ich
the
y fe
lt sup
po
rted
this
ma
them
atic
al a
rea. H
ow
eve
r this
do
es n
ot m
ea
n th
at th
ese
activ
ities a
re lim
ited
to th
is s
ectio
n,
an
d w
ou
ld b
e s
uita
ble
for u
se
in e
ach
are
a o
f flue
ncy, re
ason
ing a
nd p
rob
lem
so
lvin
g.
On
be
ha
lf of T
he
No
rfolk
an
d S
uffo
lk P
rima
ry A
sse
ssm
en
t Wo
rkin
g P
arty
Be
st w
ish
es,
Alis
on
Bo
rthw
ick
alis
on
.bo
rthw
ick@
ed
uca
tors
olu
tion
s.o
rg.u
k
David
Bo
ard
(St J
oh
n’s
Prim
ary
, No
rfolk
)
Lo
rna D
en
ham
(Saxm
un
dh
am
Prim
ary
, Su
ffolk
)
Alis
on
Bo
rthw
ick (M
ath
em
atic
s A
dvis
er)
V
icto
ria G
ate
sh
ill (Harle
sto
n P
rimary
, No
rfolk
)
Liz
Bo
nn
ely
kke (S
tan
ton
Prim
ary
, Su
ffolk
)
Ro
s M
iller (H
eth
ers
ett J
un
ior, N
orfo
lk)
Hele
n C
hatfie
ld (C
aven
dis
h P
rimary
, Su
ffolk
)
Ch
erri M
osele
y (F
reela
nce C
on
su
ltan
t)
Sh
eila
Day (W
ind
mill F
ed
era
tion
, No
rfolk
)
Hele
n N
orris
(Du
ssin
gd
ale
Prim
ary
, No
rfolk
)
Refe
ren
ces
Departm
ent fo
r Educatio
n (D
fE), (2
013), M
ath
em
atic
s
Pro
gra
mm
e o
f Stu
dy K
ey S
tages 1
an
d 2
. Lon
don
: DfE
.
McIn
tosh, J
. (201
5) F
inal R
eport o
f the C
om
mis
sio
n o
n
Assessm
ent W
ithou
t Leve
ls. L
ond
on: C
row
n C
opyrig
ht.
ww
w.N
RIC
H.m
ath
s.o
rg w
ww
.ncetm
.org
.uk
For m
ore
info
rmatio
n a
nd to
mak
e a
bo
okin
g
ww
w.e
du
ca
tors
olu
tion
s.o
rg.u
k o
r ca
ll 01
60
3 3
077
10
Big
ide
as in
Ye
ar 4
1.
Co
un
t, com
pa
re a
nd
ord
er n
um
be
rs (u
p to
1 0
00
inclu
din
g n
ega
tive
nu
mbe
rs).
2.
Re
co
gn
ise
and
use
the p
ositio
na
l, ad
ditiv
e a
nd
mu
ltiplic
ativ
e a
sp
ects
of p
lace
va
lue
(4 d
igit
nu
mb
ers
an
d d
ecim
als
to tw
o p
lace
s).
3.
De
ve
lop
num
be
r se
nse
to s
upp
ort m
en
tal c
alc
ula
tion.
4.
Ad
d a
nd s
ubtra
ct n
um
be
rs, re
co
gn
isin
g th
at th
ese
are
inve
rse
op
era
tion
s (u
p to
fou
r dig
its
an
d d
ecim
als
to tw
o p
lace
s).
5.
Mu
ltiply
an
d d
ivid
e n
um
be
rs, re
co
gn
isin
g th
at th
ese
are
inve
rse
opera
tion
s (fo
r at le
ast th
e
12
x 1
2 tim
es ta
ble
s a
nd
3 d
igit b
y 1
dig
it).
6.
Use
alg
eb
ra to
exp
ress p
atte
rns a
nd
gen
era
lisa
tion
s w
ithin
ma
them
atic
s.
7.
(a) R
eco
gn
ise
fractio
ns a
nd d
ecim
als
of s
ha
pe
s, o
bje
cts
an
d q
ua
ntitie
s (u
nit a
nd n
on-u
nit
fractio
ns, te
nth
s a
nd h
un
dre
dth
s).
(b) C
alc
ula
te w
ith fra
ctio
ns a
nd
de
cim
als
(add a
nd s
ubtra
ct w
ith th
e s
am
e d
en
om
inato
r an
d
de
cim
als
to tw
o p
lace
s).
8.
Ch
oo
se, u
se a
nd
com
pa
re a
va
riety
of u
nits
of m
ea
su
re to
an
app
rop
riate
leve
l of
accu
racy.
9.
Re
co
gn
ise
and
use
the p
rop
ertie
s o
f sh
ap
es, in
clu
din
g p
ositio
n a
nd d
irectio
n.
10
.
Co
llect, o
rga
nis
e a
nd in
terp
ret d
ata
(dis
cre
te a
nd
co
ntin
uou
s).
Ex
am
ple
s from
Te
ach
ing
for M
aste
ry m
ate
rials, te
xt ©
Cro
wn
Co
py
righ
t 20
15
, illustra
�o
n a
nd
de
sign
© O
xfo
rd U
niv
ersity
Pre
ss
20
15
, are
rep
rod
uce
d w
ith th
e k
ind
pe
rmissio
n o
f the
NC
ET
M a
nd
Ox
ford
Un
ive
rsity P
ress. T
he
Te
ach
ing
for M
aste
ry m
ate
rials
can
be
fou
nd
in fu
ll on
the
NC
ET
M w
eb
site w
ww
.nce
tm.o
rg.u
k/re
sou
rces/4
66
89
an
d th
e O
xfo
rd O
wl w
eb
siteh
)p
s://
ww
w.o
xfo
rdo
wl.co
.uk
/for-sch
oo
l/18
16
Year 4
Big idea 1: Count, compare and order numbers (up to 1 000, including negative numbers)
Fluency Reasoning Problem solving
Exemplification of fluency
• Count in multiples of 6, 7, 9, 25, 1000
• Count backwards through zero to include negative numbers
• Represent numbers in different ways (include different representations – Roman numerals and other historical representation linked to topic, abacus, base ten etc.)
• Round any number to the nearest 10, 100, 1000, including decimals to 1 d.p. to nearest whole number and justify
Exemplification of reasoning
• Say whether a particular number will be reached if a sequence continues
• Make the largest/smallest possible number using three or four digits
• Order groups of numbers from smallest to largest
• Suggest a number that comes between two given numbers
• Say what number will be in a particular position in a sequence e.g. 10
th number
Exemplification of problem solving
• Say whether a particular number will occur in a given sequence
• Recognise and describe patterns in sequences of numbers
• Order a set of weights, where the size of some is given in grams and others in kilograms
For more information and to make a booking
www.educatorsolutions.org.uk or call 01603 307710
Year 4
Big idea 1: Count, compare and order numbers (up to 1 000, including negative numbers)
Possible activities to exemplify fluency
• Count on in 9s from 23
• Count back in 25s from 650
• Say what temperature is 7 degrees colder than 4
oC
• Round the different decimal numbers made by rolling two dice to the nearest whole number Source: NRICH – ‘Round the Dice Decimals’ activity
• Can count on in 25s from 50. Circle the numbers that will be in the sequence: 990, 550,125, 755,150
Source: NCETM Mastery Booklet
• Draw 302 on an abacus with three spikes
Possible activities to exemplify reasoning
• Will 46 be in the sequence of numbers made by counting up in 6s from 10? Why or why not?
• Use the 4 digits 1, 7, 3 and 0 to make the smallest possible number and the largest possible number Source: NCETM Mastery Booklet
• Given Egyptian symbols for 1 and 10 and 100, work out the value of some Egyptian numbers
Source: NCETM Mastery Booklet
Possible activities to exemplify problem solving
• Say what could be the lowest possible number of pounds saved if an amount is, say, £300 rounded to the nearest hundred
• Aim to make the largest number possible by rolling a dice and deciding which place of your number to put the number you rolled Source: NRICH – ‘Nice or Nasty’ game
• Interpret positions on a number scale extending below 0
Source: NCETM Mastery Booklet
For more information and to make a booking
www.educatorsolutions.org.uk or call 01603 307710
Year 4
Big idea 1: Count, compare and order numbers (up to 1 000, including negative numbers)
• Use cards 1, 4, 6 and decimal point to make a number between 4.1 and 4.61
Source: NCETM Mastery Booklet
• Given the sequence 20,30,40, 50, what will the nineteenth number in the sequence be? What will the hundredth number be?
Source: NCETM Mastery Booklet
For more information and to make a booking
www.educatorsolutions.org.uk or call 01603 307710
Big idea 2: Recognise and use the positional, additive and multiplicative aspects of place value (4 digit numbers and decimals up to 2 decimal places)
Fluency Reasoning Problem solving
Exemplification of fluency
• Divide 1 and 2 digit numbers by 10 and 100 and recognise that hundredths arise when dividing an object by 100 and dividing tenths by 10, representing these as decimals
• Say how many tens is equal to a given number of hundreds
• Understand that in the number 3652 we can find the multiplicative place value of each digit by multiplying each digit by the column it is in e.g. 3 x 1000 = 3000
• Recognise the additive place value of each digit so when the individual values of the digits are added together they total the whole number
• Understand the positional place
value of each digit
•
Exemplification of reasoning
• Justify answers in terms of place value
• Convince a friend of the value of each digit in integers and decimal numbers
• Explain why 23.4 x 10 = 234 and not 23.40
Exemplification of problem solving
• Solve problems which involve converting between different units, including metric units and time
• Represent problems using apparatus to
organise thinking
For more information and to make a booking
www.educatorsolutions.org.uk or call 01603 307710
Big idea 2: Recognise and use the positional, additive and multiplicative aspects of place value (4 digit numbers and decimals up to 2 decimal places)
Possible activities to exemplify fluency
• Match numbers with the same value represented in different ways
Source: NCETM Mastery Booklet
• Complete missing number
calculations involving division by 10
or 100
Source: KS2 SAT
Possible activities to exemplify reasoning
• Explain why 53 hundreds has the same value as 530 000 hundredths
Possible activities to exemplify problem solving
• Solve problems involving conversions between metres and centimetres
• Work systematically using place value to find different ways to represent 5600
e.g. 5.6 x 1000, 56 x 100, 560 x 10
For more information and to make a booking
www.educatorsolutions.org.uk or call 01603 307710
Big idea 3: Develop number sense to support mental calculation
Fluency Reasoning Problem solving
Exemplification of fluency
• Reorders calculations to do them more easily
• Round calculations to do an easier one mentally and then adjust the answer e.g. 29 x 3 = (30 x 3) - 3 = 87
• Use jottings when needed
• Use known facts to work out
unknown facts
Exemplification of reasoning
• Discuss which method is easier
• Explain how a calculation can be more easily worked out by adjusting the numbers
• Use the relevant vocabulary when calculating
mentally
Exemplification of problem solving
• Choose operations and efficient calculation strategies to solve problems
• Find multiple solutions to a problem
• Explore different ways of solving a
problem
For more information and to make a booking
www.educatorsolutions.org.uk or call 01603 307710
Big idea 3: Develop number sense to support mental calculation
Possible activities to exemplify fluency
• Work out the cost of 4 DVDs at
£6.99 each by calculating 4 x £7
and adjusting by 4p
Possible activities to exemplify reasoning
• Justify whether it is easier to calculate the
cost of 4 DVDs at £6.99 each by calculating 4
x £7 and adjusting by 4p or by a standard
written method
Possible activities to exemplify problem solving
• How many calculations can you think of
with the answer 30?
For more information and to make a booking
www.educatorsolutions.org.uk or call 01603 307710
Big idea 4: Add and subtract numbers, recognising that they are inverse operations (up to 4 digits and decimals with up to 2 decimal places)
Fluency Reasoning Problem solving
Exemplification of fluency
• Use various formal, informal and mental methods
• Use inverse operations (solve missing number problems and check answers)
• Understand and use commutativity and associativity in addition and subtraction
Exemplification of reasoning
• Decide on which operations and methods to use and why
• Use the mathematical language for addition and subtraction
• Use rounding and approximation to estimate answers and make decisions
Exemplification of problem solving
• Solve addition and subtraction two step problems in context
• Choose and use appropriate operations and strategies
• Use different representations to understand and solve problems e.g. Bar Model
For more information and to make a booking
www.educatorsolutions.org.uk or call 01603 307710
Big idea 4: Add and subtract numbers, recognising that they are inverse operations (up to 4 digits and decimals with up to 2 decimal places)
Possible activities to exemplify fluency
• Choose an efficient method to calculate an answer depending on the numbers involved, for example, a mental method utilising adjustment to add or subtract 998, rather than a written method
• Use inverse operations to check answers
• Write families of related number
statements
Source: NCETM Mastery Booklet
Possible activities to exemplify reasoning
• Work out missing numbers from calculations which have some digits missing
• Reason about the value of missing digits
Source: NCETM Mastery Booklet
• Interpret different representations of a calculation when solving it
Source: NCETM Mastery Booklet
Possible activities to exemplify problem solving
• Identify the order of calculations needed to tackle a multi-step problem
Source: NCETM Mastery Booklet
• Work backwards from an answer by applying inverse operations to find the starting point of a sequence of calculations
• Visualise problems to work out how to tackle them
Source: NCETM Mastery Booklet
For more information and to make a booking
www.educatorsolutions.org.uk or call 01603 307710
Big idea 4: Add and subtract numbers, recognising that they are inverse operations (up to 4 digits and decimals with up to 2 decimal places)
• Use understanding of inverse
operations to solve missing box
problems
Source: NCETM Mastery Booklet
• Reason and explain why one calculation must give a larger, smaller or identical answer to another calculation
Source: NCETM Mastery Booklet
• Apply understanding of calculations crossing place value boundaries to solve ‘missing digit’ calculations
Source: NCETM Mastery Booklet
For more information and to make a booking
www.educatorsolutions.org.uk or call 01603 307710
Big idea 4: Add and subtract numbers, recognising that they are inverse operations (up to 4 digits and decimals with up to 2 decimal places)
• Explain why one method is better than another
Source: NCETM Mastery Booklet
• Give examples where particular methods would be most appropriate
Source: NCETM Mastery Booklet
For more information and to make a booking
www.educatorsolutions.org.uk or call 01603 307710
Big idea 5: Multiply and divide numbers, recognising that they are inverse operations (up to 3 digits by 1 digit and knowing multiplication and division facts up to 12 x 12)
Fluency Reasoning Problem solving
Exemplification of fluency
• Recall number facts to 12 x 12
• Use patterns, place value, factor pairs and commutativity in mental calculations
• Use distributive law, for example, 8x12 = (8x10) + (8x2) and associative law, for example (2 x 3) x 4 = 2 x (3 x 4) Another example: 2 x 6 x 5 = 10 x 6 = 60
• Relate areas to arrays and
multiplication/ division
Exemplification of reasoning
• Use apparatus and pictures to explain thinking
• Prove why one multiplication calculation gives the same answer as another one
• Explain how knowing one fact can help derive a related one
• Explain how to find the area of a rectangle with reference to arrays
Exemplification of problem solving
• Solve problems in context including multiplying and adding including using distributive law
• Systematically use correspondence between objects such as number of choices of a meal to find all possibilities
• Solve problems on integer scaling using
multiplication and division
For more information and to make a booking
www.educatorsolutions.org.uk or call 01603 307710
Big idea 5: Multiply and divide numbers, recognising that they are inverse operations (up to 3 digits by 1 digit and knowing multiplication and division facts up to 12 x 12)
Possible activities to exemplify fluency
• Match calculations with answers
• Complete multiplication grids presented in different ways
• Complete calculations with missing numbers
• Combine knowledge of multiplication facts with knowledge of doubling and halving to quickly derive related facts
Source: DFES
Possible activities to exemplify reasoning
• Use distributive property of multiplication
Source: DFES
• Apply properties of multiplication to say whether calculations are correct or not
Source: NCETM Mastery Booklet
Possible activities to exemplify problem solving
• Use patterns observed in sequences of
multiples to solve problems
Source: NCETM Mastery Booklet
• Interpret question using appropriate visualisation
Source: NCETM Mastery Booklet
For more information and to make a booking
www.educatorsolutions.org.uk or call 01603 307710
Big idea 5: Multiply and divide numbers, recognising that they are inverse operations (up to 3 digits by 1 digit and knowing multiplication and division facts up to 12 x 12)
• Use self-correcting flashcards to learn, practise and improve speed with multiplication facts
Source: DFES
• Use games to practise and develop fluency
Source: DFES
• Complete empty boxes in multiplication grids
Source: NCETM Mastery Booklet
• Apply knowledge of multiplication facts to related calculations
Source: NCETM Mastery Booklet
• Demonstrate commutative property of multiplication
Source: KS2 SAT
For more information and to make a booking
www.educatorsolutions.org.uk or call 01603 307710
Big idea 5: Multiply and divide numbers, recognising that they are inverse operations (up to 3 digits by 1 digit and knowing multiplication and division facts up to 12 x 12)
Source: KS2 SAT
• Can represent multiplications as arrays
Source: DFES
Source: DFES
For more information and to make a booking
www.educatorsolutions.org.uk or call 01603 307710
Big idea 5: Multiply and divide numbers, recognising that they are inverse operations (up to 3 digits by 1 digit and knowing multiplication and division facts up to 12 x 12)
Source: DFES
For more information and to make a booking
www.educatorsolutions.org.uk or call 01603 307710
Big idea 6: Use algebra to express patterns and generalisations in mathematics
Fluency Reasoning Problem solving
Exemplification of fluency
• Understand and use the equals sign as the balance of an equation
• Recognise symbols/ letters can represent numbers
• Use mathematical representations
to notice, continue and generate
patterns
Exemplification of reasoning
• Give another example and another and another
• Use mathematical vocabulary to generalise
• Express a rule to describe a sequence
Exemplification of problem solving
• Solve missing term problems
• Solve multi-step problems involving equivalence and more than one missing number, such as
6 x ? = ? – 2
• Understand that perimeter can be
expressed algebraically as 2(a+b)
where a and b are the dimensions in the
same unit
For more information and to make a booking
www.educatorsolutions.org.uk or call 01603 307710
Big idea 6: Use algebra to express patterns and generalisations in mathematics
Possible activities to exemplify fluency
• 14 + 13 = 30 - c
Possible activities to exemplify reasoning
• Explain what happens when two odd
numbers are added
Possible activities to exemplify problem solving
• How long could the sides of a rectangle
be, if it has the same perimeter as a
square with sides 6cm?
For more information and to make a booking
www.educatorsolutions.org.uk or call 01603 307710
Big idea 7(a): Recognise fractions and decimals of shapes, objects and quantities (unit and non-unit fractions, including tenths and hundredths)
Fluency Reasoning Problem solving
Exemplification of fluency
• Recognise and show using diagrams, families of equivalent fractions and decimals (¼, ½, ¾)
• Round decimals (1d.p.) to nearest whole number
• Represent fractions and decimals in a variety of ways and contexts
• Apply knowledge of factors and
multiples to recognise and simplify
equivalent fractions
Exemplification of reasoning
• Explain the relationship between non-unit fractions and multiplication and division of quantities (emphasis on tenths and hundredths)
• Use fraction vocabulary
• Conjecture about patterns in families of equivalent fractions
Exemplification of problem solving
• Solve problems involving non-unit fractions
• Work systematically to find families of
equivalent fractions
For more information and to make a booking
www.educatorsolutions.org.uk or call 01603 307710
Big idea 7(a): Recognise fractions and decimals of shapes, objects and quantities (unit and non-unit fractions, including tenths and hundredths)
Possible activities to exemplify fluency
• Use bars and fraction walls to find equivalent fractions
• Interpret diagrams in different ways to visualise equivalent fractions
• Know the equivalence of fractions and decimals
Source: NCETM Mastery Booklet
• Demonstrate knowledge of unit and non-unit fractions of money
Source: DFES
Possible activities to exemplify reasoning
• Explain fractions in terms of related division and multiplication facts
• Explain how different representations of fractions are the same or different
Source: NCETM Mastery Booklet
• Visualise ‘the whole’ from seeing part
Source: NCETM Mastery Booklet
Possible activities to exemplify problem solving
• Work systematically to find fractions
equivalent to
Source: NCETM Mastery Booklet
• Represent the whole when given part
Source: NCETM Mastery Booklet
• Find non-unit fractions when in context of recipe
Source: NCETM Mastery Booklet •
For more information and to make a booking
www.educatorsolutions.org.uk or call 01603 307710
Big idea 7(a): Recognise fractions and decimals of shapes, objects and quantities (unit and non-unit fractions, including tenths and hundredths)
• Position numbers on a number line
Source: NCETM Mastery Booklet
• ‘Fractional Wall’ activity
Source: NRICH
•
Source: NCETM Mastery Booklet
• Explain which is more: 6 items shared between 8 people or 9 items shared between 12 people
Source: NCETM Mastery Booklet
• Explain whether strategies to work out fractions are correct
Source: NCETM Mastery Booklet
Source: NCETM Mastery Booklet
For more information and to make a booking
www.educatorsolutions.org.uk or call 01603 307710
Big idea 7(a): Recognise fractions and decimals of shapes, objects and quantities (unit and non-unit fractions, including tenths and hundredths)
• Recognise what fraction of a shape has been shaded
Source: KS2 SAT
• ‘In the Money’ activity
Source: NRICH
• ‘Red Balloons, Blue Balloons’ activity
Source: NRICH
For more information and to make a booking
www.educatorsolutions.org.uk or call 01603 307710
Big idea 7(b): Calculate with fractions and decimals (add and subtract fractions with the same denominators and decimals to 2 decimal places)
Fluency Reasoning Problem solving
Exemplification of fluency
• Calculate with fractions giving results greater than one whole
• Convert between mixed numbers and improper fractions
• Convert between fractions and decimal
• Find the effect of dividing a 1 or 2 digit number by 100
Exemplification of reasoning
• Explain why multiplying by ten and multiplying again by ten is the same as multiplying by 100 (use a Gattegno chart)
• Explain what fraction needs to be added to any proper fraction to make a complete whole
• Use understanding of size of fractions to
convince a friend whether fraction additions
are correct or not
Exemplification of problem solving
• Make connections between fractions of a length, of a shape and as a representation
• Solve simple money and measure
problems involving fractions and
decimals
For more information and to make a booking
www.educatorsolutions.org.uk or call 01603 307710
Big idea 7(b): Calculate with fractions and decimals (add and subtract fractions with the same denominators and decimals to 2 decimal places)
Possible activities to exemplify fluency
• Represent addition and subtraction of fractions with the same denominator on diagrams and number lines
Possible activities to exemplify reasoning
• Reason about pairs of fractions with a difference of one-eighth
Source: NCETM Mastery Booklet
• Use understanding of size of fractions to explain whether fraction additions are correct or not
Source: NCETM Mastery Booklet
Possible activities to exemplify problem solving
• Work systematically to find all the possible subtractions involving sixths (proper fractions) that give an answer of one sixth
For more information and to make a booking
www.educatorsolutions.org.uk or call 01603 307710
Big idea 8:
Choose, use and compare a variety of units of measure to an appropriate level of accuracy
Fluency Reasoning Problem solving
Exemplification of fluency
• Use multiplication to convert from larger units to smaller units
• Read scales, interpreting unlabelled positions marked on the scale
• Choose appropriate equipment and units to make measurements of length, mass and capacity
• Read analogue and digital clocks
accurately
Exemplification of reasoning
• Use knowledge of units to estimate mass, length and capacity in real life contexts
• Use the vocabulary associated with measures
• Reason about different scales
Exemplification of problem solving
• Solve problems involving conversions between units
• Work logically to order a set of measures where conversion is needed
For more information and to make a booking
www.educatorsolutions.org.uk or call 01603 307710
Big idea 8:
Choose, use and compare a variety of units of measure to an appropriate level of accuracy
Possible activities to exemplify fluency
• Read scales, interpreting unlabelled positions marked on the scale
Source: DFES
Possible activities to exemplify reasoning
• Interpreting unlabelled positions marked on a scale
Source: NCETM Mastery Booklet
Possible activities to exemplify problem solving
• Solve problems involving conversions between metres and centimetres
Source: NCETM Mastery Booklet
Source: NCETM Mastery Booklet
• Order a set of weights, where the size of some is given in grams and others in kilograms
For more information and to make a booking
www.educatorsolutions.org.uk or call 01603 307710
Big idea 8:
Choose, use and compare a variety of units of measure to an appropriate level of accuracy
• Order a set of capacities, where some
are given as fractions of litres and
others in millilitres
Source: NCETM Mastery Booklet
Source: NCETM Mastery Booklet
For more information and to make a booking
www.educatorsolutions.org.uk or call 01603 307710
Big idea 9:
Recognise and use the properties of shapes, including position and direction
Fluency Reasoning Problem solving
Exemplification of fluency
• Use properties to describe shapes - include angles, regular/irregular and symmetry
• Complete a symmetric figure with respect to a specific line of symmetry, including outside shape
• Identify quadrilaterals and triangles, based on their properties
• Use coordinates to describe position
• Compare lengths and angles within shapes
Exemplification of reasoning
• Use appropriate vocabulary, including isosceles, equilateral and scalene; parallelogram, rhombus, trapezium
• Reason about the size of a polygon from knowledge of its coordinates
• Explain why a shape is or is not a specific type based on its properties
Exemplification of problem solving
• Solve problems involving translations
• Use knowledge of shape properties to solve problems
• Systematically sort shapes in logical ways
• Draw a shape from a description of its properties
For more information and to make a booking
www.educatorsolutions.org.uk or call 01603 307710
Big idea 9:
Recognise and use the properties of shapes, including position and direction
Possible activities to exemplify fluency
• Choose a shape that matches its description
• Plot specified points to draw sides to complete a given polygon
• Name and match particular quadrilaterals and triangles to their images
Source: NCETM Mastery Booklet
• Say the coordinates of the point which will complete a given polygon
Possible activities to exemplify reasoning
• Draw examples of different shapes and describe their properties
• Explain whether having four right angles means a rectangle is a regular shape
Source: NCETM Mastery Booklet
• Explain why a line is or is not a line of symmetry
Source: NCETM Mastery Booklet
Possible activities to exemplify problem solving
• Work out the perimeter of a polygon, given its coordinates
• Put shapes in Venn diagrams and Carroll diagrams
• Draw shapes with specified properties
Source: NCETM Mastery Booklet
For more information and to make a booking
www.educatorsolutions.org.uk or call 01603 307710
Big idea 9:
Recognise and use the properties of shapes, including position and direction
• Reason about the coordinates of a vertex using knowledge of the properties of a shape
Source: KS2 SAT
• ‘A Cartesian Puzzle’ activity
Source: NRICH
For more information and to make a booking
www.educatorsolutions.org.uk or call 01603 307710
Fluency Reasoning Problem solving
Exemplification of fluency
• Use a range of scales
• Read points on one axis that correspond to given measures on the other axis
• Represent data as graphs and charts
• Complete tables by reading graphs and charts
• Interpret tables of data to answer
questions
Exemplification of reasoning
• Use the correct vocabulary associated with statistics
• Justify opinions about whether particular statements about a set of data are true or not
• Explain why one type of graph is more
appropriate than another
Exemplification of problem solving
• Solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs
• Use logic to make up a story to fit a line
graph
Big idea 10:
Collect, organise and interpret data (discrete and continuous)
For more information and to make a booking
www.educatorsolutions.org.uk or call 01603 307710
Big idea 10:
Collect, organise and interpret data (discrete and continuous)
Possible activities to exemplify fluency
Source: NCETM Mastery Booklet
Possible activities to exemplify reasoning
• Justify opinions about whether particular statements about a set of data are true or not
Source: NCETM Mastery Booklet
Possible activities to exemplify problem solving
• Interpret graphs to solve problems
• Make up a story to fit a line graph
Source: NCETM Mastery Booklet
For more information and to make a booking
www.educatorsolutions.org.uk or call 01603 307710
Big idea 10:
Collect, organise and interpret data (discrete and continuous)
• Justify why one type of graph is more appropriate than another
Source: NCETM Mastery Booklet
For more information and to make a booking
www.educatorsolutions.org.uk or call 01603 307710
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