Math Teaching Methods Page 2
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1
2Division
Calculate
m athematical
Write
a nd
c alculate
m athematical
Divide
n umbers
u p
t o
Divide
n umbers
u p
t o
4 -‐digits
b y
statements
f or
m ultiplication
a nd
statements
f or
÷
u sing
t he
x
4
d igits
b y
a
o ne-‐digit
194
÷
6
a
t wo-‐digit
w hole
n umber
u sing
division
w ithin
t he
m ultiplication
tables
t hey
k now
p rogressing
t o
number
u sing
t he
the
f ormal
w ritten
m ethod
o f
tables
a nd
w rite
t hem
u sing
t he
formal
w ritten
m ethods.
formal
w ritten
short
d ivision
w here
a ppropriate
3
2
Written
1
multiplication
( ×),
d ivision
( ÷)
a nd
method
o f
s hort
for
t he
c ontext
6
1
9
2
Methods
1
13
equals
( =)
s igns
division
a nd
i nterpret
2
26
564
÷
1
3
remainders
192
÷
6
Using
4
52
known
5
130
appropriately
f or
t he
4
3
r
5
=
3 2
multiplication
facts
4
context
13
5
6
4
8
104
10
260
6 ÷2 = 3 by sharing into 2 groups and by
15 ÷ 3 = 5 in each group (sharing)
Grouping using partitioning
Grouping using partitioning
192 ÷ 6 using place value counters to
grabbing groups of 2
43 ÷ 3 If I know 10 x 3 …
196 ÷ 6 If I know 3 x 6 … then 30 x 6…
support written method
!
564
÷
1
3
=
4 3
r
5
=
4 3
=
4
3.38...
!"
4
3
.
3
8
…
4
5
11
13
5
6
4
.
0
0
Exchange 100
for ten 10s
Divide
n umbers
u p
t o
4
d igits
b y
a
Link to fractions
‘Chunking up’ on a number line
196 ÷ 6 = 32 r 4
two-‐digit
w hole
n umber
u sing
t he
formal
w ritten
m ethod
o f
l ong
15 ÷ 3 = 5 groups of 3 (grouping)
19 tens into
division,
a nd
i nterpret
groups of 6
remainders
a s
w hole
n umber
Use language of division linked to tables
Use language of division linked to tables.
Developing
10 ÷2 = 5
remainders,
f ractions,
o r
b y
conceptual
3 groups so that is 30 x 6,
rounding,
a s
a ppropriate
f or
t he
exchange remaining 10 for ten 1s
context
understanding
How many 3s?
564
÷
1
3
4
3
.
3
8
…
13
5
6
4
.
0
0
…
Use language of division linked to tables
5
2
How many 2s?
4
4
So 192 ÷ 6 = 32
-‐
3
9
How many 2s?
5
0
-‐
3
9
1
1
0
-‐
1
0
4
6
!
=
4 3
r
5
=
4 3
=
4 3.4
( to
1
dp)
!"
Solve
o ne-‐step
p roblems
i nvolving
Show
t hat
m ultiplication
o f
t wo
n umbers
Write
a nd
c alculate
m athematical
Use
p lace
v alue,
k nown
a nd
d erived
f acts
Multiply
a nd
d ivide
n umbers
m entally
Perform
m ental
c alculations,
i ncluding
multiplication
a nd
d ivision,
b y
c alculating
can
b e
d one
i n
a ny
o rder
( commutative)
statements
f or
m ultiplication
a nd
d ivision
to
m ultiply
a nd
d ivide
m entally,
drawing
u pon
k nown
f acts
with
m ixed
o perations
a nd
l arge
n umbers
With
j ottings
the
a nswer
u sing
c oncrete
o bjects,
and
d ivision
o f
o ne
n umber
b y
a nother
using
t he
m ultiplication
t ables
t hat
t hey
including:
m ultiplying
b y
0
a nd
1 ;
d ividing
Multiply
a nd
d ivide
w hole
n umbers
a nd
pictorial
r epresentations
a nd
a rrays
w ith
cannot
know,
i ncluding
f or
t wo-‐digit
n umbers
by
1 ;
m ultiplying
t ogether
t hree
n umbers
those
i nvolving
d ecimals
b y
1 0,
1 00
a nd
the
s upport
o f
t he
t eacher
Solve
p roblems
i nvolving
m ultiplication
times
o ne-‐digit
n umbers,
u sing
m ental
Recognise
a nd
u se
f actor
p airs
a nd
1000
…
o r
i n
y our
and
d ivision,
u sing
m aterials,
a rrays,
methods
commutativity
i n
m ental
c alculations
repeated
a ddition,
m ental
m ethods,
a nd
head
… .
multiplication
a nd
d ivision
f acts,
including
p roblems
i n
c ontexts
Recall
p rime
n umbers
u p
t o
1 9
Recall
a nd
u se
x
a nd
÷
f acts
f or
t he
2 ,
5
Recall
a nd
u se
x
a nd
÷
f acts
f or
t he
3 ,
4
Recall
x
a nd
÷
f acts
f or
x
t ables
u p
t o
1 2
x
know
a nd
u se
t he
v ocabulary
o f
p rime
Just
k now
i t!
Count
i n
m ultiples
o f
t wos,
f ives
a nd
t ens
and
1 0
x
t ables,
i ncluding
r ecognising
o dd
and
8
t imes
t ables.
12.
numbers,
p rime
f actors
a nd
c omposite
and
e ven
n umbers.
(non-‐prime)
n umbers
Year
1
2
3
4
5
6
Review
d ivision
f acts
( 2x,
5 x,
1 0x
Division
f acts
( 4x,
8 x
t ables)
Division
f acts
( 4x,
8 x
t ables)
Count
b ack
i n
2 s
Division
f acts
( 2
x
t able)
Division
f acts
( up
t o
1 2
x
1 2)
table)
10
t imes
s maller
100,
1 000
t imes
s maller
Division
f acts
( 3x,
6
x ,
1 2x
t ables)
Count
b ack
i n
1 0s
Division
f acts
( 10
x
t able)
Division
f acts
( 4
x
t able)
Division
f acts
( 3x,
6
x ,
1 2x
t ables)
Partition
t o
d ivide
m entally
Partition
t o
d ivide
m entally
Halves
u p
t o
1 0
Halves
u p
t o
2 0
Halve
t wo
d igit
n umbers
Halve
l arger
n umbers
a nd
d ecimals
Halve
l arger
n umbers
a nd
d ecimals
Halve
l arger
n umbers
a nd
d ecimals
Division
f acts
( 3x,
9 x
t ables)
Count
b ack
i n
5 s
Division
f acts
( 5
x
t able)
Division
f acts
( 8
x
t able)
Division
f acts
( 3x,
9 x
t ables)
Division
f acts
( up
t o
1 2
x
1 2)
100,
1 000
t imes
s maller
Foundations
Review
d ivision
f acts
( 11x,
7 x
t ables)
Halve
m ultiples
o f
1 0
Count
b ack
i n
3 s
Division
f acts
( 3
x
t able)
Division
f acts
( 11x,
7 x
t ables)
Partition
t o
d ivide
m entally
Partition
d ecimals
t o
d ivide
m entally
Review
d ivision
f acts
( 2x,
5 x,
1 0x
Division
f acts
( 6
x
t able)
o r
r eview
Review
d ivision
f acts
( 6x,
1 2x
t ables)
How
m any
2 s?
5 s?
1 0s?
Division
f acts
( 6x,
1 2x
t ables)
Halve
l arger
n umbers
a nd
d ecimals
table)
others
Halve
l arger
n umbers
a nd
d ecimals
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