Download Multiplication and Division Progressions

Multiplication and Division Progressions
Multiplication – using equal sets/ factors
Early Additive Part Whole
Basic
Within
I can link problems using repeated addition to a multiplication
fact, like
3+3+3+3=
As 4 sets of 3 which is 4 x 3
I can draw or group an array to show a multiplication fact 4 x 3
and show how it is different to
3 x 4 but is the came value
Or 5 + 5 = 2 x 5 as doubling 5 because you have 2 equal sets
added together
Proficient
I can solve a multiplication
problem by using repeated
addition more efficiently,
like
Basic
I can solve a problem by
using my x2. x5, x10
multiplication facts and adding
or taking a little bit more (
compensating), like
4x6=
As 6 + 6 = 12
12 + 12 = 24
So  =24
6x5=
5 x 5 = 25
1 x 5 =5
25 + 5 = 30
So  =30
5x5=
As 10 + 10 + 5 = 25
6x5=
As 15 +15 = 30
I can use my x 10 tables to
work out my x 5 tables, like
2 x 10 = 20 so 4 x 5 = 20
Proficient
Basic
Advanced Multiplicative
Within
Proficient
I can use a trebling and
thirding to solve multiplication
problems, like
I can use doubling / halving,
and adjusting to solve
multiplication problems, like
180 x 6 =  as
60 x 18 = 30 x 36 as 10 x
108
10 x 108 = 1080
So  = 108
12 x 49 = 
4 x 150= 600
600 – 12 = 588
4 x 30 =120
So 4 x 28 is
120 – (2 x 4)
120 – 8 =112
4x6=
5 x 6 =30
1x6=6
30 – 6 = 24
So  = 24
Or 4 x 6 = 
(5 x 6 ) – (1 x 6 )
30 - 6 = 24
I can use a doubling and
halving strategy to solve
multiplication fact problems,
like
4 x 3 =  as
4x3= 2x6
So  = 12
Doubling and halving / trebling and thirding
Advanced Additive Part Whole
Within
I can use multiplication facts I
know to solve larger
multiplication problems by
rounding and compensating,
like
I can use a doubling and
halving strategy to solve
multiplication problems, like
I can use a trebling and
thirding strategy to solve
multiplication problems,
like
I can use the doubling and
halving strategy to solve
multiplication problems with
large numbers, like
14 x 4 =  as
14 x 4 = 7 x 8
So  = 56
3 x 18 =  as
9 x 6 = 54
6 482 x 5 =  as
6 482 x 5 = 3 2 4 1 x 10
So  = 32 410
4 x 8 =  as
4 x 8 = 2 x 16
So  = 32 using my
knowledge of doubles
I can solve division problems
by
using a doubling and halving
strategy, like
I can solve division
problems by
using a doubling and
halving strategy, like
32 ÷ 8 =  as
32 ÷ 16 = 2
so  = 4
64 ÷ 4 =  as
64 ÷ 8 = 8
So  is 16
because double 8 is16
or
64 ÷ 4 =  as
64 ÷ 2 = 32
So  is 16
because halve of 16 is 8
or
170 ÷ 5 =  as
170 ÷ 10 = 17
So  = 34
because double 17 is 34
I can use a trebling /
thirding and adjusting to
solve multiplication
problems, like
12 x 33 =  as
12 x 33 = 4 x 99
So 4 x 100 = 400
400 – 4 = 396
I can use a place value
partitioning strategy to
solve multiplication
problems using tens and
ones, like
I can use a place value
partitioning strategy to solve
multiplication problems using
hundreds, tens, and ones, like
6 x 12 as (6 x 10 ) + (6 x 2) =
72
5 x 68 as
8 x 236 as
(5 x 60) + ( 5 x 8)
(8 x 200) + ( 8 x 30) + ( 8 x
300 + 40 = 340
6)
or
1600 + 240 + 48 = 
Place value partitioning
I can use a place value
partitioning strategy to solve
multiplication problems, like
x
60
8
5
300 + 40 = 340
I can use standard written
form to record my
multiplication by a single digit
problems, like
I can use standard written
form to record my
multiplication by two digits
problems, like
68
5x
340
23
37 x
161-------(7 x 23) +
690 ------(30 x 23)
851
Or
875
6x
5250
1840 + 48 = 1888
or
x
200
8
1600 + 240 + 48 =
30
6
1888
I can use standard written
form to record my
multiplication problems, like
68
5x
40 ---- 5 x 8
300 ---- 5 x 60
340
Exponents
I can solve problems using
simple square numbers
and can draw what they
represent and make a table
to show the pattern
numerically, like
I can solve problems using simple cube numbers and can build
what they represent and make a table to show the number
pattern, like
as 3 x 3 x 3 = 27 and draw the pattern to show this
as 4 x 4 = 16
I can solve problems by
knowing the that adding the
exponent of the factor gives
the exponent of the product
and can use a table to show
the link, like
64 x 8 =512
x =
and draw the pattern to
show this
2x 2x 2x 2x 2x 2x 2x 2x
2=512
Or
X
Division by using equal shares
I can solve problems by
making equal shares, like
20 ÷4 = 5
Because 5 + 5 + 5 + 5 = 20
I can solve problems by
making equal shares, like
20 ÷4 = 5
Because 5 + 5 = 10
10 + 10 = 20
I can solve problems by
making equal shares and
linking them to x2 x5 x10
multiplication facts, like
I can solve division problems with numbers up to a 100 by using a
reversing strategy, like
40 ÷ 5 = 8
because I have shared 40
into 5 sets of 8 so I know
63 ÷ 7 = 9 because 9 x 7 = 63
5 x 8 = 40
8 x 5 = 40
40 ÷ 5 = 8
40 ÷ 8 = 5
Or
I can solve division
problems which have
remainders, like
43 ÷ 5 = 8 r 3 because
5 x 8 = 40 with 3 left over
Or 39 ÷ 4 = 9 ¾ or 9.75
I can solve division problems
which have remainders, like
472 ÷ 5 = 94 r2 or 94 2/5 or 94.4
I can use standard written form to
record my division problems, like
Or
Partitioned as
= 23
I can use standard written
form to record my division
problems, like
=
3 x 3 x 3 x 3 x 3 =243
I can use standard written
form to record my division
problems, like
or