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Multiplication and Division Progressions
Progression
Example
CA
Solve simple problems by counting all the objects from one.
Rote skip count in 2’s 5’s,10’s (then 3’s, 4’s)
3 x 2 = 1,2,
3,4,
5,6
5,10, 15, 20, 25, 30, 35, 40, 45, 50
AC
Use skip counting to solve multiplication problems (involving 2’s,5’s10s)
6 x 5 = 5, 10, 15, 20, 25, 30
Understand meaning of “x” using arrays.
See that 3 x 6 and 6 x 3 may have the same answer but ‘look’ different.
3 x 6 = ******
******
******
Understand the link between addition and multiplication and use
repeated addition to solve problems.
5x3=3+3+3+3+3
=6+6+3
Understand division as a ‘sharing” context.
8  4 = ** ** ** **
8 lollies shared between 4 children, how
many lollies does each child have?
8  4 = **** ****
8 lollies put into sets of 4, how many sets?
EA
Stage
5
Understand division as a ‘grouping“ context.
AA
Stage
6
AM
Stage
7
Solve division problems by skip counting or repeated addition
12  3 = 3,6,9,12 therefore the answer is 4.
Understand x 2 by doubling, Understand x5 by halving x 10
KNOWLEDGE: Recall x 2 x 5 and x 10 mult and div facts
2 x 8 = double 8, or 8 + 8
5 x 8 = half of 10 x 8
Derive unknown basic multiplication facts from known facts using:
commutative property to make problems easier (change the order)
6x3=3x6
distributive property
x 6, x7, x8 from x5 known facts (splitting)
x4 and x9 facts from x5 or x10 known facts (tidy numbers)
8 x 6 = (8 x 5) + (8 x 1)
9 x 7 = (10 x 7) – (1 x 7)
associative property
x4, x8 by doubling and doubling again
Apply these strategies to larger numbers. e.g. 6 x 19 = (6 x 20 ) - 6
8 x 6 = 2 x 2 x (2 x 6)
Multiply by tens and hundreds
28 x 10=280, 36 x 100=3600
Solve division problems by reversing into a multiplication problem
(inverse operations)
36  4 is the same as 4 x ? = 36
KNOWLEDGE: Recall all basic multiplication facts to 10x10 & some
division facts (all division facts to be learnt at Stage 7).
6 x 7,
4x3, 9x8
Choose efficiently from a range of mult/div strategies to a full range of contexts and whole numbers.
Division Example
Multiplication Example
76  4 is the same as (80  4) – (4 4)
= 20 – 1 = 19
Tidy Numbers
29 x 6 = (30 x 6) – (1 x 6)
76  4 is the same as (40  4) + (36 4)
= 10 + 8
108  12 is the same as (108  2)  6
Place Value
24 x 6 = (20 x 6) + (4 x 6)
Splitting Factors
23 x 12 = 23 x 3 x 2 x2
Adjusting both numbers proportionally by
finding a common factor.
108  12 is the same as 54  6 = 9
Proportional Adjustment
(associative Property)
18 x 3 = 9 x 6 (doubling and halving)
33 x 27 = 99 x 9 (thirding and trebling)
Standard Written Forms
AP
108  12 is the same as 12 x ? = 108
Reversibility (inverse)
Not Applicable
39  4 =
Express remainders as
whole numbers, fractions,
or decimals
Not Applicable
Divisible by.. 3 and 9 if sum of digits are
divisible by 9.
Use divisibility rules for
2,3,5 9 (then 4,6,8),
Not Applicable
9 = 3
Use exponents (powers
and roots of numbers)
32 = 3 x 3 = 9
9r3 or
9 ¾ or
9.75
Apply properties of multiplication and division across a full range of contexts with fractions and decimals and
manipulating relationships algebraically.
Marie Hirst, Numeracy Facilitator,
Facilitator name, Month, year [version ie. Draft v3]
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