Progression in Teaching and Learning Multiplication - Age related expectations - Yr R to Yr6
Useful Things-Focus
Step
Practise counting in 2s, 5s and 10s,
including using visual images for support
Written Calculations
Models & Images
Mental Calculations
Known Facts
Counting on 1s and 2s
Informal jottings, mathematical mark making,, problem
Repeated groups of the same size
Count repeated groups of the same
size
solving process, use of blank paper
3 plates, 2 cakes on each plate
Respond to/make up number stories
Recording using ICT
There are 2 sweets in 3 bags. How many sweets are there
all together?
Use number tracks/Number lines (Modelled using bead
strings)
2x3 or 3x2
Numicon Practise showing the difference between an addition
sentence and a mult sentence
- Use counting up in 2s, 5s and 10s
(using fingers to keep track of groups)
Instant recall
• Doubles of numbers to 10
• Count on/back in 1s, 2s, 5s,
and 10s
• Derive/recall 2, 5, 10 time
tables
Practise counting in 3s
Use repeated addition to solve
multiplication problems
Vocabulary: lots of, groups of
times, multiply, repeated addition, array
Repeated addition on a number line
e.g. 3 x 4 = 12
Arrays
- Use counting up in 3s, 5s and 10s
(using fingers to keep track of groups)
to start to derive multiplication facts,
phrased as
‘what is 4 times 3’ or ;how many in
four groups of 3’
Instant recall
• Doubles of numbers to 20
• Begin to know times table
facts for 3x, 4x 6x 7x 8x
and 9x
Vocabulary: lots of, groups of
times, multiply, repeated addition, array,
factor, multiple
Chn need to get VERY confident with
all 2x, 3x, 4x, 5x,
10x should be instant recall; Can use
double of 3x and
4x for 6x and 8x Can use finger
method initially for 9x;
Grid method
Multiply a 2 digit number by 2, 3, 4 5 6 7 8 & 9 use
partitioning – use PV counters to model
‘Rows of chairs in hall’ (array) as visual representation
of grid method
Multiply a number by doubling and
doubling again
- Multiply a 2 digit whole number
by 10
Partitioning
Multiply teens numbers
by single digit by
visualised partitioning
Instant recall
• Double 15, 25, 35, 45
• Mental recall of 2, 3, 4, 5 6
7 8 9 and 10
• Begin to know times table
facts for 11x and 12x
Derived
• Times tables & place value
calculations such as 70 x
3
Use place value to multiply a
whole number by 10 or 100
Multiply two multiples of 10
together, e.g. 40 x 30
Instant recall
Recall multiplication facts up to 12 x 12
Quickly derive corresponding division
facts
Derived
Times tables & PV calculations with
decimals such as 0.7 x 3
1
Recording using ICT
Step
Solve practical problems that involve
combining groups of 2, 5 or 10
2
Step
3
Step
4
x
30
2 =arrays
5
- Start3to+use
3x2=6
These show commutative
properties ie 1 array shows 3x4=4x3
Counting stick times tables
NB Its worth watching 17x table on youtube
2
-
120to 2 digit
8 by 2 digit - dotty paper
Extend grid4method
useful to model this.
-Partitioning (use of number line to record steps)
Step
- Recognise and describe number
relationships, incl multiple,
factors and squares, prime
5
Short multiplication for single digit multiplication
- Use efficient methods of short multiplication
- Multiply a simple decimal
by a single digit, e.g. 36.2 x 8
Grid method
Use grid method to use with 2 digit by 2 digit and extend
to a single digit x decimal as well
Step
6
Refine and use efficient methods
Integer x O
2304x8
Decimal x O
31.7 x 7
Short multiplication or grid
Multiply decimal numbers by a single digit, e.g. 31.62 x 8
Multiply any 3 digit number by any 2 digit number
Expanded column
43
X 6
_____
18 ( 3 x 6)
240 (40 x 6)
258
Introduce short multiplication linked to grid for 2/3 digit
by 1 digit
Grid method
Extend grid method to use with a single digit x decimal
Expand column for 2, 3 and 4 digit by 1 digit
Interim method between grid and long multiplication
Yr5: x 4 digits by 1 or 2 digits, long multiplication
Yr6: 4 digits x 2 digits see NS example
-
Multiply decimals and whole
number by 10, 100 and
1000
-Multiply a two digit number by a
single digit
-
Instant recall
Times tables & place value calculations
such as 40 x 3
Derived Times tables & PV calculations
with decimals such as 0.7 x 0.3