APPENDIX 1
Hawkes Farm Primary School progression in calculation (multiplication)
Vocabulary
Skills and knowledge
Representing & recording mental
calculations
Th H T U
Repeated addition
Lots of
Groups of
Multiply
Multiple
Times
Product
Array
Scaling
Rows
Columns
Double
Grid method
Practical activities:
I’ve got 3 pairs of socks.
How many socks altogether?
2+2+2=6
2x3=6
How many wheels are there on 3 cars?
4 + 4 + 4 = 12
4 x 3 = 12
Jottings to support mental strategies
Informal methods
Draw arrays and relate to
x and ÷ ’sentences’
Multiplication is repeated addition: use
hops or jumps along a number line.
5 x 2 = 10
2 x 5 = 10
Make 5 equal jumps to land on 15.
How big is each jump?
5 jumps of 3 = 15
Repeated addition with drawings:
4 people can sit round 1 table.
How many tables do we need for 20
people?
Formal methods
Short multiplication
10 ÷ 5 = 2
10 ÷ 2 = 5
Patterns formed when numbers are multiplied by 1, 10, 100
Use symbols to stand for unknown numbers in multiplication ‘sentences’.
5 x Δ = 10
3x8=Δ
Long multiplication
Grid method:
Zero as a placeholder
15 x 3 =45
Doubling is x 2.
Multiplication can be done in any
order
X 3
10
30
15 x 12 = 180
5
15
X 10
X 2
Partitioning numbers
Good knowledge of x tables (and
division tables)
Spots on 4 ladybirds?
4 + 4 + 4 + 4 = 16
4 x 4 = 16
Counting on/back in regular
repeated jumps
Doubling
Multiplication can be seen as
repeated addition of numbers
to make a total.
Use symbols to stand for unknown
numbers in x ‘sentences’
5 x Δ = 10
Multiplication is the inverse of
division
Introduce children to BIDMAS to
determine the order of operations
in a calculation (Brackets, Indices,
Division, Multiplication, Addition
and Subtraction).
Arrays: what does this show?
****
****
****
Check calculations with the inverse
operation.
5
50
10
150 +
30
Using this method: H T U x U and T U x T U
Th H T U x U and H T U x T U when ready
Extend to larger numbers and decimal numbers
Start to estimate answers.
Most children should be using this method by the end of Year 4.
Check answers with the inverse operation.
Partitioning method:
3x2=Δ
Start to estimate answers.
10
100
20
X
158
9
72
450
900
1422
1
(9x8)
(9x50)
(9x100)
APPENDIX 1
Hawkes Farm Primary School progression in calculation (division)
Vocabulary
Skills and knowledge
Representing & recording mental
calculations
Jottings to support mental
strategies
Informal methods
Practical investigations
Sharing equally with no remainder eg
Introduce remainders after sharing or grouping.
Can you share 8 spots on these 4 ladybirds
so they all have the same number?
10 socks shared between 5 people.
How many people get a pair of socks?
Round answer up/down in context of problem eg
Formal methods
Sets of
Sharing
Grouping
Divided between
Factor
These bags hold 4 sweets each.
How many bags will I need to hold
18 sweets?
Chunking
Divisor
Dividend
Remainder
How many sets of 3 can you make with
these crayons?
Find halves/quarters by halving and halving again.
Long division
Fraction
Half/halve
Solve problems with mystery symbols:
Quotient
Numbers cannot be divided
in any order
Place value understanding
Partitioning of various
numbers
Multiplying by 0 always = 0
Division can be seen as:
- sharing
- grouping into required
amounts
- repeated subtraction
Division is the inverse of
multiplication
Introduce children to
BIDMAS to determine the
order of operations in a
calculation (Brackets,
Indices, Division,
Multiplication, Addition and
Subtraction).
Short division
12 ÷ 4 = Δ
If there are 8 shoes on the floor, how
many children could each wear 2 shoes?
Share 6 coins equally into 3 money
boxes: how many in each box?
Δ ÷ 2 = 16
Informal chunking (using multiples of divisor)
72 ÷ 5 = 14 r 2
Repeated subtraction on a number line
(including chunking)
72
- 50
22
- 20
2
(5 x 10)
(5 x 4)
Round answer up/down in context of problem.
Go on to: TU ÷ U (using multiples of divisor)
HTU ÷ U (using multiples of divisor)
HTU ÷ TU (using multiples of divisor}
Most children should be using this method by the end of Year 5.