MULTIPLICATION CALCULATION GUIDANCE
Year 1
Pupils should be taught to:
• solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with
the support of the teacher.
Year 2
Pupils should be taught to:
• recall and use multiplication … facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers
• calculate mathematical statements for multiplication … within the multiplication tables and write them using the multiplication (×), … and equals (=)
signs
• show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot
• solve problems involving multiplication … using materials, arrays, repeated addition, mental methods, and multiplication … including problems in
contexts.
Year 3
Pupils should be taught to:
• recall and use multiplication … facts for the 3, 4 and 8 multiplication tables
• write and calculate mathematical statements for multiplication … using the multiplication tables that they know, including for two-digit numbers times
one-digit numbers, using mental and progressing to formal written method
• solve problems, including missing number problems, involving multiplication … including integer scaling problems and correspondence problems in which
n objects are connected to m objects.
Year 4
Pupils should be taught to:
• recall multiplication … facts for multiplication tables up to 12 × 12
• use place value, known and derived facts to multiply … mentally, including: multiplying by 0 and 1; multiplying together three numbers
• recognise and use factor pairs and commutativity in mental calculations
• multiply two-digit and three-digit numbers by a one-digit number using formal written layout
• solve problems involving multiplying and adding, including using the distributive law to multiply two digit numbers by one digit, integer scaling problems
and harder correspondence problems such as n objects are connected to m objects.
Copyright. This material has been produced by Essex Education Services and may not be copied, duplicated or otherwise reproduced whether for profit or otherwise without the express permission
in writing of Essex Education Services
Year 5
Pupils should be taught to:
• solve problems involving multiplication and division where larger numbers are used by decomposing them into their factors
• multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers
•
multiply … numbers mentally drawing upon known facts
• multiply … whole numbers and those involving decimals by 10, 100 and 1000
• solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals
sign
• solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates.
Year 6
Pupils should be taught to:
•
•
•
•
•
multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication
perform mental calculations, including with mixed operations and large numbers.
use their knowledge of the order of operations to carry out calculations involving the four operations
solve problems involving addition, subtraction, multiplication and division
use estimation to check answers to calculations and determine, in the context of a problem, levels of accuracy.
STAGE 1
Develop multiplication as repeated grouping (repeated addition of sets of the same size) using practical apparatus and diagrams.
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in writing of Essex Education Services
STAGE 2
Develop an understanding of multiplication using arrays and number lines showing repeated groups.
Use number lines to show repeated grouping (repeated addition of sets of the same size).
STAGE 3
Develop the use of x and = symbols to record calculations horizontally.
Use arrays and other practical apparatus to illustrate commutativity (that multiplication calculations can be carried out in any order) e.g. 2 x 5 arrives at the
same product as 5 x 2.
Begin to derive new facts from known facts
e.g. 3 x 2 = 6 (known fact)
30 x 2 = 60
300 x 2 = 600 etc.
Copyright. This material has been produced by Essex Education Services and may not be copied, duplicated or otherwise reproduced whether for profit or otherwise without the express permission
in writing of Essex Education Services
40
20
STAGE 4
Begin to use understanding of place value and partitioning to carry out multiplication of two- digit by one -digit numbers
15 x 4
10 5
10 x 4 = 40
5 x 4 = 20
40 + 20 = 60
Use grid approaches to illustrate as appropriate using practical apparatus to support.
10
5
4
Develop expanded recording in columns and then
T
U
T
1
5
1
x
4
x
2
0 (5 x 4)
6
4
0 (10 x 4)
2
6
0
move to formal written method, using practical apparatus to support as required.
U
5
4
0
Copyright. This material has been produced by Essex Education Services and may not be copied, duplicated or otherwise reproduced whether for profit or otherwise without the express permission
in writing of Essex Education Services
STAGE 5
Extend written approaches to HTU x U, then to ThHTU x U
Illustrate using partitioning approaches as required
215 x 4
200 10
5
200 x 4 = 800
10 x 4 = 40
5 x 4 = 20
800 + 40 + 20 = 860
Illustrate using grid approaches as required
Develop expanded recording in columns and then move to formal written method, using practical apparatus to support as required.
H
1
T
1
8
8
2
4
0
6
x
U
5
4
0 ( 5 x 4)
0 ( 10 x 4)
0 ( 200 x 4)
H
2
T
1
8
6
2
x
U
5
4
0
Copyright. This material has been produced by Essex Education Services and may not be copied, duplicated or otherwise reproduced whether for profit or otherwise without the express permission
in writing of Essex Education Services
200
60
60
18
STAGE 6
Extend written approaches to HTU x TU and ThHTU x TU
Illustrate using grid approaches as required
26 x 13
20
6
10
3
200 + 60 + 60 + 18 = 338
Develop expanded recording in columns and then move to formal written method of long multiplication, using practical apparatus to support as required.
H
x
2
3
1
T
2
1
1
6
6
0
3
U
6
3
8
0
0
0
8
H
x
( 6 x 3)
( 20 x 3)
( 6 x 10)
( 10 x 20)
2
3
1
T
2
1
7
1
6
3
U
6
3
8
0
8
226 x 13
10
3
200
2000
600
20
200
60
6
60
18
2000 + 600 + 200 + 60 + 60 + 18 = 2938
Copyright. This material has been produced by Essex Education Services and may not be copied, duplicated or otherwise reproduced whether for profit or otherwise without the express permission
in writing of Essex Education Services
Develop expanded recording in columns and then move to formal method of long multiplication, using practical apparatus to support as required.
H
2
x
6
2
2
2
0
9
1
T
2
1
1
6
0
6
0
0
3
U
6
3
8 ( 6
0 ( 20
0 ( 200
0 ( 6
0 ( 20
0 ( 200
8
H
2
x
x 3)
x 3)
x 3)
x 10)
x 10)
x 10)
6
2
2
2
9
1
T
2
1
7
1
6
3
U
6
3
8
0
8
In addition to these stages, staff should also refer to the Big Maths scheme when planning their lessons. Children should be encouraged to
follow the FAB (mental maths) progression, which is a key feature of the Big Maths scheme.
Below are the Progress Drives related to Subtraction, which teachers should address when planning Maths.
Fact Families
•
I know the fact families for 1d+1d (L2) 3+4=7, 4+3=7, 7-3=4, 7-4=3
• I can turn 1d+1d facts into multiples of 10 (L2) 30+40=70, 40+30=70, 70-30=40, 70-40=30
• When given a single fact, I know the fact family (L3) 23+41=64, 41+23=64, 64-23=41, 64-41=23
• I know the fact families for 1dx1d facts (L4) 2x9=18, 9x2=18, 18÷2=9, 18÷9=2
• I know ‘smile multiplication’ fact families (L4) 20x90=1800, 90x20=1800, 1800÷20=90, 1800÷90=20
Multiply by 10,100,1000
• I can multiply whole numbers by 10 (L1)
• I can multiply whole numbers by 100 (L2)
• I can multiply decimals by 10 (L3)
• I can multiply decimals by 100 (L4)
• I can multiply whole numbers and decimals by 1000 (L5)
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in writing of Essex Education Services
Smile
•
•
•
•
•
Multiplication
I can multiply multiples of 10 (L3)
I can write smile multiplication times tables
I can write smile multiplication fact families (L4)
I can do smile multiplication for tenths (L4)
I can do smile multiplication for hundredths (L5)
Coin Multiplication
• I can complete a 1,10, card
• I can complete a 1,2,5,10 card
• I can complete a full coin card
• I know when to add 2 multiples together
• I know when to add 3 multiples together
Multiple…Factor, Square,Prime
• I know what a multiple is (L4)
• I know what a factor is (L4)
• I understand square numbers (L4)
• I understand prime numbers (L5)
Doubling the Big Maths way
43
214
/
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/ | \
40
3
200 10 4
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/
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86
400 20 8
\ | /
428
Copyright. This material has been produced by Essex Education Services and may not be copied, duplicated or otherwise reproduced whether for profit or otherwise without the express permission
in writing of Essex Education Services