Multiplication Calculation Guidance
THE FOLLOWING ARE STANDARDS THAT WE EXPECT THE MAJORITY OF CHILDREN TO ACHIEVE







Pupils should be taught to: 

 solve onestep problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher.







Lower Key Stage Two
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 twodigit and threedigit numbers by a onedigit 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.











Pupils should be taught to: 



Solve problems with subtraction: 

 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.







Upper Key Stage Two
Year 5 




Pupils should be taught to: 

 multiply numbers up to 4 digits by a one or twodigit number using a formal written method, including long multiplication for twodigit 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.
 Know and use the vocabulary of prime numbers, prime factors and composite (nonprime) numbers
 Identify multiples and factors, including all factor pairs of a number, and common factors of two numbers
 Establish whether a number up to 100 is prime and recall prime numbers up to 19







Lower Key Stage Two
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 twodigit numbers times onedigit numbers, using mental and progressing to formal written methods
 solve problems, including missing number problems, involving multiplication including positive integer scaling problems and correspondence problems in which n objects are connected to m objects.







Upper Key Stage Two
Year 6 




Pupils should be taught to: 

 multiply multidigit numbers up to 4 digits by a twodigit 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 multi step problems, deciding which operations and methods to use and why
 use estimation to check answers 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.





STAGE 2 

Develop an understanding of multiplication using arrays showing repeated groups.






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. 
4 x 2 = 8 (known fact) 

40 x 2 = 80 


400 x 2 = 800 etc. 




STAGE 4 

Begin to use understanding of place value and partitioning to carry out multiplication of two digit by one digit numbers


Simple case 
Crossing tens barriers 



The term crossing the tens barrier is reference to any calculation where the sum of the digits
moves from one column to the next.

e.g. 4 x 5 = 20 which moves from the unit column into the tens.




STAGE 5 

Extend written approaches to HTU x U, then to ThHTU x U


Illustrate using partitioning approaches as required



216 
x 
3 

/ 
 
\ 


200 
10 
6 







3 
x 
6 
= 
18 
3 
x 
10 
= 
30 
3 
x 
200 
= 
600 





600 
+ 
30 
+ 
18 



Develop expanded recording in columns and then move to formal written method, using practical apparatus to support as required.



H 
T 
U 


2 
1 
6 

x 


3 






1 
8 



3 
0 


6 
0 
0 





6 
4 
8 






H 



2 



x 










6 

























STAGE 6 

Extend written approaches to HTU x TU and ThHTU x TU 

Develop expanded recording in columns and then move to formal written method of long multiplication, using practical apparatus to support as required. 


H 
T 
U 



2 
6 

x 

1 
3 






1 
8 



6 
0 



6 
0 


2 
0 
0 





3 
3 
8 





1 








H 






x 





(3 x 6) 


(3 x 20) 


(10 x 6) 


(20 x 10) 

2 









3 









1 

T 
U 



2 
6 



1 
3 







7 
8 







1 




6 
0 







3 
8 














Develop expanded recording in columns and then move to formal method of long multiplication,
using practical apparatus to support as required.



H 
T 
U 


2 
2 
6 

x 

1 
3 





1 
8 



6 
0 


6 
0 
0 



6 
0 


2 
0 
0 

2 
0 
0 
0 



2 
9 
3 
8 




1 
















x 





(3 x 6) 


(3 x 20) 


(3 x 200) 

2 
(10 x 6) 


(10 x 20) 

2 
(10 x 200) 























H 
T 
U 


2 
2 
6 



1 
3 





6 
7 
8 



1 



2 
6 
0 





9 
3 
8 





1 























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