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







Pupils should be taught to: 

 solve onestep problems involving 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 division facts for multiplication tables up to 12 × 12
 use place value, known and derived facts to divide mentally, including: dividing by 1;
 recognise and use factor pairs and commutativity in mental calculations











Pupils should be taught to: 

 recall and use division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers
 calculate mathematical statements for division within the multiplication tables and write them using the division (÷) 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 division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts.







Upper Key Stage Two
Year 5 




Pupils should be taught to: 

 solve problems involving division where larger numbers are used by decomposing them into their factors
 divide numbers mentally drawing upon known facts
 divide numbers up to 4 digits by a onedigit number using the formal written method of short division and interpret remainders appropriately for the context
 divide 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.







Lower Key Stage Two
Year 3 




Pupils should be taught to: 

 recall and use division facts for the 3, 4 and 8 multiplication tables
 write and calculate mathematical statements for division 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 division, including 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: 

 divide numbers up to 4 digits by a twodigit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context
 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 division as sharing 



Develop division as repeated grouping (repeated subtraction of sets of the same size) using practical apparatus and diagrams. 






STAGE 2 

Develop an understanding of division using arrays and number lines showing repeated groups. 

Use number lines to show repeated grouping (repeated subtraction of sets of the same size). 





STAGE 3 

Develop the use of ÷ and = symbols to record calculations horizontally 
Use arrays and other practical apparatus to illustrate making of repeated groups. 

Begin to derive new facts from known facts 

e.g. 
6 ÷ 2 
= 
3 

(known fact) 


60 ÷ 2 
= 
30 




600 ÷ 2 
= 
300 





Begin to carry out division of two digit by one digit numbers, illlustrating this using informal methods first if required. 

First without remainders 



Then introducing remainders 





STAGE 4 

Division using larger multiples of the divisor, first with no remainders, then with remainders 

36 ÷ 3 
37 ÷ 3 









STAGE 5 

Move to develop the standard method for short division, first with no remainders, then with remainders. 

36 ÷ 3 
37 ÷ 3 









STAGE 6 

Extend written calculation methods to HTU ÷ U, then to ThHTU ÷ U, first with no remainders, then with remainders, illustrating this using informal methods first if required. 

No carrying forward required 
336 ÷ 3 
(as above, but with additional hundreds column) 

No carrying forward required, but with remainders 
337 ÷ 3 
(as above, but with additional hundreds column) 

Carrying forward required 
536 ÷ 4 

Carrying forward required, but with remainders 
539 ÷ 4 





STAGE 7 

Extend written approaches to the formal method of long division when dividing by twodigit numbers, illustrating this using informal methods first if required. 








becomes 

28 
r 
12 




28 
r 
12 




15) 

4 
3 
2 


15) 

4 
3 
2 




3 
0 
0 

(15 x 20) 


3 
0 
↓ 














1 
3 
2 




1 
3 
2 




1 
2 
0 




1 
2 
0 















1 
2 





1 
2 






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