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Division Calculation Guidance

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

   
 
  Key Stage One
  Year 1
   
    Pupils should be taught to:
 
  • solve one-step 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
   
   
 
  Key Stage One
  Year 2
   
    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 one-digit 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 two-digit numbers times one-digit 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 two-digit 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 1-1  
Develop division as repeated grouping (repeated subtraction of sets of the same size) using practical apparatus and diagrams.
1-2
 
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).
2-1
 
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 3-1 3-2
Then introducing remainders 3-3 3-4
 
STAGE 4
Division using larger multiples of the divisor, first with no remainders, then with remainders
36 ÷ 3 37 ÷ 3  
4-1 4-2  
 
STAGE 5
Move to develop the standard method for short division, first with no remainders, then with remainders.
36 ÷ 3 37 ÷ 3  
5-1 5-2  
 
 
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
6-1 6-2 6-3 6-4
 
 
STAGE 7
Extend written approaches to the formal method of long division when dividing by two-digit 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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