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Multiplication 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 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 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.
   
   
 
  Key Stage One
  Year 2
   
    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 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.
  • Know and use the vocabulary of prime numbers, prime factors and composite (non-prime) 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 two-digit numbers times one-digit 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 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 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.

3.1    
     
 
STAGE 2

Develop an understanding of multiplication using arrays showing repeated groups.

3.1      
 
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.

3.1 3.1    
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
12 x 3    
| \      
10 2      
         
3 x 2 = 6
3 x 10 = 30
30 + 6 = 36
3.1
15 x 4    
| \      
10 5      
         
4 x 5 = 20
4 x 10 = 40
40 + 20 = 60
4-1 4-3

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

  T U    
  1 2    
x   3    
 
   
    6 (3 x 2)
  3 0 (3 x 10)
 
   
  3 6    
4-4
  T U    
  1 5    
x   4
 
 
  2 0 (4 x 5)
  4 0 (4 x 10)
 
   
  6 0    
  T U    
  1 5    
x   4    
 
   
  6 0  
 
 
  2      
         
4-5

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    
         
3 x 6 = 18
3 x 10 = 30
3 x 200 = 600
         
600 + 30 + 18
         
         
         
         
         
         
         
         
= 648      

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
       
         
         
         
T U      
1 6      
  3      

     
4 8      

     
1        
         
         
 
 
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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