Children\'s Mathematics

Comparison of strategies to add and subtract when counting

continuously

Addition Subtraction

Additional features when representing subtraction

Children show that they have taken away some items by:

• rubbing out items or numerals they have represented (see for example Figure 7.2b,
  Louisa)


• crossing out items or numerals (see for example Alice’s flowers, Figure 7.2a)


• circling items or numerals to be ‘taken away’


• using arrows – either to show which ones have been removed, or to show the
  direction of ‘taking away’ (see examples in Figures 7.4 and 7.5 ‘subtracting beans’).

An extension of this is when:

• some children begin to show the actionof ‘taking away’, often showing the hand
  removing or holding some items or numerals (see for example Figures 7.4 and 7.5)


• some children begin to put the total that remains after subtraction.
  
  
  • They count one-to-one
  
  
  • Children understand the need to
    count everything to arrive at a total
    
    
    • They count one-to-one
    
    
    • Children understand the need to
      count everything to arrive at a total,
      then count those that remain after they
      have removed some
    
    
    
    
  
  
  • To add the totals of two sets, children
    count the items or numerals
    continuously, starting at one (or the
    first item they have shown)
    
    
    • To subtract, children count the first
      amount and then use some means to
      show how they removed the second
      amount (see below)
    
    
    
    
  
  
  • Where numerals are used, the two
    sets to be added are represented as one,
    the numbers continuing in sequence for
    the whole amount
    
    
    • Where numerals are used, the first
      amount is shown in sequence beginning
      with 1, then children count back the
      amount that is to be taken away
    
    
    
    
  
  
  • The pictures, icons or numerals
    representing the two sets are often
    arranged in a horizontal linear
    arrangement, or occasionally in a
    vertical arrangement (see for example,
    Figure 7.1. The points in the remainder of
    this column also apply to Figure 7.1)
    
    
    • Horizontal or vertical layout as in
      addition, to show the total of the first
      amounts (before ‘taking away’) (see for
      example Figure 7.3a and b. The points in
      the remainder of this column also apply to
      this figure)
    
    
    
    
  
  
  
  

Children can represent and count

things they choose but cannot see, and

also some things they physically count

and then represent.

Features of counting continuously to add

may include:

They can represent and count things

they choose but cannot see, and also

some things they physically count and

then represent.

Features of counting continuously, then

removing some to subtract may include:

110 Children’s Mathematics

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