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* Separating sets: including children's own signs for '='

     Children use a wide range of strategies to show that the two amounts are distinctly separate. They do this in a variety of ways including:


  • grouping the two sets of items to be added, leaving a space between them,
  • separating theses with words,
  • drawing vertical line between the the sets,
  • drawing an arrow or a personal signs  between them.

Equals signs

Young children begin to use their own means to signify the equals symbol. For example, Louisa (below) ended her calculations by writing "altogether there's '6' (circled)' and Jack drew a horizontal line before his totals, whereas Fred and John just added the number of their total, without anything to indicate the equals sign.


Louisa (5 years, 1 month), was adding

strawberries. Between her two sets she

wrote "and four more", then finally wrote

"altogether there's '6' (circled)'. Louisa has

chosen a means of representing that she

felt comfortable without the same time

showing that she understands the



  • Taxonomy: Calculations, children's own


  • Early addition







Jack (5 years, 3 months), wrote two sets of grapes,

leaving a space that allows this to breed as '4 and 3',

then writing the quantity of each to be added. Finally

he drew a horizontal line (to signify the equals sign),

followed by the total of each calculation.


  • Taxonomy: Calculations, children's own


  • Early addition



Fred, (5 years, 8 months), has separated his

two sets of grapes with a line (drawn above

one finger of the hand). The plus and equals

signs are implied, since the whole canoe read

as '5 plus1 equals 6'. Finally he wrote the

numerals '5' and 1 on the left, and the '6'



  • Taxonomy: Calculations, children's own


  • Early addition

John (5 years, 5 months), chose to write a

written response: "2 grapes there is two [,]

4 grapes there is four." He also wrote the total

'6' on the left.


  • Taxonomy: Calculations, children's own


  • Early addition