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Separating sets, including children's own signs for '='

Separating sets

Children use a wide range of strategies to show that their two amounts are distinct and 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 sets,
  • drawing an arrow or a personal sign between them.


Equals signs

Young children begin by using their own means to signify the equal’s symbol. For example, Louisa (below) ended her calculations by writing the words "altogether there's '6'" (circled) and John merely wrote "is" before his total, whereas Fred just added the number of their total, without anything to indicate the equal’s sign. In his calculation, Jack used a horizontal line to signify 'equals'.


Louisa's strawberries

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

       methods / explorations with signs and


  • Early addition

Adding grapes

In this class, the children had been invited to

choose some grapes to add, dividing them

between two dishes (they could eat them


   John (5 years, 5.5 months), wrote and

drew two sets of grapes, leaving a space

that allowed this to be read 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

       methods  / explorations with signs and


  • Early addition

Fred adds grapes

Fred, (5 years, 8 months), was also adding

grapes 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' beneath as the total.


  • Taxonomy: Calculations, children's own

       methods / explorations with signs and


  • Early addition







Jack's addition response

Jack explored abstract symbols in a diferent 

way. He has drawn two separate sets of

grapes, leaving a gap that allows this to be

read as '4 and 3'. Following this he

confirmed the amounts to be added by

writing the numerals and drawing a

horizontal line between these and the final

'7' (his answer). The line functions as an

equals sign for Jack.


  • Taxonomy: Calculations, children's own


  • Early addition