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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 symbol. In his calculation, Jack used a horizontal line to signify 'equals'. (These children had been doing a project ton 'fruit').

 

Louisa's strawberries

Louisa (5 years, 1 month), was adding

strawberries. Between her two sets she wrote

"and four more" (as her personal addition 

symbol), then finally wrote "Altogether there's '6'

(circled), the word 'altogether' standing for

the equals symbol. Louisa has chosen a means of representing that she felt comfortable with, at the same time showing that she understands the operation.

 

  • Taxonomy: Calculations, children's own

       methods / explorations with signs and

       symbols

  • Early addition

Adding grapes

In this class, the children had been invited to choose some grapes to add, dividing them between two

dishes (they would eat them later).

   John chose to use a combination of writing and drawing that he read as '2 grapes, there is two, 4 grapes, there is four'. It's interesting to see that he used both numerals and words in his calculation.

 

  • Taxonomy: Calculations, children's own

       methods  / explorations with signs and

       symbols

  • 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). Fred drew a vertical line to separate the two sets. 

   The plus and equals symbols are impliedsince the whole can be 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

       symbols

  • 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', the word 'and' suggesting the addition symbol.

   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 symbol for Jack.

 

  • Taxonomy: Calculations, children's own

       methods / explorations with signs and

       symbols

  • Early addition

 

 

           

 

 

                   

 

 

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