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.
methods / explorations with signs and symbols
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![]() | 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.
methods / explorations with signs and symbols
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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 implied, since 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.
methods / explorations with signs and symbols
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![]() | 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.
methods / explorations with signs and symbols
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