This is a sub-page of our page on Interactive Learning Objects.

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This Arrow Board introduces addition and subtraction of integers as addition of signed numbers (= one-dimensional vectors). For example, 4 - 3 is conceptualized as 4 + (-3).

Subtraction (a, b) = Addition (a, Negation(b)).

The expression -a is interpreted as the vector a turned around 180˚. Hence we have (-(-a)) = a.

The associative law: a + (b + c) = (a + b) + c

and the commutative law: a + b = b + a

are established by experiment. Later, they will turn into definitions.

When the properties of this one-dimensional vector addition has been established, the arrows can be expanded into the two-dimensional space provided by the black/white-board. Then the associative and commutative laws of vector addition can be experimentally verified there.

See this picture for an example of what this could look like.