# Arrow Board

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.