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Why is the meter stick a math tool?

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Because it measues distance between lengths of object of the SI (System Of International Units)
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What is is meter stick?

A meter stick is a device one meter in length, with centimeters and millimeters marked out along it's edges for measuring.
In Science

What do a meter stick does?

First of all, it is "what does a meter stick do?" And the answer is that it measures length in the metric units of decimeters, millimeters, centimeters and/or meters.
In Science

What are the math tools?

A brain, paper, pencil, compass, straight edge. <-- from ancient times more modern slide rule, tables for logs/trig values, now replaced by calculators and computers.