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). Also if you give math the teacher a bad answer she might swat you with one!
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What is an meter stick?

A stick that is one meter long, commonly with markings for centimeters and millimeters.

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 Length and Distance

What can you do with a meter stick?

Measure things, add fishing line and fish. scratch your back, spank bad people, many others.
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 Math and Arithmetic

What are the math tools?

A brain, paper, pencil, compass, straight edge.