Understanding measurement

or A LESSON UNITS, UNCERTAINTY AND SIGNIFICANT FIGURES

I find students when they start a physics course, have a weak understanding of how measurement works and how values are discussed, and so I cover key concepts of units, uncertainty and quoting of significant figures, before I start the physics course proper.
What follows is a an activity I do with the students over the course of 1-2 hours.
(I include some thoughts in red)

 Determining the Density of a pice of paper
 
Divide your class into groups of 3
Give each group a single sheet of A4 (or 'letter') sheet of paper and ask the to determine its density as accurately as possible.
Give as little instructions possible but provide them only a meter ruler and access to a set of digital scales.

Finding the length and width is relatively straight forward, but the thickness is another matter.
I find the students generally fall into two camps, they either fold the paper multiple times to ge a thicker section (which has its limitations) or they ask for a stack of paper and measure that (again, the size of the stack contributes to uncertainty)

Once they determine the dimensions and the mass, and thus calculate density, get them to write their answer on the board.

When I survey their responses, most get similar 'numbers', however, there will be some with different units (I insist on them quoting units) and many over quote significant figures.
So as I discuss the results in the class I ask
"Are these results the same?" 
To the ones who over quote numbers, I ask "how confident are you of those number?"
I then ask about the thickness measurements, "How certain are you about the number being that precise value?"
This then all leads to a discussion on 
- talking the same 'language' - SI units
- how we express our uncertainties
- the role of significant figures (check out my video here)

At this point , teach the points measured above, including how to express uncertainties

Once you have covered the concepts , get students to repeat the task, but prior, teach them how to use a micrometer.
Students now need to determine the density, using same units, and quoting with % error and in correct significant figures.

When results are compared on the board, all their results should fall within the uncertainty of the over the results (hopefully :) ). This could be graphed to make it more clear.

Feel free to provide feedback below and any modifications you tried