The fountain at the National Gallery of Art Sculpture Garden changes height over time.

I am considering starting my Algebra 2 class next year with sketching situations in two variables.  For example:

• Sketch the height of a triangle with area of 12 as a function of the length of the base.
• Sketch the height of a ball thrown into th air as a function of time.
• Sketch your ability to solve word problems over time.
• Sketch the height of the tallest building over time.

When a student sketches a situation, I would expect axes and a reasonable scale.  I would also expect a brief explanation of why they sketched it they way they did.  From the sketches we could introduce the ideas of: domain (in terms of problem), range, end behavior, function, period, max, min, slope... I would like to keep the "best" sketches on the walls.

We would then start grouping sketches in different ways.  I am imagining lots of sketches taped on the wall and physically moving them around.  Then perhaps we could also move them online for further work.  

Then I think I will begin introducing all of the parent functions.  I am not sure how I would begin that: possible operations with numbers?, just introduce them?, start with lines if they know one more it may lead into operations?.  We would then start seeing connections between functions and groups of sketches.

What I need suggestions for:

• A computer program where students could draw sketches and then later add axes and functions. Ideally free, downloadable, relatively easy to use.  Mostly basic functions, though regression might be cool if we get to that later.  If there isn't one that does both, perhaps they could draw sketches in one program, then import and add the graphs in another.  Ideas for that?
• Sketching situations.  I know this isn't that original and many people do these types of sketches.  Do you know of any sources?  Thanks to @druinok for a suggestion.
• Thoughts on the plan.  Most importantly: what are the problems with this plan?  Where am I going to mess up?
  

After this start we would focus on modeling functions to sketches and conducting experiments (find data from others) if there are disagreements about the shapes of sketches.  I really hope there are disagreements.  

Once we have functions we can then begin simplifying and solving functions to learn the algebra.