Day 2 – Reading Graphs

My goal today was for students to be able to interpret line graphs.  We discussed what it meant when the line on graphs go up, straight, and down.  I started out with an unlabled line graph that we made our own story for to illustrate them the basics.  Then, I moved on to fun!  I used plenty of line graphs from Jessica Hagy’s hilarious site Indexed.  I showed them a few completed graphs as examples.  I then gave them the axes only and let them figure out how the graph should go.  When they drew the line incorrectly I would ask them questions.

For example, when I gave them axes labeled education level and poverty, several students drew the line y=x.  I asked them,  “So, you are telling me that you have ZERO years of education, but also have ZERO poverty?  Does this EVER happen in real life?”  After thinking for a minute an insightful student got the “light bulb” expression and said, “YES! Paris Hilton”!   (This entertaining but pretty accurate comment led to the discussion of outliers.)  I then explained that they needed to consider the average situation (or even the expected situation), not the exceptions.

Day 3 – FUNCTIONS

What math teacher does NOT like the function machine?  I introduced my students to the fabulous function machine.  I named my function machine Fred the Function Machine, and then gave the students inputs and outputs (with dramatic illustrations for each one).  I put the inputs and outputs into a table.  It was up to them to guess what Fred was doing inside of his box!  Once they figured out what Fred was doing, we then wrote Fred as a mathematical expression.  For the first one, Fred was doubling all of the numbers.   My kids answers were, “Times two!” and “Fred is multiplying by two!”   2(input) = output.  I talked about x and y as input and output at this point, using my table as my example.  And Fred became y = 2x.  I explained that a function was a rule and that Fred had to do this rule every time an input went in.  This led to great discussions about how different numbers produced different outputs, and that if you put the same number in you had to get the same output.

Their Own Function:

We did a few more examples and then I had them draw their own function machine.  I let them name their own function anything they wanted (they loved this), make up their own function, and only write down the inputs and outputs in an x|y table.  They, they switched with their neighbor to see if their neighbor could guess what their function was.

Function Table (Table of Values):

Next we drew and completed a table of values with four columns.  The columns were input (x), our function (rule), output, and ordered pairs.  They completed several function tables and plotted lots of points.  I am not sure about this “function table”.  As a former high school teacher, all I ever drew for the kids were the old two-column x|y tables.  However, I wasn’t sure that this was enough information for them to understand what was happening “between the lines”.  So, I decided to instruct them with all four columns because it really leads them along the way with the input, rule, output, ordered pairs idea.  BUT, I was worried because this table very large (and thus probably impossible to remember).  This prophecy came true several nights later when I instructed them to create a function table for homework and they were all lost.  I am hoping it is just lack of experience, as this is the first time they have tackled the table of values.

Overall not very original, but the Hagy graphs were fun!  Next year I would love to do something more engagine with these two days…ideas welcome.  : )