Linear vs Non-Linear Functions

In Algebra I, we are working on determining whether a function is linear or non-linear.  We have been using visualpatterns.org as Thursday bellringer problems each week, so I started this lesson by showing the students 3 patterns (2 linear, 1 non-linear) and asked them to write an equation for each pattern and graph the points using my version of Sheri Walker's handout from visual patterns.org.

The first two were pretty easy for them since they looked like the bellringer patterns (nice and linear).  The third one was a little tricky.  With some assistance the students were able to figure out the pattern.  We then talked about what made the third pattern different than the first two.  A lot of students picked up on the fact that the rate of change was different, some even mentioned that the equation had an exponent.  We compared the graphs and discovered that we couldn't connect the points with a line.  This opened up the discussion about how a constant rate of change (here's the INB page for rate of change from @mathequalslove) is what determines a linear pattern.  We practiced with a few examples and that was a wrap for day 1.

Today we started by reviewing with Plickers.  First time I've used them...LOVE!!!  I gave them four patterns and they had to determine if they were linear or non-linear.  Plickers are seriously awesome.  I will definitely be using them more often.  Great formative assessment.

Then we built our own non-linear and linear patterns with pattern blocks.  This was a great opportunity for my co-teacher and I to walk around, get a feel for who was still struggling and offer more one-on-one instruction.  I asked students to write their names on post-its and put them on their desks.  Then each student figured out the equation for their own linear pattern.  I had the students switch a few times, record whose pattern they were working on and figure out the equation.  I made sure I got a picture of each student's desk with name so that I could do some error checking.

 

 

 




Overall, this was a great activity.  I feel like students are really developing an understanding of rate of change and the fact that constant rate of change determines a linear function.

Next we will be delving deeper into linear functions and start making the connection between rate of change and slope.  I'm planning on doing a lot of experiments and investigations to help develop really solid understanding of linear functions.  I LOVE Andrew Busch's resources and will probably be using several of them.