Math = Love: Fun With Linear Regression Labs

## Sunday, October 6, 2013

### Fun With Linear Regression Labs

My Algebra 2 students just finished with our second unit of the year on linear functions.  The unit didn't exactly go as I had planned.  Their prior knowledge of linear functions was shockingly low.  They knew it had something to do with y=mx+b, but they couldn't tell me what m and b stood for.  They knew there was some formula for slope that involved x1, x2, y1, and y2, but they could never remember the order.

So, I basically ended up starting from scratch with these students which took much more time than I had planned on devoting to this unit.  I will share the interactive notebook pages and specific activities we did later, but I do want to share the linear regression labs I did with my students.  I wish I could say that my students loved these, but they didn't.  They regularly told me how boring algebra was.  I think the day I heard the most complaints was the day we performed a linear regression on data we gathered by eating twizzlers.  How can eating twizzlers in math class be anything but exciting?!?

## Linear Regression Lab 1: Personality Test Results

To introduce my students to linear regression, I had them do the True Colors Personality Test that I wrote about this summer.  I had wanted to do this with my students at the beginning of the school year, but after two days of getting to know you activities, I was ready to jump straight into some mathematics!  So, I saved the activity for later in the semester.  We spent about 2/3 of the fifty-minute class period taking the personality test and learning about or results.  My kids got really into this!  I may have encouraged their interest a little by telling them this personality test would help them better understand their boyfriend/girlfriend.  I ended up having to make copies of what each color means to give to the students because so many of my students wanted to give the personality test to someone and interpret the results.

The last third of the class period was full of data collection and graphing calculator action.  I made a table on the Smart Board.  Number of People vs. Time.  I asked one student to volunteer to use the stopwatch on their phone to time the students for this activity.  The students at table one took turns saying their name and their color from the personality test.  We stopped the time and recorded the number of students and total time.  We repeated this with table one and table two.  We repeated it again with the students at tables one through three.  Eventually we got a time for the students at all five tables saying their name and color.

Together as a class, the students walked through the process of performing a linear regression of the form y=a+bx.  This summer, I went to two separate week-long workshops that told me that I should stop teaching y=mx+b and start teaching y=a+bx.  The first time I heard that, I wrote it off as crazy talk.  After all, y=mx+b and I have been friends since middle school.  But, the second time I heard that, I started to think that there might be some merit to the idea.  This year, I am experimenting with teaching y=a+bx for the first time.  I'm still not quite sure how I feel about it, though.  I guess time will tell.  (I also would have never thought that I would have given up my trusty TI-84 for a TI-Nspire, but that has also happened.  I was helping a student with their TI-84 on Friday, and it was such a weird experience.  I've started to forget where some of the buttons are already!)  We discussed the slope and the y-intercept and their meaning in this situation.  We also discussed reasons why our data was not perfectly linear.  The bell rang before we could delve much deeper into it.

I have also done this activity without having the students share results.  At one workshop, we called this "Pass the Buck."  The presenter took a dollar bill out of his wallet and gave it to someone sitting at the first table.  That person said their name and passed the buck to the next person.  We stopped at the end of the first table and recorded the time.  The buck made it's way back to the original person, and we timed the amount of time it took to pass the buck to the end of the second table.  This process continued until the buck had made it to every table.

## Linear Regression Lab 2: Bouncing Tennis Balls

 Bouncing Tennis Balls Lab

This lab was another activity that I learned about through the OGAP Common Core Training I attended this summer.  It is based on an Illuminations activity from NCTM.  Students are given a tennis ball to bounce for two minutes.  Every ten seconds, the number of bounces is recorded.  I learned a lot from doing this activity for the first time.

1.  When you teach in a building that was built in 1919 and your room is on the second floor, it's not a good idea to do this lab in your classroom.  The science teacher whose classroom is directly beneath you will send a student upstairs to ask you to stop doing whatever you are doing because it is distracting them.  Oops...  I guess five bouncing tennis balls can make quite a bit of racket.  We ended up going down the hall to the auditorium and doing our bouncing on the stage.

2.  Do not hand out the tennis balls to the groups until the last minute possible.  Otherwise, students will start their practice bounces before you demonstrate the proper way to bounce a tennis ball for this lab.  Then, you will find yourself in a scenario like this.

Student - Can we have another tennis ball?
Me - What did you do with the tennis ball I just gave you?
Student - We might have lost it?
Me - How could you lose it?  I just gave it to you a few seconds ago!
Student - Well, I only bounced it once, but...

Immediately, all eyes in the classroom were drawn to the ceiling.  Other perks of working in such an old building are that there are incredibly high ceilings and random pipes running EVERYWHERE.  Okay, maybe only one of those is a perk.  I looked up above the light fixtures to see the tennis ball resting on some pipes.  If you look closely, you should be able to see it.

I told the students that they would not be given another tennis ball.  If they could get the tennis ball up there, they could find a way to get it down.  Eventually, one of the students stood on top of their desk and used an umbrella to dislodge the tennis ball.

3.  Even if you show students the proper way to bounce a tennis ball so their data is linear, they will not listen.

4.  The provided table asks students to count the number of bounces in each ten-second interval.  Then, afterwards, they are supposed to fill in a third column with the cumulative number of bounces.  This will confuse students INCREDIBLY.  Have students mark out the middle column and ONLY record the cumulative number of bounces.

5.  Yes, having each student collect their own set of tennis ball data sounds like a great idea.  But, you will be much saner if you have each group collect one set of data.  That was a lesson learned the hard way!

Here is the handout I created to use with my students.  I took the activity a step farther than Illuminations did and used it as an opportunity to review a lot of the concepts that we had started working with in Unit 1.  Students were asked to classify variables as dependent and independent, calculate the rate of change between various intervals, classify a scatter plot as linear or non-linear, determine if the produced scatter plot is a function, describe the relation as increasing or decreasing, perform a linear regression using their calculator, interpret the meaning of the slope and y-intercept in this particular situation, and use the regression equation to make predictions.  Once students were done with the lab, their page could be folded in half and glued in their interactive notebooks.

## Linear Regression Lab 3: Twizzlers!

 Twizzlers Linear Regression Lab

The Twizzler Lab was not an original idea.  I stole the idea from here and modified it to fit my group of students and their needs.  The idea is simple.  Give students a twizzler to eat.  Before students take a bite from their twizzler, they measure its length.  After each bite, they remeasure the twizzler until they have eaten the entire thing.  They use this data to create a scatter plot and perform a linear regression.

I used almost the exact same set of questions from the tennis ball lab with the twizzlers lab.  I was surprised by the number of students who claimed to not like twizzlers.  I mean, I don't like twizzlers, but I figured most teenagers did.  I'm more of a chocolate person myself!  I told those students who didn't like twizzlers to have someone else eat their twizzler for them.  But, they still had to participate and take the measurements.

Files can be found here.