Unit 5 Scatter Plots, Correlation, and Line of Best Fit

Right after mid term exams we cover this mini-unit. The lessons take about a week (remember we meet every day for 82 minute blocks) then we work on our performance task. We use one class block to get started on this and then students get about a week to complete it.

Students worked with scatter plots in eighth grade, so they know about creating scatter plots and correlation. They might not have done much with lines of best fit and probably didn't learn how to do it on the graphing calculator yet. We do them both "by hand" and using the graphing calculator (TI-84 or TI-83 also works).

PreAssessment

Here's a "preassessment" kind of thing that works well in determining understanding and having students think about what we will be doing next. I started doing these in a multiple choice format so I could "plicker" to quickly assess how students are doing. If you have checked out https://www.plickers.com/ it's great!  You have to have a smart phone of some type (android or iphone) and the students hold up cards to display their answers and you read the answers by scanning across the room with your phone. It works really well and gives you a quick real time summary of what students know.

The Lessons

Correlation:

We start with what they understand correlation to mean. Then we fill in our left hand learning page about correlation.

Then students sort cards that indicate possible relationships. They decide if they have positive, negative or no correlation. Here are the "cards", caution students can take a long time cutting things out, you can hand this out the night before and have them cut them out for class (use envelope on inside back cover to hold the cut out cards).

I have them glue in a few cards of each. I think next year I'll make this into a foldable - just fold an 8.5x11 sheet of paper in half and create a little booklet. Front cover could be positive correlation, inside negative correlation and no correlation. It will give us more space. At bottom of each can have "sample correlation sentence" corresponding to one of the examples on that page. 

Scatter Plots by Hand:

Then we do work with making scatter plots by hand. Here are some materials I use with students: NBA players and Full Analysis example. And a foldable to summarize the steps. 

 We also talk about interpolation & extrapolation. Here's a foldable to illustrate this:

We fill in definitions of interpolation and extrapolation (apparently I didn't do that, this was before I started using a document camera). Next year I'll add a place to also write a correlation sentence for this example plus what type of correlation is shown.

Correlation and Causation:

The tricky thing about correlation is that most people assume the correlation implies causation, wrong!  This is a common misconception and something that warrants a bit of discussion. Here is an introduction worksheet that I have students work together on. *updated in 2016 I used a powerpoint to lead the discussion on this topic. All materials in the link at the at of this post.

Then we summarize with an ISN foldable. (but I put the examples from the foldable on the board before handing it out for some discussion first).

with cute little saying I found on pinterest:

Common misconception - students think a relationship is either a correlation or a causation. They don't see that something is either a correlation OR a correlation and causation. It's a bit tricky and abstract for them. 

Outliers & Influential Observations:

Next topic is Outliers and Influential Observations. I've started to do both because not all "distant data points" are outliers. If they follow the general trend line they are influential observations. I didn't actually know that and I think it's important to know. Here's a classwork discussion worksheet. And here is my ISN foldable for summarizing. *again in 2016 I used a powerpoint to lead the discussion on this. files all available at the end of the post.

Scatter Plots on the Graphing Calculator:

Now we bring in some technology. Students learn how to create scatter plots on their calculators. Not all my students have the same operating system so my foldable has instructions for both. I like to have students use the [VARS] menu to insert the linear regression equation directly into Y1 and calculating the linear regression looks a bit different depending upon the operating system. Here is their instruction foldable. I expect advanced students to learn this and know how to do it without instructions on assessments. (they need to get very fluent with graphing calculator).

I also like the "diagnostics" to be "on" so they can examine the regression coefficient to evaluate the strength of the correlation. Here is the foldable for that.

Data Sets:

Here are some data sets that I then have students work with and here is the answer key. 

Performance Task:

Our summative assessment for this unit is a performance task that has students compare fat and carbohydrate content of snack foods. It's a fun activity with some good analysis. *previously I had a question that introduced an item that would be an outlier. After correcting my 2016 performance tasks I tweaked my write up a bit more (in addition to fixing typos on the rubric) so that we have a weird item in our data to start (steak!) and let students discuss what that does in the write up. All update files below.

All my files for this unit can be found HERE. I did update some of my ISN inserts in 2016. They are not hugely different and the window for blogging about them is gone so I'll probably blog about them in 2017! But all the documents can be found in my box file posted above.