SBAC Practice Activities: Regression and Desmos

Links:
Assignment (Google Doc)
SBAC High School Calculator
Desmos

This task is for students in Algebra II or Trig/Math Analysis.  The problems on the Google doc are modified from the textbook for Trig/Math Analysis.  The mathematical goal for this lesson is to find the equation of a linear regression for a set of data, and use the equation to make predictions.  The technology goal was to find needed information and solve problems by navigating between various windows.  Below is one of the problem sets we asked students to work on.

We had students open a separate link to access data so that they could easily copy and paste the data into Desmos in order to find the regression equation.  Below is a snapshot of the data stored in a Google Sheet.

After you copy the data from a spreadsheet, you can go to the first input line in a Desmos sheet and paste the data.  It's as simple as control-C and control-V copy and pasting.  In line 2 you type y1~ax1+b.  Desmos automatically makes the subscripts for you.  Note that we use "~" instead of "=" when finding a regression equation.  See the regression parameters on line 2.

You might be asking why we used Desmos for regression when SBAC has its own regression calculator.  The answer is that Desmos makes regresssion sooooo easy, and it also automatically scales your graph to fit the data (see below).  We didn't want students to be focusing on too many new technology skills for this lesson, so we stuck to Desmos for the regression piece.

Once students find the regression equation, they need to use the equation to make predictions/answer the questions on the worksheet.  For this part we encouraged students to have two browser windows open side by side.  They can also use paper to do some of the work, though final answers will be scored from the Google Doc. Below is a screenshot of what students see when they are working with the SBAC calculator to answer questions 9 and 10.

One of our findings from this activity was that students were not clear on how to show their math work on the computer, or they weren't sure how much work to show.  We have started coaching students on the expectations by adopting a 3-point rubric for each problem.  Students can earn credit on each problem for the following items:

-1 point earned for showing work

-1 point earned for explaining thinking (when the problem specifies)

-1 point for final answer with units.

Below is a sample response for problem 9 that earns full credit.