Regression Models

The Common Core State Standard for investigating patterns of association in bivariate data begins in MATH-8 and is further expanded in Algebra 1. However, these standards are merged in Acclerated Algebra 1.

The Tongue Twister Lab Activity prompts students to gather data, analyze visually, and use an informal model to make a prediction. (CCSS 8.SP.A.2) This activity not only gives students a context as a foundation, but it also compartmentalizes the process used with regression via technology. Each student is provided a list of Halloween tongue twisters to review, select, and present to his team. Then the team selects one twister to use for data collection. This activity is intended to be completed manually...think large graph paper, meter sticks, etc.

Tongue Twister Lab Activity

Teachers can integrate a class discussion to review proportional vs. non-proportional relationships, linear vs. nonlinear, comparing rate of change between trend lines from different teams, etc. And then it's time to formally fit a function to the data with the use of technology. The duration of this lesson generally spans two 80-minute periods.

It may be helpful to provide students with a Regression Guide to follow when completing the steps in a graphing calculator. Don't be discouraged if it takes several attempts for students to become fluent with the graphing calculator. Additional problems can provide formative assessment on their progress with technology and an opportunity to interpret the rate of change and initial value within new contexts of data.

Cell Phone Problem

And this Election Day problem is time-sensitive; however, the idea can be adjusted to any election being conducted in your area.

Election Day Problem

The following activity is most conducive to cooperative learning teams. Students are provided details about three players gathering gold coins in a marathon month of the Super Mario game. The scenarios yield linear, exponential, and quadratic function models. Not only does this activity prompt students to investigate patterns and utilize regression via technology, but it also overviews the three major functions included in Algebra 1.

Team Problem

Super Mario Functions Record Sheet

This activity set highlights Common Core State Standards 8.SP.A.2, HSS-ID.B.6a, HSS-ID.B.6c, and HSS-ID.C.7 included in 7th and 8th Accelerated Algebra 1.

Characteristics of Functions

The Common Core State Standards include three functions in Algebra 1.

• linear
• exponential
• quadratic

Linear and quadratic functions are exhausted. Exponential functions are introduced with respect to making comparisons between arithmetic and geometric sequences but not exhausted. Absolute value functions are optional for Algebra 1; however, the spin-off from linear functions is seamless. And absolute value functions are perfect for initial practice with function transformations.

Several linear function concepts are introduced in MATH-8, but these are the same standards that are pushed to Accelerated Algebra 1 in the CCSS Accelerated Pathway outlined in Appendix A. The Retro Race activity contains a problem set that can be integrated throughout a linear functions unit or used as a cumulative review at the conclusion of the unit. (This activity stems from CPM Sample Chapters and LTF Training.)

A portion of the problem set highlights one of the participants in the race. Based on the information provided, students are prompted to create a table of values to view the participant's distance as a function of time and subsequently graph the results.

Characteristics of Functions Record Sheet

Students use the context of the situation to understand key features of the function including intercepts and intervals where the function is increasing, decreasing, positive, or negative.

This investigation highlights Common Core State Standard HSF-IF.B.4 that is included in 7th and 8th Accelerated Algebra 1.