# Track the Trends

## Predict the Future?

#### Unit Summary

Taking on the role of statisticians, students choose a subject of interest (AIDS rate, rise of average baseball salaries, state population growth, and so forth) and collect statistical information about the subject over time. Using a graphing calculator and an exponential regression function or a spreadsheet and regression trendline function, students derive the equation for curve of best fit for the data. The actual data and curve of best fit are graphed, and future predictions are made using the equation. Finally, students evaluate and present the socioeconomic implications of their predictions and the validity of their statistical investigation as a tool for predicting the future.

Curriculum-Framing Questions

**Essential Question**

What does the past tell us about the future?**Unit Questions**

What variables limit or sustain the continuation of a trend?

How does a trend affect people’s choices?

What will our quality of life be like in the future?**Content Questions**

What is an exponential regression, curve of best fit, and correlation coefficient?

What are the advantages and limitations of linear regression for analysis of data?

Assessment Processes

View how a variety of student-centered assessments are used in the Track the Trends: Predict the Future? Unit Plan. These assessments help students and teachers set goals; monitor student progress; provide feedback; assess thinking, processes, performances, and products; and reflect on learning throughout the learning cycle.

Instructional Procedures

Students present their investigations in slideshow presentations and either newsletters or wikis. Instruction in the development of these pieces should be threaded throughout the daily lessons.

**Day 1
**Begin the unit by asking the Essential Question,

*What does the past tell us about the future?*Ask students to think individually about the question and then discuss their responses with each other. Ask for volunteers to share their responses with the whole class.

Introduce the following Unit Question,

*What variables limit or sustain the continuation of a trend?*Explain to students that they will be exploring this question throughout their work on the project.

Begin the project by sharing the project presentation. Brainstorm possible topics that might have appropriate data sets. Discuss and evaluate the ideas students contribute. Ask if statistical analysis using linear regression would be appropriate for the topics suggested. (Note: A

*limitation of regression analysis*is that it assumes trends are linear, that is, straight lines without turning points. If turning points occur, they need to be controlled for, and controls introduce other problems. For this reason, regression analysis can lead to erroneous results when dealing with these kinds of data. Careful guidance is necessary to help students pick projects for which linear regression is appropriate.) Discuss print and electronic resources for collecting data. Possible topics include:

- AIDS deaths
- Crime and crime rates
- Deaths
- Divorces
- Education
- Energy consumption
- Families and households
- Gold reserves of central banks and governments
- Gross national product (GNP)
- Health expenditures
- Housing
- Live births
- Marriages
- Natural disasters
- Pollution
- Sports leaders

Hand out the project rubric and discuss. This rubric provides an overview of the project expectations for the students. Have students use the rubric to help them assess their progress and learning.

**
Day 2
**Ask students to discuss the Unit Questions,

*How does a trend affect people’s choices?*and

*What will our quality of life be like in the future?*Write answers on chart paper and post around the room. Have student teams choose roles that fit with their topic and explore the Unit Questions. Tell students that they will create two projects that incorporate answers to the questions as well as the Unit Question that was introduced on Day 1,

*What variables limit or sustain the continuation of a trend?*The projects are:

- A slideshow about the trend and possible implications, using mathematical tools of statistical analysis

AND either - A newsletter with brief articles and graphs about possible effects and implications of the trend

OR - A wiki* about the topic, including implications and effects (The wiki should include data or a graphical representation of data to back up any predictions.)

Allow students to choose team members. Membership may be formed based on topic of interest. A different topic should be explored by each team of students. Remind students to use the Unit Questions in their projects.

Pass out the slideshow checklist to all students and either the newsletter checklist or wiki checklist, depending on the publication format each team chooses. Review the checklists and have students use them to monitor their progress while working.

**Day 3**

Instruct students to begin researching their topics. Conference with students individually and as teams to answer questions, discuss their progress, and assess higher-order thinking.

**Day 4**

Show students how to do exponential regression and explain the following mathematical terms:

- Correlation coefficient
- Curve of best fit
- Exponential regression

Have students create equations of curve of best fit using their own data. Allow students to choose either their graphing calculator or a spreadsheet to enter data. If they choose the spreadsheet, have them examine the data graphically and then choose regression trendlines that best fit their data, allowing them to make reliable predictions. For students unfamiliar with spreadsheet use and regression trendlines, provide them with a copy of the adding trendlines document and the spreadsheet sample of the California Population data.

Next, have students calculate future predictions.

**Day 5**

Have students create graphs of historical data versus curve of best fit and brainstorm the ramifications of predictions. Provide students with time to complete additional research as needed.

**Day 6**

Ask students to complete the research on their topic, incorporating their mathematical knowledge.

**Days 7 and 8**

Have students complete their slideshow presentations and their newsletters or wikis. Remind students to use their checklists to review and finalize their work.

**Day 9**

Provide time for students to present their final projects to the class. Use the project rubric to assess students’ work.

**Day 10
**Give the class an essay examination by instructing students to respond to the following:

- Define linear regression and give strengths and weaknesses of using this type of model to predict a future value for your data.
*What variables limit or sustain the continuation of a trend?**How does a trend affect people’s choices and quality of life?*- Think of another way to predict a future value for your data (imagine you are asked to do this and you have never heard of linear regression). Describe your approach, and discuss the advantages and disadvantages of your approach.

Prerequisite Skills

- Experience using graphing calculators
- Experience creating a scatter plot and curve of best fit by hand
- Some experience with creating multimedia presentations, newsletter publications, and wikis
- Familiarity with conducting Internet research

Differentiated Instruction

**Special Needs Student**

- Reduce assignment or allow more time as needed

**Gifted/Talented Student**

- Have the student create a linear function for the same data and compare it to the exponential function, and answer the question,
*Which function is more realistic and why?*

**Nonnative Speaker**

- Allow students to access Internet sites in student's first language
- Pair students with a peer

**Credits**

Doug Cox participated in the Intel® Teach Program, which resulted in this idea for a classroom project. A team of teachers expanded the plan into the example you see here.

**Background:** From the Classroom in California, United States

#### At a Glance

**Grade Level:**9-12**Subjects:**Algebra, Social Issues**Topics:**Graphing, Regression Functions**Higher-Order Thinking Skills**: Analysis, Interpretation, Evaluation**Key Learnings:**Organizing Data, Critical Thinking, Statistical Analysis**Time Needed:**10 class periods (or more) of block schedule, 90-105 minutes per period

#### Mobile Learning

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#### Common Core Alignment

This unit is aligned to Common Core State Standards for Math.

Math: N-CN The Complex Number System, A-CED Creating Equations, A-REI Reasoning with Equations and Inequalities