# Illustrative Examples of Units of Practice

## Snapshot

Students form hypotheses based on preliminary research about trends in the ages of Academy Award winning actors and actresses. To test their hypotheses, students use the measures of central tendency to analyze the ages of Academy Winners for the last 50 years. They determine the averages (mean, median, mode), construct box plots and interpret the results. Students write reports and make presentations justifying their conclusions.

Unit Details:

Subjects: Math, Science, Social Studies

Author(s): Douglas Blackmore

## Invitation

How can we help students draw inferences from data and graphs to support hypotheses? Using the Academy Awards and the ages of award winning leading actors and actresses, we can determine trends in the age of future Award winners.

## Outcomes

Mathematics 9-12

Statistics: Mean, Median, & Mode

Social Studies 9-12

Behavioral Studies

National Council of Teachers of Mathematics 9–12 Standards:

• Create hypotheses from real world situations

• Construct and draw inferences from graphs that summarize data from real-world situations

• Use and value connections between mathematics and other disciplines

• Express generalizations discovered through investigations

• Express mathematical ideas orally and in writing

National Science Education 9–12 Standards:

• Use technology and mathematics to improve investigations

• Formulate and revise scientific explanations using logic and evidence

## Situations

All discussions take place in the classroom. The students should be able to find mean, median, mode, quartiles and create box plots. The activity can be completed using pen and paper or technology.

For wired classrooms; Internet research, Excel spreadsheet graphs and Power Point presentations are completed using both the school computer lab and classroom computers.

Pen and Paper assignments can be used to complete the project. Graphing calculators can be used to calculate the measures of central tendency.

This project takes a period of approximately 8 hours.

Phase 1

Students will discuss recent Academy Award Films, actors, and actresses. Ask students if they think the ages of the award winning Hollywood famous are changing. From the discussion/research, have students formulate an hypothesis about a possible trend.

Obtain hard statistical data about Hollywood leading actors and actresses ages for the last fifty years.

Phase 2

Have students divide the data into 25 year periods. A spreadsheet or a graphing calculator can be used to calculate mean, median, mode and quartiles for each 25 year period. Use the statistical data to create a box plot for each period.

Phase 3

Have students interpret the data for each period for actors and for actresses. Determine if the change in the measures of central tendency show a trend in the ages of present Academy Award winners.

Phase 4

Students are to write a report supporting their hypotheses.

Optional: Support your findings using a slide show presentation software or multimedia.

## Interactions

This activity involves whole class presentations as well as students working in pairs or groups of three. Within each group, decisions must be made regarding organization, tasks, and responsibilities. Members should collaborate as needed to share technology and content knowledge.

Each student is responsible for completing a report presenting findings.

The teacher will advise group members on organization, assist with research and technology. The teacher may lead small group discussions to help students to make inferences about the age trends from the data.

Some of the activities involve visiting designated web sites and working on spreadsheets. An html document with the URL's of sites to be used should be created and stored either on a teachers/school web site, or as a document on the individual workstations. A well-designed "student work sheet" with a suggested sequence of steps is often helpful and worth the effort to create.

## Assessment

Give individual scores based on a 3-2-1 rubric for participation in group discussions and collection of data, data analysis and graphing, and report writing and presentation.

For further consideration:

• Do students state clearly the hypotheses they are investigating?

• Do they accurately analysis the data?

• Do they accurately construct the relevant graphs?

• Are their interpretations of the graphs valid?

• Are the students’ conclusions justified by the data?

• Do they provide convincing justifications?

## Tools

Pen and paper

Spreadsheet software and graphing calculators are optional resources.