Preinstructional Planning
Objectives
Students will:
- Learn how to use a scatterplot to compare two sets of data to determine if they are related
- Learn the definition of regression line (the "line of best fit")
- Learn how scientists and actuaries use math and data to study earthquake probability
See standards below.
Materials
- Shake, Rattle, and Roll Worksheet: Shake It Up With Scatterplots printable
- Answer Key: Shake, Rattle, and Roll Worksheets printable
- Standards Chart: Shake, Rattle, and Roll printable
- Chart paper or large graph paper
- Measuring tapes
- Introducing Shake, Rattle, and Roll: A Letter to Parents printable
- Shake, Rattle, and Roll Family Activity: Insuring for the Uncertain printable
- Shake, Rattle, and Roll Family Activity: Banking on Inflation printable
- Shake, Rattle, and Roll Family Activity: Planning for the Future printable
Set Up
1. Make a class set of the Shake, Rattle, and Roll Worksheet: Shake It Up With Scatterplots printable.
2. Print a copy of the Answer Key: Shake, Rattle, and Roll Worksheets printable for your use.
3. On a sheet of chart paper or large graph paper, draw a horizontal axis labeled "height in inches" and a vertical axis labeled "wingspan in inches."
4. Make class sets of the following printables, then staple together in packets to send home with students:
- Introducing Shake, Rattle, and Roll: A Letter to Parents printable
- Shake, Rattle, and Roll Family Activity: Insuring for the Uncertain printable
- Shake, Rattle, and Roll Family Activity: Banking on Inflation printable
- Shake, Rattle, and Roll Family Activity: Planning for the Future printable
Lesson Directions
Introduction to Scatterplots
Step 1: Group students in pairs. Distribute measuring tapes. Ask each student to measure his or her partner's "wingspan," i.e., the distance from left-hand fingertip to right-hand fingertip when arms are extended parallel to the floor. To ensure that the relationship between wingspan and height is accurately depicted, make sure your students have a common understanding of how to make these two measurements.
Step 2: When measuring has been completed, ask students to plot their heights and wingspans on the large graph you prepared ahead of class. When all students have entered their data, ask the students, in pairs, to:
- Review the graph and determine whether or not there is a relationship between height and wingspan.
- Considering the points that have been placed on the graph, is there a straight line that could be drawn that captures the connection between height and wingspan? Students should be prepared to explain their answers.
Step 3: Indicate to the class that they have drawn a "scatterplot," a graph that shows the relationship between two sets of data. Most height-versus-wingspan scatterplots show a correlation, so be sure to point this out.
Step 4: Review the straight lines drawn by the class. Indicate that a line that best shows the direction of the data is called a "line of best fit."
Independent Practice
Step 5: Distribute copies of the Shake, Rattle, and Roll Worksheet: Shake It Up With Scatterplots printable. Explain that students will be looking at information about an earthquake event near the real town of Parkfield, California, which is famous for its seismic activity. Explain that the data used here are distance from the epicenter of the earthquake (in kilometers) and intensity at that location. Magnitude is measured at the source of an earthquake, while intensity is measured wherever the earthquake is felt. Often, but not always, the closer to the epicenter, the greater the intensity.
Step 6: Have students complete the Shake, Rattle, and Roll Worksheet: Shake It Up With Scatterplots printable independently.
Step 7: Check for Understanding: After students have completed their worksheets, review the answers with the class using the Answer Key: Shake, Rattle, and Roll Worksheets printable.
Lesson Extensions: Real-World Conncections
Explain to students that an actuary is a statistical expert who determines the financial impact of randomly occurring events like earthquakes, injuries from an accident, even death. Actuaries work primarily in the insurance industry and for state and federal government agencies. Actuaries use math and statistics to determine the probability of major events in a geographic area (like an earthquake in central California). They also use additional information, like the expected magnitude of an earthquake, to help an insurance company set premium rates. A premium is the amount paid by a customer, usually annually, for a given amount of insurance coverage.
For additional information about the Modified Mercalli Intensity Scale and the Richter Scale, visit the U.S. Geological Survey website.
Home Connections
Send home the Shake, Rattle, and Roll Family Activity packets, which should include:
- Introducing Shake, Rattle, and Roll: A Letter to Parents printable
- Shake, Rattle, and Roll Family Activity: Insuring for the Uncertain printable
- Shake, Rattle, and Roll Family Activity: Banking on Inflation printable
- Shake, Rattle, and Roll Family Activity: Planning for the Future printable
Post Instructional
Standards
- Grade 8: Statistics and Probability (CCSS 8.SP.A.1 and 2)
- Grades 6–8: Reason Abstractly and Quantitatively and Construct Viable Arguments, (CCSS MP2 and 3); NCTM Data Analysis and Probability
For more information, download the comprehensive Standards Chart: Shake, Rattle, and Roll printable.