# Shake It Up with Scatterplots

**STANDARDS (CCSS AND NCTM)**

**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- Standards Chart: Common Core State and NCTM Standards (PDF)

**OBJECTIVE**

Students will understand:

- How to use a scatterplot to compare two sets of data to determine if they are related.
- The definition of regression line (the "line of best fit").
- How scientists and actuaries use math and data to study earthquake probability.

**MATERIALS**

- Activity 1: Shake It Up with Scatterplots (PDF); Rulers
- Large sheet of paper with drawn horizontal axis (labeled "height in inches") and vertical axis (labeled "wingspan in inches")
- Measuring Tapes

**REPRODUCIBLES**

**DIRECTIONS**

**Introduction to Scatterplots**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.

2.

**Guided Practice:**When measuring has been completed, ask students to plot their heights and wingspans on the graph. When all students have entered their data, ask the 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.

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.

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."

5. **Independent Practice:** Distribute copies of Shake It Up With Scatterplots (PDF) to students. Explain that they 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.

6. **Check for Understanding:** After students have completed their worksheets, review their answers with the class.

**Real-World Connections:**

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.

**Background:**

For additional information and statistics about earthquakes and their intensity, visit www.ngdc.noaa.gov/seg/hazard/intsrch.shtml. For additional information about the Modified Mercalli Intensity Scale and the Richter Scale, visit http://pubs.usgs.gov/gip/earthq4/severitygip.html.

**HOME CONNECTION**

Welcome Families (PDF)

Family Activity 1: Insuring for the Uncertain (PDF)

Family Activity 2: Banking on Inflation (PDF)

Family Activity 3: Planning for the Future (PDF)