Data gathering - Linear regressions

In groups of three, students gather data by experiment or observation in one of nine activities. Each group models the data they gathered, creates a display, and presents results to the class using an overhead projector.

A lesson plan for grades 8–12 Mathematics

By Judy Pickering

Learn more

Related pages

• Solid graphing: The students will review solid figures using a baggie of assorted snack mix (cones, cubes, cylinders, and spheres) and will begin a vertical bar graph showing the number of each solid figure in a bag of assorted snack mix.
• Chocolate! Chocolate! Chocolate!: Using chocolate as a theme, students will become involved in reading, writing, math, word study/spelling and other developmentally appropriate (integrated) activities. The unit includes centers for the classroom along with whole group activities.
• Graphing the week's temperature: Students will collect data, create a graph, and analyze information about the temperatures for a week using Graph Club Software.

Related topics

• Learn more about cooperative learning, data analysis, data collection, graphing, linear regressions, mathematics, and measurement.

Help

Please read our disclaimer for lesson plans.

Legal

Learning outcomes

• Students will be able to gather at least ten sets of data, use an automatic grapher to graph the sets into a scatter plot, determine the line and equation of best fit, and use the results to make predictions.
• Algebra I students will estimate a line of best fit instead of determining the linear equation using an automatic grapher.

Teacher planning

Time required for lesson

90 minutes

Materials/resources

• string and weight pendulum
• stopwatch
• twelve different sized jar lids
• a bag of beans
• three ping pong balls
• thirty dice
• rulers, metersticks or yard sticks
• graph paper, colored pencils
• list of data gathering activities cut into separate activities
• tape measure
• grid paper
• overhead pens and transparency sheets

Technology resources

automatic grapher (optional for Algebra I), overhead projector (or other presentation device)

Pre-activities

For most classes: The student must have already practiced entering data into an automatic grapher and using the result to find the line and equation of best fit. (Optional for Algebra I)

Algebra I students will have practiced graphing bivariate data sets and drawing in an estimated line of best fit.

Activities

1. Review the procedure for using the automatic grapher to find the line and equation of best fit.
2. Divide the students into groups of three.
3. Each group will randomly pick an activity from the previously prepared list (see Supplemental Information).
4. Each group will read its activity and then go to the area where all the materials have been laid out and pick up the equipment that is needed to gather the data. One member of the group will perform the activity while one the others measures the outcomes and the last member of the group records the data.
5. The group will record the results on a transparency with a Cartesian Coordinate Plain copied on the upper half. The graph must include:
   • a descriptive title
   • properly numbered scale on the axes
   • clearly labeled axes
   • scatter plot of the data points
   • regression line (estimated for Algebra I classes)
   • three regression points

   The results recorded below the graph will include:

   • ten data points
   • slope of the line of best fit
   • y-intercept of the line of best fit
   • equation of the line of best fit
   • correlation coefficient r (this is not covered in most Algebra I and Algebra II classes…teacher could substitute “type of association: positive or negative” and “strength of association: strong, moderate, or weak”)
   • type of regression (this is not covered in Algebra I, where all regressions would be linear)
   • one extrapolated and one interpolated prediction and a statement on the reliability of each (optional in Algebra I and Algebra II)

Assessment

Each group will present its data results and findings to the class using the overhead transparencies on which the results were recorded.

Supplemental information

Data Gathering Activities

1. Students measure height and foot length (no shoes). Use at least ten sets of data. (Equipment: Measuring device)
2. Students drop a ball from various heights and measure the height of the first bounce. A tape measure hung vertically and a wall will improve accuracy. As the record ordered pairs (drop height, height of rebound), students will probably have quite a bit of experimental error. This can be minimized by having two or three students sight the rebound height and averaging their sightings. Use at least ten sets of data. (Equipment: Tape measure, ping pong ball)
3. Students measure the diameter and circumference of empty cans or jar lids. When you plot diameter on the horizontal axis then the slope or their linear model will be ?? Use at least ten sets of data. (Equipment: cans/lids, tape measure)
4. The size of the image made by an overhead projector changes as the distance between the projector and screen changes. Students gather ordered pairs of the form (distance from screen, length of projected image). You must be sure to focus the image at each distance.Use at least ten sets of data. (Equipment:overhead projector, measuring device, image on the screen)
5. Students will count the number of dry beans that will fill a jar lid without any overlapping. They will also measure the diameter of each jar lid. The number of beans that will fit in each lid provides a relative measure of its area. Use at least ten sets of data. (Equipment: Jar lids, dry beans, ruler)
6. Students will vary the length of the string and measure how the period of the pendulum (time to complete one swing across and back) changes. To measure the period, students should hold one end of the string stable, pull the weight to one side, let the weight make ten complete swings, record the time, and then divide the time by 10. Ordered pairs (Length of string, period) should be recorded at about 10 cm intervals. Use at least ten sets of data. (Equipment: pendulum, string (about 1 meter), measuring device, stopwatch)
7. Roll all the dice: after each roll remove every die that is showing a 6. Continue rolling until all dice have been removed. Record ordered pairs of the form (number of roll, number of remaining dice). (Equipment: dice)
8. Draw different sizes of equilateral triangles with bases along lines of grid paper. Students should measure the size of the base using grid lengths and count squares to estimate the area of each triangle. Use at least ten sets of data. (Equipment: grid paper, rulers)
9. Students measure the height of a car and the height of it’s tires. Use at least ten sets of data. (Equipment: measuring device)