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Lesson plan Grade 8 Math

Pellingford Summer Demand: Finding the Outlier in a Scatter Plot

A 50-minute grade 8 lesson where students plot a fictional town's daily water use against temperature, describe the association, and explain a single outlier.

Objectives

  1. Students will construct a scatter plot from a table of paired summer measurements.
  2. Students will describe the association between two quantities as positive, negative, or absent.
  3. Students will identify an outlier and explain why it should not be used to make predictions.

Vocabulary

Key words: scatter plot, association, outlier, linear

Teacher overview

Water demand in a small town climbs on hot days, mostly because lawns get watered and pools get filled, so a utility that plots daily demand against the daily high temperature usually sees a clear upward pattern. This lesson gives students twelve summer days from the fictional town of Pellingford, eleven of which follow that pattern and one of which does not, because a large main break released water that no customer used. Students plot the data, describe the association, and then argue about what to do with the day that does not fit.

Procedure

Hook (5 min): Ask the class to predict whether a town uses more water on a 95-degree day or a 75-degree day, and to say why. Write two or three reasons on the board, then say that the class will check the prediction against twelve days of records from the fictional town of Pellingford.

Direct instruction (10 min): Model plotting three of the twelve points on a board-sized set of axes, with the daily high temperature on the horizontal axis and water use on the vertical axis. Name the three things students will describe once the plot is finished: the direction of the association, whether the points fall near a straight line, and whether any point sits far away from the others. Define outlier as a point that does not follow the pattern of the rest.

Guided practice (12 min): Have students plot the first six points from the handout table with a partner while you circulate. Ask the check-for-understanding question: "As you move to the right on this plot, are the points generally going up or down?" Expect students to say up, and to connect that to a positive association. If more than a quarter of the class cannot answer, stop and rebuild the axes together.

Independent practice (18 min): Students finish plotting the remaining points and complete all ten items on the Student Handout.

Closure and exit ticket (5 min): On an index card, students write one sentence naming the outlier day and one sentence saying why the utility should leave it out when predicting normal summer demand. Collect the cards and check that students name the 79-degree day rather than the hottest day.

Pellingford Summer Demand: Finding the Outlier in a Scatter Plot — Grade 8 Math
Name: ____________________________ Date: ______________

Student Handout

The table below shows twelve summer days from the fictional town of Pellingford. Water use is measured in thousands of gallons.

Daily high temperature (degrees F) Water use (thousands of gallons)
72 410
75 430
78 455
79 780
80 470
82 495
84 505
86 530
88 545
90 560
92 585
94 600
  1. Plot all twelve points on graph paper. Put temperature on the horizontal axis and water use on the vertical axis.
  2. As the temperature rises, does water use generally rise or fall? Name the type of association.
  3. One point sits far away from the others. Give the temperature of that point.
  4. On the day in item 3, a large water main broke and released water for several hours. Explain how that event pushed the point away from the others.
  5. Should the town use the day from item 3 to predict water use on a normal summer day? Explain.
  6. Leave out the day from item 3. Do the remaining eleven points fall close to a straight line, or do they curve? Name the shape.
  7. Using the pattern of the eleven ordinary days, estimate the water use on a day with a high of 85 degrees.
  8. Using the pattern of the eleven ordinary days, estimate the water use on a day with a high of 77 degrees.
  9. Describe what the plot would look like if there were no association at all between temperature and water use.
  10. Explain why temperature is treated as the input and water use as the output rather than the other way around.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key
  1. Answer: A completed scatter plot. Accept any plot with temperature on the horizontal axis running from about 70 to 95, water use on the vertical axis running from about 400 to 800, and all twelve points placed correctly.
  2. Answer: Water use rises, so the association is positive. Points move upward as they move to the right across the plot.
  3. Answer: 79 degrees. That day shows 780 thousand gallons, far above the 455 to 470 thousand gallons used on the days near it in temperature.
  4. Answer: The broken main released water that no customer used, and the meter at the plant still counted it, so the recorded use for that day was much higher than the weather alone would explain. The point lands well above the pattern the other days form.
  5. Answer: No. The high reading came from a pipe failure rather than from customer demand, so including it would overstate what customers use on an ordinary summer day.
  6. Answer: They fall close to a straight line, so the association is roughly linear. Accept any answer that says linear and refers to the points lying near a line rather than curving.
  7. Answer: About 515 thousand gallons. Accept any estimate from 500 to 530 thousand gallons, since 85 degrees sits between the 84-degree day at 505 and the 86-degree day at 530.
  8. Answer: About 445 thousand gallons. Accept any estimate from 435 to 460 thousand gallons, since 77 degrees sits between the 75-degree day at 430 and the 78-degree day at 455.
  9. Answer: The points would be scattered with no upward or downward trend, forming a shapeless cloud instead of a rising band, and knowing the temperature would not help predict water use.
  10. Answer: The weather is not caused by how much water the town uses, while hot weather does lead people to water lawns and fill pools. The quantity that does the explaining goes on the horizontal axis, so temperature is the input.

Differentiation

Support

Provide graph paper with the axes already drawn, labeled, and scaled, and mark the first three points so students can see the spacing. Allow these students to answer items 4, 5, 9, and 10 orally or with a partner rather than in writing.

Extension

Ask students to recompute the range of the water use column with and without the outlier, then write a short paragraph explaining how a single unusual day changes a summary number. Have them suggest one additional measurement the utility could record that would confirm the cause.

ELL supports

Preview "association," "outlier," and "trend" with a picture of a plot for each word, and label the axes on a sample plot in both English and, where possible, students' home language. Provide the sentence frames "As the temperature goes up, the water use goes ___" and "The point at ___ degrees is an outlier because ___."

Extensions

If your utility publishes monthly production totals, have students plot those totals against the month and describe whether the pattern matches the summer rise they saw in the Pellingford data, noting that monthly totals hide single unusual days.