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Worksheet Grade 8 Math

Hollowfield Orchard Irrigation: Fitting a Line to Rain Data

A grade 8 worksheet in which students plot ten weeks of rainfall and pumping records from a fictional orchard, use a given line of fit, and read its slope.

Objectives

  1. Students will construct a scatter plot from a two-column irrigation record.
  2. Students will describe the association between rainfall and pumping in words.
  3. Students will find the slope and equation of a given line of fit and use it to predict.

Vocabulary

Key words: scatter plot, association, line of fit, slope, y-intercept

Teacher overview

Hollowfield Orchard is a fictional fruit farm that irrigates its trees with well water. In a rainy week the manager runs the pump less, and in a dry week she runs it more, so ten weeks of records make a scatter plot with a clear negative association. This worksheet supplies the manager's own line of fit so that every student works from the same line and the answers can be checked. Teaching note: eighth graders frequently report a negative slope as a positive number because they subtract the coordinates in a different order in the numerator than in the denominator. Watch for a reported slope of 12 on item 4, and ask those students to check the answer against the direction the points travel.

Hollowfield Orchard Irrigation: Fitting a Line to Rain Data — Grade 8 Math
Name: ____________________________ Date: ______________

Student Worksheet

Hollowfield Orchard is a fictional farm. The table lists ten weeks of records. Rain is the rainfall for the week in inches. Water pumped is the irrigation water used that week, in thousands of gallons.

Week Rain (inches) Water pumped (thousands of gallons)
1 0.0 44
2 0.2 42
3 0.5 38
4 0.8 35
5 1.0 32
6 1.2 30
7 1.5 26
8 1.8 24
9 2.0 20
10 2.5 14
  1. Make a scatter plot of the ten weeks. Put rain on the horizontal axis and water pumped on the vertical axis. Write the ordered pair you plotted for week 10.
  2. Is the association between rain and water pumped positive or negative? Tell what that means for the orchard.
  3. Is the association linear or nonlinear?
  4. The manager drew a line of fit through the points (0, 44) and (2.5, 14). Find the slope of her line.
  5. Write the equation of the manager's line in slope-intercept form. Use x for rain and y for water pumped.
  6. What does the slope tell the manager about her orchard?
  7. What does the y-intercept tell the manager?
  8. Use the equation to predict the water pumped in a week with 1.6 inches of rain.
  9. Which week's point sits farthest above the manager's line?
  10. How far above the line is that point?
  11. Find the total water pumped across all ten weeks.
  12. The equation predicts a negative amount of water for a week with 4 inches of rain. Explain why that prediction cannot be correct.

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: (2.5, 14).
    Week 10 had 2.5 inches of rain and 14 thousand gallons pumped, so the point sits at the far right and near the bottom of the plot.
  2. Answer: Negative.
    As rain goes up, water pumped goes down. More rain means the trees need less irrigation water.
  3. Answer: Linear.
    The points fall in a nearly straight path rather than a curve.
  4. Answer: -12 thousand gallons per inch.
    Slope = (14 - 44) divided by (2.5 - 0) = -30 divided by 2.5 = -12.
  5. Answer: y = -12x + 44.
    The line crosses the vertical axis at 44 and falls 12 units for each inch, so y = -12x + 44.
  6. Answer: 12 thousand gallons less per inch of rain.
    Each extra inch of rain in a week lowers the pumping by about 12 thousand gallons.
  7. Answer: 44 thousand gallons.
    With no rain at all, the line predicts about 44 thousand gallons of irrigation water for the week.
  8. Answer: 24.8 thousand gallons. y = -12(1.6) + 44 = -19.2 + 44 = 24.8 thousand gallons.
  9. Answer: Week 8.
    The line predicts -12(1.8) + 44 = 22.4 for week 8, and the record shows 24, which is the largest gap in the table.
  10. Answer: 1.6 thousand gallons.
    24 - 22.4 = 1.6 thousand gallons above the line.
  11. Answer: 305 thousand gallons.
    44 + 42 + 38 + 35 + 32 + 30 + 26 + 24 + 20 + 14 = 305 thousand gallons.
  12. Answer: A negative amount of water is impossible.
    The line gives -12(4) + 44 = -4, and the orchard cannot pump less than zero. The value 4 inches is far outside the range of the data, so the line should not be used that far out.

Differentiation

Support

Provide graph paper with the axes already drawn and labeled, with rain marked in steps of 0.5 inch and pumping marked in steps of 4 thousand gallons. For item 4, give students the slope frame "change in pumping divided by change in rain" with the two ordered pairs already written underneath.

Extension

Ask students to find the predicted value for every week from the manager's equation, list the ten gaps between the record and the line, and decide from that list whether the line fits the early weeks or the late weeks more closely.

ELL supports

Pre-teach association, slope, and line of fit using a picture of a rising line beside a falling line, labeled positive and negative. Provide the sentence frame for item 2: "The association is ___ because when rain goes up, pumping goes ___."

Extensions

Have students collect a week of local rainfall from a rain gauge or a public weather record and place their own point on the plot to see whether it lands near the manager's line. Ask them to explain what one nearby point can and cannot tell them about how well the line describes a different orchard.