Lesson plan Grade 8 Math
Gildersby Farms Irrigation: Two Clusters in One Scatter Plot
A grade 8 lesson where students plot a fictional farm's irrigation records, find two soil-type clusters and one outlier, and name the association.
Objectives
- Students will construct a scatter plot from a two-column table of bivariate measurement data.
- Students will describe the association between rainfall and applied water as positive, negative, or absent.
- Students will identify clusters and an outlier in a scatter plot and give a reason for each from the scenario.
Vocabulary
Key words: scatter plot, bivariate, cluster, outlier, negative association, soil type
Teacher overview
The fictional Gildersby Farms keeps a log of every irrigation event on two fields, recording how much rain fell in the week before and how much water was applied per acre. Sandy soil drains quickly and takes more water, while the heavier soil on the second field holds moisture and takes less, so the plotted points fall into two separate groups rather than one band. Students build the plot and then describe what they see in the vocabulary of the standard. The misconception this lesson addresses is that a scatter plot always shows one trend that one line can summarize; students frequently draw a single line through two clusters and report a relationship that neither field actually has.
Procedure
Hook (5 min): Ask students to predict what happens to the amount of irrigation water a farm applies during a week with heavy rain. Collect predictions and write the expected direction on the board as "more rain, less water applied." Tell students they will check that prediction against the irrigation log from the fictional Gildersby Farms.
Direct instruction (12 min): Set up the axes together, with rainfall in inches on the horizontal axis from 0 to 2.5 and applied water in gallons per acre on the vertical axis from 0 to 10,000. Plot the first three rows of the table as a class, saying each ordered pair aloud. Introduce the four descriptions the handout asks for: the direction of the association, whether the pattern looks linear, whether there are clusters, and whether any point sits away from the rest. Model the difference between a cluster and an outlier by sketching a quick example on the board that is not the farm data.
Guided practice (13 min): Students plot the remaining rows in pairs, using one color for Field 2 and a second color for Field 7. Circulate and check that both axes carry units. Ask a check-for-understanding question once most pairs have finished: "Raise your hand if most points of the two colors land in the same part of the graph." Very few hands should go up. If more than about a quarter of the class raises a hand, stop and re-plot three points of each color together.
Independent practice (15 min): Students answer the handout items individually, writing full sentences for the description items rather than one-word answers. Remind them that item 5 asks for the location of a point, not a calculation.
Closure and exit ticket (5 min): On an index card, students answer: "A classmate draws one straight line through every point on this plot. Give one reason that line would mislead the farm manager." Collect and look for answers that mention the two soil types or the outlier.
Student Handout
The fictional Gildersby Farms irrigates two fields. Field 2 has sandy soil and Field 7 has heavier clay soil. For each irrigation event the log records the rain that fell in the previous week, in inches, and the water applied, in gallons per acre.
| Field | Rain the week before (inches) | Water applied (gallons per acre) |
|---|---|---|
| Field 2 | 0.2 | 9,500 |
| Field 2 | 0.5 | 9,000 |
| Field 2 | 0.8 | 8,600 |
| Field 2 | 1.1 | 8,100 |
| Field 2 | 1.4 | 7,700 |
| Field 2 | 1.7 | 7,200 |
| Field 2 | 2.0 | 6,800 |
| Field 7 | 0.3 | 5,400 |
| Field 7 | 0.6 | 5,000 |
| Field 7 | 0.9 | 4,700 |
| Field 7 | 1.2 | 4,300 |
| Field 7 | 1.5 | 3,900 |
| Field 7 | 1.8 | 3,500 |
| Field 7 | 2.1 | 3,200 |
| Field 7 | 1.0 | 8,900 |
The last row is the event on the night a valve stuck open on Field 7 and ran for several extra hours before the crew noticed.
Plot all fifteen events on one graph. Use rain on the horizontal axis and water applied on the vertical axis. Use one color for Field 2 and another for Field 7. Label both axes with units.
- Within each field, does more rain in the previous week go with more water applied or less water applied? Name the type of association.
- Within each field, does the pattern look linear or nonlinear? Support your answer with two or three points from the table.
- How many clusters do you see on your plot, and what separates them?
- Which cluster sits higher on the graph, and what does that position mean for the two soils?
- One point sits far away from the rest of its own field's group. Name the field and give the ordered pair.
- Give the reason from the log for the point you named in item 5.
- Would one straight line drawn through all fifteen points describe this farm well? Explain your answer in two sentences.
- Explain why extending the pattern past 2.1 inches of rain would be risky, using what the plot does and does not show.
From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.
Answer Key
- Answer: Less water applied, which is a negative association. In both fields the points fall as they move to the right, so more rain in the previous week goes with less irrigation water.
- Answer: Roughly linear within each field. Field 2 drops from 9,500 to 9,000 to 8,600 gallons per acre in nearly equal steps, and Field 7 drops from 5,400 to 5,000 to 4,700 in nearly equal steps, so each group of points is close to a straight path.
- Answer: Two clusters, separated by the field and therefore by the soil type. The Field 2 points form an upper group and the Field 7 points form a lower group, with a gap between them.
- Answer: The Field 2 cluster sits higher. Sandy soil drains faster and holds less moisture, so that field needs more water per acre than the heavier clay soil in Field 7 at the same rainfall.
- Answer: Field 7, at the ordered pair 1.0 inch of rain and 8,900 gallons per acre. Every other Field 7 event sits much lower on the graph, so this point is far from its own cluster.
- Answer: A valve stuck open that night and the system ran for extra hours before the crew noticed, so the recorded amount reflects an equipment failure rather than an irrigation decision.
- Answer: No. A single line would pass through the empty gap between the two clusters and would predict amounts that neither field ever uses. The farm would be better served by one line for each soil type, drawn from that field's own points.
- Answer: The log contains no events above 2.1 inches of rain, so the plot gives no evidence about what happens in a wetter week. Irrigation may stop entirely once rain is heavy enough, which would break the steady pattern the plotted points suggest.
Differentiation
Support
Provide graph paper with both axes already scaled and labeled for the fictional Gildersby Farms data, and plot the first four rows in advance. Assign items 1, 3, 5, and 6, and supply the sentence frame "As rain goes up, water applied goes ___, which is a ___ association."
Extension
Ask students to remove the stuck-valve event, draw a separate line of fit for each field by eye, and write two sentences comparing how steeply each field's water use falls as rain increases. They should say which soil responds more to a wet week and support the claim with their two lines.
ELL supports
Pre-teach cluster, outlier, and applied with a simple sketch showing two groups of dots and one lone dot. Post a word bank with negative association, positive association, linear, and nonlinear, each paired with a small arrow diagram. Allow students to answer items 1 through 4 orally, pointing to their own plot, before writing the sentences.
Extensions
Give students a third field at the fictional Gildersby Farms with a silt soil that falls between the two clusters, supplying six new ordered pairs, and ask them to add that field in a third color. Have them write a short note to the farm manager explaining how many separate patterns the plot now shows and why one summary number for the whole farm would hide the difference between the soils.