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Classroom activity Grade 9 Math

Sallowfield Farms Soil Moisture Rounds: A Six-Week Pivot Game

A grade 9 activity where teams run a fictional center-pivot field through six weekly rounds, holding stored soil water inside a band while applying as little as possible.

Objectives

  1. Students will track a running water balance across six rounds using a stated weekly rule.
  2. Students will solve an equation for the irrigation depth needed to reach a target soil moisture.
  3. Students will convert an applied depth in inches into acre-feet, gallons, and pumping hours.

Vocabulary

Acre-foot
The amount of water it takes to cover one acre of land, about the size of a football field, one foot deep. Western states use acre-feet to measure large amounts of water.

Also: center pivot, soil moisture, crop water use, water balance

Teacher overview

This is a six-round table game for teams of three, set on a fictional center-pivot field at the fictional Sallowfield Farms. Each round is one week of the growing season. Teams receive the same rain card and the same crop-use card every round, so every team faces identical weather, and the only decision they make is how much water to apply. The stored water in the root zone must stay between 2.0 and 6.0 inches: below that the crop is stressed, above it the extra water drains past the roots and is wasted. The round structure follows the water balance an irrigation manager runs, since adding rain and irrigation and subtracting crop use is how stored soil water is tracked, and the scoring rewards the team that stays inside the band while applying the least total water. The error to watch for during play is a sign error in the balance: teams add the crop-use value instead of subtracting it, and their stored water climbs every week until the field is impossibly wet. A second error is treating a rainy week as a reason to apply more, on the reasoning that the soil can hold it.

Activity Directions

  1. Before class, print one set of six rain cards and six crop-use cards per team, in the round order listed on the Student Handout, plus one recording sheet per team. Arrange desks so each team of three has a flat surface for the cards and the sheet.

  2. Open by stating the rule the whole game runs on, and write it where every team can see it: ending stored water = starting stored water + rain + irrigation - crop use. Every quantity is measured in inches of water in the root zone. Announce that the fictional field begins the season with 4.0 inches stored, and that the band runs from 2.0 to 6.0 inches.

  3. Explain the pump limit: the fictional pivot can apply at most 2.0 inches in a single week, and applied depths are chosen in tenths of an inch. A team may also choose to apply nothing.

  4. Run round 1. Each team turns over its week 1 rain card and week 1 crop-use card at the same time, then has 90 seconds to agree on an irrigation depth, compute the ending stored water, and record both on the sheet. Call time and have each team read its ending value aloud.

  5. Run rounds 2 through 6 the same way, each round starting from the stored water the team ended the previous round with. A team whose stored water leaves the 2.0 to 6.0 inch band records a mark on the sheet and continues playing from the value it reached.

  6. End the game after round 6, or after 30 minutes of play, whichever comes first. Score each team by adding its six irrigation depths. The winning team is the one with the smallest total that never left the band, so a team that applied less water but stressed the crop does not outrank a team that stayed inside it.

  7. Distribute the Student Handout and have teams complete questions 1 through 12, which walk through one demonstration team's season and then convert that season's applied water into acre-feet, gallons, and pumping hours.

  8. Close with a debrief. Ask which round forced the hardest decision and why, then ask teams to explain what the game would look like if the pump limit were 1.0 inch per week instead of 2.0, and whether their winning strategy would still work.

Sallowfield Farms Soil Moisture Rounds: A Six-Week Pivot Game — Grade 9 Math
Name: ____________________________ Date: ______________

Student Handout

All numbers below describe the fictional Sallowfield Farms pivot field. The field begins the season with 4.0 inches of stored water in the root zone, and stored water must stay between 2.0 and 6.0 inches. Every week, ending stored water = starting stored water + rain + irrigation - crop use, with all quantities in inches.

The table lists the same six weeks every team played, along with the irrigation depths one demonstration team chose.

Week Rain (in) Crop use (in) Irrigation applied (in)
1 0.4 1.2 0.8
2 0.0 1.5 1.0
3 1.6 1.4 0.0
4 0.2 1.8 1.4
5 0.0 2.0 1.6
6 0.9 1.7 1.0

Season questions. Answer questions 1 through 12 on your recording sheet, one answer per question.

  1. Week 1 starts with 4.0 inches stored. Rain adds 0.4 inches, the team applies 0.8 inches, and the crop uses 1.2 inches. Find the ending stored water.
  2. Week 2 starts with 4.0 inches stored. There is no rain, the team applies 1.0 inch, and the crop uses 1.5 inches. Find the ending stored water.
  3. Week 3 starts with 3.5 inches stored. Rain adds 1.6 inches, the team applies nothing, and the crop uses 1.4 inches. Find the ending stored water.
  4. Week 4 starts with 3.7 inches stored. Rain adds 0.2 inches, the team applies 1.4 inches, and the crop uses 1.8 inches. Find the ending stored water.
  5. Week 5 starts with 3.5 inches stored. There is no rain, the team applies 1.6 inches, and the crop uses 2.0 inches. Find the ending stored water.
  6. Week 6 starts with 3.1 inches stored. Rain adds 0.9 inches, the team applies 1.0 inch, and the crop uses 1.7 inches. Find the ending stored water.
  7. In week 4 the field started at 3.7 inches, rain added 0.2 inches, and the crop used 1.8 inches. Write and solve an equation for the irrigation depth that would have ended the week at exactly 4.0 inches.
  8. Add the six irrigation depths in the table to find the demonstration team's total applied water for the season, in inches.
  9. The pivot covers 130 acres. Convert your total from question 8 into acre-feet. There are 12 inches in a foot.
  10. Convert your answer from question 9 into gallons. One acre-foot equals 325,851 gallons.
  11. The pivot's pump delivers 900 gpm. Find the hours of pumping needed to apply 1.0 inch of water across the whole 130 acres.
  12. Suppose the team had applied no irrigation at all in week 5, starting from 3.5 inches with no rain and a crop use of 2.0 inches. Find the ending stored water for that week.

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: 4.0 inches.
    Substituting into the rule gives 4.0 + 0.4 + 0.8 - 1.2 = 4.0 inches, so the week ends where it began.

  2. Answer: 3.5 inches.
    Substituting gives 4.0 + 0.0 + 1.0 - 1.5 = 3.5 inches. The crop used more than the team replaced, so storage fell.

  3. Answer: 3.7 inches.
    Substituting gives 3.5 + 1.6 + 0.0 - 1.4 = 3.7 inches. The rain more than covered the crop's use, so no irrigation was needed.

  4. Answer: 3.5 inches.
    Substituting gives 3.7 + 0.2 + 1.4 - 1.8 = 3.5 inches.

  5. Answer: 3.1 inches.
    Substituting gives 3.5 + 0.0 + 1.6 - 2.0 = 3.1 inches. This was the season's driest week, and the team applied less than the crop used, so storage fell.

  6. Answer: 3.3 inches.
    Substituting gives 3.1 + 0.9 + 1.0 - 1.7 = 3.3 inches, which finishes the season inside the 2.0 to 6.0 inch band.

  7. Answer: 1.9 inches.
    The equation is 3.7 + 0.2 + i - 1.8 = 4.0, which simplifies to 2.1 + i = 4.0, so i = 1.9 inches. That depth is within the 2.0-inch weekly pump limit.

  8. Answer: 5.8 inches.
    Adding gives 0.8 + 1.0 + 0.0 + 1.4 + 1.6 + 1.0 = 5.8 inches applied across the season.

  9. Answer: 62.8 acre-feet.
    Converting the depth gives 5.8 divided by 12 = 0.4833 feet, and 0.4833 feet x 130 acres = 62.83 acre-feet.

  10. Answer: 20,474,000 gallons.
    Carrying the unrounded 62.8333 acre-feet gives 62.8333 x 325,851 = 20,474,305 gallons, or 20,474,000 rounded to the nearest thousand. A student who multiplies the rounded 62.8 from question 9 gets 20,463,000, and one who uses 62.83 gets 20,473,000. All three are correct arithmetic; the spread of about 11,000 gallons is the point, and it is worth asking the class which figure a farm should plan on and why rounding waits until the end.

  11. Answer: 65.4 hours.
    One inch over 130 acres is 130 divided by 12 = 10.833 acre-feet, which is 10.833 x 325,851 = about 3,530,000 gallons. Dividing gives 3,530,000 divided by 900 gpm = 3,922 minutes, and 3,922 divided by 60 = 65.4 hours.

  12. Answer: 1.5 inches.
    Substituting gives 3.5 + 0.0 + 0.0 - 2.0 = 1.5 inches, which falls below the 2.0-inch floor and would have cost the team a stress mark.

Differentiation

Support

Give these teams a recording sheet for the fictional field with the rule printed across the top and a worked week 1 already filled in, so the first entry is a model rather than a blank. Allow these teams to choose irrigation depths in half-inch steps instead of tenths, which shortens the decision each round without changing the mathematics.

Extension

Have teams replay the six fictional weeks with a stricter pump limit of 1.0 inch per week and report whether staying inside the band is still possible. A second challenge is to find the smallest total irrigation, to the nearest tenth of an inch, that keeps the field inside the band for all six weeks, and to justify why no smaller total works.

ELL supports

Post the water-balance rule as a labeled picture with an arrow into the soil for rain and irrigation and an arrow out for crop use, so the signs in the equation are visible rather than only stated. Provide a card with the words "stored," "applied," and "crop use" matched to their columns on the recording sheet, and allow teams to record answers as numbers without written explanations during play.

Extensions

Students can look up the growing-season crop water use published by their state's extension service for one local crop and compare those weekly numbers with the fictional crop-use cards in this game. A follow-up task is to redesign the six rounds using the real weekly values, then explain how the different weather pattern changes the winning strategy.