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Math problem set Grade 6 Engineering & Design

Hollisgate Farm Drip Line Emitter Spacing Problems

Ten problems where students divide a row length by two emitter spacings on a fictional pepper farm, then test each drip design against a permit and a crop rule.

Objectives

  1. Students will divide a row length by a decimal emitter spacing to find how many emitters a drip line needs.
  2. Students will calculate the hourly water delivery of a drip design for one row and for a whole field.
  3. Students will choose the drip design that satisfies both a pumping permit and a crop water requirement.

Vocabulary

Drip irrigation
Watering plants through tubes that release water slowly, drop by drop, right at the roots. Very little water is wasted along the way.

Also: emitter, spacing, permit, constraint

Teacher overview

Hollisgate Farm is fictional, and every length, flow, permit, and price in this set was invented for it. The farm grows peppers in twelve long rows and waters them with overhead sprinklers, which lose water to wind and evaporation, so the owner is pricing two drip lines instead. A drip line is a hose laid along the row with small emitters spaced along it, and the spacing decides both how many emitters a row needs and how much water the field draws each hour. Students size each design and then test it against the farm's pumping permit. The misconception this set is built to correct is the assumption that a wider spacing means more emitters, which follows from multiplying the row length by the spacing rather than dividing by it.

Hollisgate Farm Drip Line Emitter Spacing Problems — Grade 6 Engineering & Design
Name: ____________________________ Date: ______________

Problems

Every number below belongs to the fictional Hollisgate Farm scenario.

  1. Each pepper row is 315 feet long. Drip Line A puts an emitter every 1.5 feet. How many emitters does one row of Line A need?
  2. Drip Line B puts an emitter every 2.5 feet. How many emitters does one row of Line B need?
  3. Every emitter releases 0.5 gallons in one hour. How many gallons does one row of Line A release in an hour?
  4. How many gallons does one row of Line B release in an hour?
  5. The field has 12 rows. How many gallons would the whole field release in one hour with Line A?
  6. How many gallons would the whole field release in one hour with Line B?
  7. The farm's well permit allows no more than 1,000 gallons per hour for this field. Which line or lines fit that permit?
  8. The farm's agronomist says every row must receive at least 60 gallons an hour. Which line or lines meet that requirement?
  9. Using your answers to problems 7 and 8, which line should Hollisgate install?
  10. Emitters cost $0.30 each, and the field has 12 rows. What do the emitters cost for the line you chose in problem 9?

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: 210 emitters. The row is 315 feet long with an emitter every 1.5 feet, so 315 / 1.5 = 210 emitters.
  2. Answer: 126 emitters. A wider spacing needs fewer emitters: 315 / 2.5 = 126 emitters.
  3. Answer: 105 gallons per hour. Each of the 210 emitters gives 0.5 gallons an hour, so 210 x 0.5 = 105 gallons.
  4. Answer: 63 gallons per hour. Line B has 126 emitters, so 126 x 0.5 = 63 gallons.
  5. Answer: 1,260 gallons per hour. Twelve rows at 105 gallons each give 105 x 12 = 1,260 gallons.
  6. Answer: 756 gallons per hour. Twelve rows at 63 gallons each give 63 x 12 = 756 gallons.
  7. Answer: Line B only. Line B draws 756 gallons an hour, which is under the 1,000 gallon limit, while Line A draws 1,260 gallons an hour and goes over it.
  8. Answer: Both lines. Line A delivers 105 gallons to a row each hour and Line B delivers 63 gallons, and both are at least 60 gallons.
  9. Answer: Line B. It is the only design that appears in the answer to problem 7 and in the answer to problem 8, so it is the only one that satisfies the permit and the crop at the same time.
  10. Answer: $453.60. Line B needs 126 emitters in each of 12 rows, which is 126 x 12 = 1,512 emitters, and 1,512 x 0.30 = 453.60 dollars.

Differentiation

Support

Give students a printed strip that stands for the fictional row, marked at every 1.5 feet for the first 15 feet, so problem 1 can begin by counting marks before the division is written. Provide a filled ratio table pairing 1, 2, and 3 emitters with 0.5, 1.0, and 1.5 gallons an hour.

Extension

Ask students to find the widest whole-tenth emitter spacing that would still deliver at least 60 gallons an hour to each row on this fictional farm, then to report what the whole field would draw at that spacing and whether it stays under the permit.

ELL supports

Provide a top-view drawing of one row with the drip line running down it and emitters shown as evenly spaced dots, labeled with the words "row," "spacing," and "emitter." Allow students to answer problems 7 through 9 by circling a line letter in a two-column chart headed "fits permit" and "waters the crop."

Extensions

Have students measure the spacing of the sprinkler heads or drip emitters in a garden bed at school or at home, then calculate how many emitters a 315-foot row would need at that spacing, keeping the result clearly separate from the fictional Hollisgate figures.