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Math problem set Grade 5 Engineering & Design

Sorrelton School Garden: A Grade 5 Sprinkler or Drip Decision

A grade 5 problem set where students test a sprinkler and a drip line against a school garden's water allowance, watering slot, and budget, then recommend one.

Objectives

  1. Students will calculate the water each system uses in one watering and across a season.
  2. Students will test both systems against one criterion and two constraints and name the requirement each system fails.
  3. Students will recommend one watering system in writing and cite the numbers that decide the choice.

Vocabulary

Key words: criterion, constraint, trade-off, drip line, sprinkler, water allowance

Teacher overview

A school garden needs a watering system, and the choice between an overhead sprinkler and a drip line is decided by more than which one waters faster. In this problem set, students at the fictional Sorrelton Elementary weigh two systems against three requirements the garden club has written down. The criterion is the water itself, since every bed must get at least 12 gallons on a watering day, and the two constraints are the club's 30-minute morning slot and the garden's summer water allowance. Neither system satisfies all three on its own, so the choice is a trade-off: students calculate first, then decide which shortfall can be repaired and at what cost. A misconception worth correcting here is that the system using less water is automatically the better choice; the drip line does save water, yet it runs long enough to break the club's schedule unless a timer is added.

Sorrelton School Garden: A Grade 5 Sprinkler or Drip Decision — Grade 5 Engineering & Design
Name: ____________________________ Date: ______________

Problems

Sorrelton Elementary is a fictional school, and every number below belongs to that scenario. The garden club waters 6 raised beds, and each bed needs at least 12 gallons on a watering day. The club has a 30-minute slot before school, a summer allowance of 2,500 gallons for the garden, and $200 for equipment. Option 1 is an overhead sprinkler that sprays over the beds and the paths between them. Option 2 is a drip line that releases water into the beds only. Show your work.

  1. The sprinkler sprays 4.5 gallons each minute, and the club runs it for 20 minutes. How many gallons does one watering use?
  2. Of the 4.5 gallons the sprinkler sprays each minute, 0.9 gallon lands on the paths instead of in a bed. In a 20-minute run, how many gallons land on the paths?
  3. A 20-minute sprinkler run uses 90 gallons, and 18 of those gallons land on the paths. The rest is shared equally by the 6 beds. How many gallons does each bed get?
  4. The drip line releases 1.5 gallons each minute, all of it into the beds. How many minutes must it run to deliver 72 gallons?
  5. The club's watering slot is 30 minutes long, and the drip line needs a 48-minute run. How many minutes longer than the slot is that run?
  6. The sprinkler uses 90 gallons on a watering day, and the garden is watered on 30 days over the summer. How many gallons does the sprinkler use in the season?
  7. The drip line uses 72 gallons on a watering day, and the garden is watered on 30 days over the summer. How many gallons does the drip line use in the season?
  8. The garden's summer allowance is 2,500 gallons, and the sprinkler's season total is 2,700 gallons. How many gallons over the allowance is that?
  9. A drip kit costs $126 and a battery timer costs $34. The club has $200 for equipment. How many dollars are left after buying both?
  10. The club wrote three requirements: at least 12 gallons in every bed, a run that fits the 30-minute slot, and a season total no greater than 2,500 gallons. With no timer added, the drip line puts 12 gallons in each bed, runs 48 minutes, and uses 2,160 gallons in a season. How many of the three requirements does it meet?

After problem 10, write two sentences to the principal. Name the system the club should install, and give the two numbers that decided it.

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

Answer Key

Every value below belongs to the fictional Sorrelton garden scenario.

  1. Answer: 90 gallons.
    4.5 x 20 = 90 gallons in one 20-minute run.
  2. Answer: 18 gallons.
    0.9 x 20 = 18 gallons land on the paths, which is water no bed receives.
  3. Answer: 12 gallons per bed.
    90 - 18 = 72 gallons reach the beds, and 72 divided by 6 = 12 gallons for each bed. That meets the club's 12-gallon requirement exactly, with nothing to spare.
  4. Answer: 48 minutes.
    72 divided by 1.5 = 48 minutes. Checking the answer, 1.5 x 48 = 72 gallons.
  5. Answer: 18 minutes.
    48 - 30 = 18 minutes longer than the slot, so the run has to start before the club arrives or else finish short of 72 gallons.
  6. Answer: 2,700 gallons.
    90 x 30 = 2,700 gallons across the season.
  7. Answer: 2,160 gallons.
    72 x 30 = 2,160 gallons across the season, which is 540 gallons less than the sprinkler uses.
  8. Answer: 200 gallons over.
    2,700 - 2,500 = 200 gallons over the allowance. The drip line finishes under it, since 2,500 - 2,160 = 340 gallons to spare.
  9. Answer: $40 remaining.
    126 + 34 = 160 dollars spent, and 200 - 160 = 40 dollars left.
  10. Answer: 2 requirements.
    The drip line puts 12 gallons in each bed and uses 2,160 gallons in the season, so it meets the water requirements, but its 48-minute run does not fit the 30-minute slot. The sprinkler also meets two: 12 gallons per bed and a 20-minute run, while its 2,700-gallon season total is 200 gallons over the allowance. The choice turns on which shortfall can be repaired. A $34 timer starts the drip line 18 minutes before the club arrives and settles the schedule, while nothing recovers the 18 gallons per watering the sprinkler puts on the paths and the allowance does not move. A recommendation naming the drip line with a timer, and citing the 2,160-gallon season total against the 2,500-gallon allowance, is a complete answer.

Differentiation

Support

Give students a rate table for the fictional garden listing 4.5 gallons per minute sprayed, 0.9 gallon per minute onto the paths, 1.5 gallons per minute through the drip line, and 12 gallons needed per bed, with the first row worked as an example. Allow a calculator, and let students record each answer with its unit before moving on, since problems 5, 8, and 10 build on earlier results.

Extension

Ask students to find how many watering days the sprinkler could run in the fictional Sorrelton garden before its 2,500-gallon allowance is used up, then explain what the club would have to do for the watering days left in the season. Students who finish can compare that number with the 30 watering days the season actually needs.

ELL supports

Pre-teach "sprinkler," "drip line," "allowance," and "requirement" with a labeled drawing of the fictional garden showing water reaching a bed and water landing on a path. Offer sentence frames for the written recommendation: "The club should install ___ because ___," and "This system uses ___ gallons in a season, which is ___ the allowance."

Extensions

Have students measure a third option for the fictional Sorrelton garden: hand watering with two hoses, timed in the schoolyard with a bucket and a stopwatch, so the class can compare its gallons per minute and the labor it takes against the two systems in this set. Many water utilities and university extension programs offer free irrigation audits, and some donate drip kits to school gardens, which turns the written recommendation into a proposal the garden club can actually send.