Math problem set Grade 6 Math

Kilmory Farm's Irrigation Timer: Inches per Hour on Four Zones

A grade 6 problem set on a farm's sprinkler timer: students work with inches per hour, convert depth of water to gallons, and adjust the schedule after a rainy week.

Grade: Grade 6
Subject: Math
Material: Math problem set
Time: 40 min
Prep: No prep
Materials: Printed problem set, Calculators

Standards

6.RP.A.2 Common Core Math

Understand the concept of a unit rate a/b associated with a ratio a:b with b not equal to 0, and use rate language in the context of a ratio relationship.

How this material aligns: Problems 1, 3, and 9 use the unit rate of 0.25 inch of water applied each hour to move between hours of run time and depth applied, and problem 7 uses the well's rate of 40 gallons each minute the same way.

All materials for 6.RP.A.2 →

6.RP.A.3 Common Core Math

Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations, including finding a percent of a quantity and converting measurement units.

How this material aligns: Problems 4 and 5 convert a depth of water on a known area into gallons using the stated conversion figure, and problem 10 finds what percent of the weekly need one rainfall supplied.

All materials for 6.RP.A.3 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-09-03.

Objectives

Students will use a rate in inches per hour to find the run time a crop's weekly need requires.
Students will convert a depth of water on a known area into gallons using a stated conversion.
Students will adjust an irrigation schedule after rainfall and express the saving as a percent.

Vocabulary

Key words: irrigation zone, unit rate, depth of water, timer

Teacher overview

Irrigation is measured the same way rain is measured, as a depth of water spread over an area, so a sprinkler's output is written in inches per hour rather than in gallons. The fictional Kilmory Farm waters four equal zones from one timer and needs 1.5 inches of water on its crop each week. The misconception this set corrects is that inches of water describe how deep the water sits on the soil. They describe the depth the water would reach if none soaked in, which is why a quarter inch per hour still adds up to thousands of gallons on a large field.

Kilmory Farm's Irrigation Timer: Inches per Hour on Four Zones — Grade 6 Math

Name: ____________________________ Date: ______________

Problems

Use these two facts for every problem.

The sprinklers apply 0.25 inch of water each hour.
One inch of water on one square foot of ground is 0.623 gallons.

The crop needs 1.5 inches of water in a week. At 0.25 inch each hour, how many hours must a zone run in a week?
The timer runs each zone for 2 hours at a time. If a zone needs 6 hours a week, on how many days does it run?
A zone runs for 2 hours at 0.25 inch each hour. How many inches of water does that one run apply?
Zone 1 covers 8,000 square feet. How many gallons does it take to apply 0.5 inch to that zone?
Zone 1 covers 8,000 square feet. How many gallons does it take to apply 1.5 inches to that zone in a week?
All four zones cover 8,000 square feet each and each needs 7,476 gallons a week. How many gallons does the whole farm use in a week?
The farm's well pumps 40 gallons each minute. How many minutes does it take to pump the 7,476 gallons that Zone 1 needs in a week?
One week, 0.6 inch of rain falls. The crop still needs 1.5 inches in all. How many inches must the timer supply that week?
The timer must supply 0.9 inch, and the sprinklers apply 0.25 inch each hour. How many hours must a zone run that week?
The crop needs 1.5 inches a week, and 0.6 inch of it came from rain. What percent of the week's water came from the rain?

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: 6 hours.
Divide the weekly need by the hourly rate. 1.5 divided by 0.25 is 6, so each zone runs 6 hours a week.
Answer: 3 days.
6 hours divided by 2 hours per run is 3 runs, so the zone runs on 3 days.
Answer: 0.5 inch.
2 hours times 0.25 inch per hour is 0.5 inch.
Answer: 2,492 gallons.
Multiply area, depth, and the conversion: 8,000 times 0.5 is 4,000, and 4,000 times 0.623 is 2,492 gallons.
Answer: 7,476 gallons.
8,000 times 1.5 is 12,000, and 12,000 times 0.623 is 7,476 gallons. This is three times the answer to problem 4, which matches 1.5 inches being three times 0.5 inch.
Answer: 29,904 gallons.
4 zones times 7,476 gallons each is 29,904 gallons.
Answer: 186.9 minutes.
7,476 gallons divided by 40 gallons per minute is 186.9 minutes, which is a little over 3 hours.
Answer: 0.9 inch.
1.5 inches needed minus 0.6 inch of rain leaves 0.9 inch for the timer.
Answer: 3.6 hours.
0.9 divided by 0.25 is 3.6 hours, which is 2.4 hours less than the usual 6 hours.
Answer: 40 percent.
0.6 divided by 1.5 is 0.4, which is 40 percent.

Differentiation

Support

Give these students a conversion strip for the fictional Kilmory Farm that reads "hours times 0.25 equals inches" and "area times inches times 0.623 equals gallons." Assign problems 1, 2, 3, 8, and 9, which stay in inches and hours, then add problem 4 with the multiplication already set up.

Extension

Ask these students to design a new schedule for the fictional Kilmory Farm using sprinklers that apply 0.4 inch each hour, and to state how many hours a week each zone would run and how many gallons the farm would use. They should explain whether the faster sprinklers change the total gallons, and why.

ELL supports

Pre-teach zone, timer, and depth of water using a sketch of four rectangles labeled with the same area and a ruler standing upright to show a quarter inch. Provide this sentence frame for problem 1: "The crop needs ___ inches, the sprinkler gives ___ inch each hour, so the zone runs ___ hours."

Extensions

Set out a line of straight-sided cans under a sprinkler or a hose on the school grounds, run it for a measured time, and have students read the depth caught in each can with a ruler to work out the inches applied per hour. This is the catch-can test an irrigation technician runs on a real system, and comparing the measured rate with the 0.25 inch figure used for the fictional Kilmory Farm shows the class why a watering schedule depends on an accurate measured rate.