Math problem set Grade 6 Math
Cedar Hollow Farm Stand's Well Pump: Unit Rate and Percent Problems
A grade 6 math set using a fictional farm stand's well pump to practice unit rates, percent of a tank's capacity, and a common unit-rate mistake, all from one scenario.
Objectives
- Students will find and apply a unit rate in gallons per minute from a stated ratio.
- Students will convert a rate from gallons per minute to gallons per hour.
- Students will calculate a percent of a tank's total capacity and work backward from a target percent to a time.
Vocabulary
- Pump
- A pump is a machine that adds energy to water to move it or push it uphill, doing the job gravity cannot do on its own. Water systems use many different kinds of pumps to move water from wells, through treatment, and out to customers.
Teacher overview
Cedar Hollow Farm Stand (a fictional farm stand used for this problem set) fills the 300-gallon tank at its outdoor wash station using a well pump. A worker clocked the pump moving 90 gallons of water into the tank in 6 minutes at a steady rate. This problem set uses that one measurement to find the pump's unit rate and then applies it to fill times, an hourly rate, and percent of the tank's capacity.
A common misconception to watch for: students sometimes use the raw numbers from a measurement, such as "90 gallons in 6 minutes," as if 90 itself were the rate, instead of dividing to find gallons per single minute. Problem 8 confronts this directly by asking students to compare the real fill time with the fill time a person would predict after making exactly that mistake.
Problems
A worker timed the well pump. It moved 90 gallons of water into the tank in 6 minutes, at a constant rate. What is the pump's unit rate, in gallons per minute?
Use the unit rate from problem 1. How many gallons will the pump move in 20 minutes?
The wash station's tank holds exactly 300 gallons when full. Use your answer to problem 2. How many minutes does it take the pump to fill the empty tank?
Convert the pump's rate from problem 1 into gallons per hour.
The pump runs for 8 minutes. How many gallons are in the tank now? What percent of the tank's 300-gallon capacity is that?
Complete the ratio table below. Use the pump's unit rate to find how many gallons are in the tank after each number of minutes.
Minutes pumping Gallons in tank 2 4 10 16 Farm stand rules say the tank must be at least 80 percent full before the day's produce washing can start. How many gallons is 80 percent of the tank's 300-gallon capacity? How many minutes of pumping does it take to reach that amount?
Challenge. A new farmhand misreads the measurement "90 gallons in 6 minutes." The farmhand thinks the pump's rate is 90 gallons per minute. Using that wrong rate, how many minutes would the farmhand predict it takes to fill the 300-gallon tank? Compare that prediction with the correct answer from problem 3. Then explain the farmhand's error.
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: 15 gallons per minute.
90 gallons ÷ 6 minutes = 15 gallons per minute.Answer: 300 gallons.
15 gallons per minute × 20 minutes = 300 gallons.Answer: 20 minutes.
300 gallons ÷ 15 gallons per minute = 20 minutes. This matches problem 2, since 20 minutes of pumping at 15 gallons per minute produces exactly 300 gallons.Answer: 900 gal/hour.
15 gallons per minute × 60 minutes per hour = 900 gallons per hour.Answer: 120 gallons, which is 40 percent of the tank.
8 minutes × 15 gallons per minute = 120 gallons. 120 ÷ 300 = 0.40, or 40 percent.Answer: 30 gallons after 2 minutes (full table: 30, 60, 150, 240 for 2, 4, 10, and 16 minutes).
2 min × 15 = 30 gallons; 4 min × 15 = 60 gallons; 10 min × 15 = 150 gallons; 16 min × 15 = 240 gallons.Answer: 240 gallons, requiring 16 minutes of pumping.
80 percent of 300 gallons = 0.80 × 300 = 240 gallons. 240 gallons ÷ 15 gallons per minute = 16 minutes. This matches the last row of the ratio table in problem 6.Answer: 3.33 minutes predicted (about 3 1/3), versus the correct 20 minutes.
Using the mistaken rate of 90 gallons per minute: 300 gallons ÷ 90 gallons per minute ≈ 3.33 minutes. The correct fill time from problem 3 is 20 minutes, six times longer, because the real unit rate (15 gallons per minute) is only one-sixth of the mistaken rate (90 gallons per minute). The farmhand's error was treating the total gallons measured (90) as the rate itself, instead of dividing by the 6 minutes it took to pump that amount.
Differentiation
Support (below grade level)
Give students the completed unit rate (15 gallons per minute) from problem 1 already written on their paper, along with a labeled arrow rule ("minutes × 15 = gallons"), so they can focus on applying the rate in problems 2 through 7 rather than deriving it. Reduce problem 6's ratio table to two rows (2 and 10 minutes) instead of four.
Extension (above grade level)
Ask students to figure out the pump's rate in gallons per second, and then to calculate how many seconds it would take to fill a small 5-gallon bucket at that rate, showing every conversion step.
ELL supports
Provide a simple labeled diagram of the pump filling the tank, with the rate (15 gallons per minute) written directly on the pump icon. Allow the ratio table in problem 6 to be completed using numbers alone, without requiring a written explanation, and pre-teach the phrase "unit rate" alongside the phrase "gallons per minute" as meaning the same idea.