Classroom activity Grade 9 Math
Pump Station Flow Relay: Matching Tables to Average Rate of Change
A grade 9 relay activity where teams match pump-station flow data tables to scenario cards and calculate the average rate of change for each.
Objectives
- Students will calculate the average rate of change of pump flow over a stated time interval from a data table.
- Students will match a written scenario description to the data table that fits its described pattern of change.
Vocabulary
Key words: average rate of change, constant rate, variable rate
Teacher overview
This relay activity has teams of three or four students race between four stations set up around the classroom, each showing a data table of pump flow readings from a fictional pump station over time. A separate stack of scenario description cards describes four situations a real pump station operator might see: a steady well pump, a pump ramping up after startup, a pump losing capacity as a filter clogs, and a station with changing demand throughout the day. Each station's data table matches exactly one description, and the pattern each table shows, whether the flow stays constant, rises, falls, or changes at different rates in different intervals, is the method students use to make the match. Correctly matching a scenario to its table requires calculating the average rate of change over the interval the table covers, turning the physical act of running between stations into repeated practice with this calculation.
Activity Directions
Before class, set up four stations around the room, each labeled Station 1 through Station 4, with a laminated data table posted at each showing readings from this fictional pump station scenario (see the Student Handout for the four tables). Place one shuffled stack of the four scenario description cards for each team on a central table equidistant from all four stations.
Divide the class into teams of three or four students. Each team starts together at the central table.
Explain how the activity works: each team sends one runner at a time to the central table, where that runner draws one scenario description card, reads it, and decides which of the four stations' data tables best matches the description based on the pattern of change it shows.
The runner carries the scenario card to the station they believe matches, calculates the average rate of change over the interval shown on that station's table using the data posted there, and writes both the match and the calculated rate on the team's shared answer slip. The runner then returns to the team, tags the next teammate, and that teammate repeats the process with a newly drawn scenario card.
Play continues in this relay pattern until either all four scenario cards have been matched and their rates calculated, or 20 minutes have elapsed, whichever comes first. Each runner draws from the team's own stack, so no team draws the same card twice.
When time is called or a team finishes all four matches, gather the class and reveal the correct scenario-to-station matches and rates together, comparing them to what teams recorded on their answer slips.
Close with a debrief discussion: ask which scenario was hardest to match to its table and why, and specifically ask teams who worked with Station 4 (the variable-demand station) to explain why a single overall average rate of change can hide the ups and downs that happened within that interval.
Student Handout
Station 1 data table (time in minutes, flow in gallons per minute):
| Time (min) | Flow (gpm) |
|---|---|
| 0 | 220 |
| 5 | 220 |
| 10 | 220 |
| 15 | 220 |
Station 2 data table (time in minutes, flow in gallons per minute):
| Time (min) | Flow (gpm) |
|---|---|
| 0 | 0 |
| 2 | 60 |
| 4 | 120 |
| 6 | 180 |
Station 3 data table (time in minutes, flow in gallons per minute):
| Time (min) | Flow (gpm) |
|---|---|
| 0 | 500 |
| 10 | 470 |
| 20 | 440 |
| 30 | 410 |
Station 4 data table (time in hours, flow in gallons per minute):
| Time (hr) | Flow (gpm) |
|---|---|
| 0 | 300 |
| 2 | 380 |
| 4 | 380 |
| 6 | 300 |
| 8 | 340 |
Scenario description cards (print one set of four cards per team, shuffle each set before play):
- Card A: "This fictional pump station's well pump runs at a fixed setting all day. Flow never changes."
- Card B: "This fictional pump just started up and is gradually ramping up to full flow at a steady pace."
- Card C: "This fictional pump station's intake filter is slowly clogging, so flow steadily drops as the shift goes on."
- Card D: "This fictional pump station serves a neighborhood where demand rises in the morning, holds steady at midday, then falls and partly recovers by evening."
Relay questions. Record one answer for each question on your team's answer slip, and write a falling rate as a negative number.
- Card A matches one of the four station tables. Identify that station, then find its average rate of change in flow from 0 minutes to 15 minutes, where the flow reads 220 gpm at every listed time. Give the rate in gpm per minute.
- Card B matches one of the four station tables. Identify that station, then find its average rate of change in flow from 0 minutes to 6 minutes, where the flow rises from 0 gpm to 180 gpm. Give the rate in gpm per minute.
- Card C matches one of the four station tables. Identify that station, then find its average rate of change in flow from 0 minutes to 30 minutes, where the flow falls from 500 gpm to 410 gpm. Give the rate in gpm per minute.
- Card D matches one of the four station tables. Identify that station, then find its overall average rate of change in flow from 0 hours to 8 hours, where the flow goes from 300 gpm to 340 gpm. Give the rate in gpm per hour.
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: 0 gpm per minute.
Card A matches Station 1. Station 1's flow stays at 220 gpm for every time reading, an average rate of change of 0 gpm per minute, which matches Card A's description of a fixed pump setting with no change.Answer: 30 gpm per minute.
Card B matches Station 2; rate = 30 gpm/min. Station 2's flow rises steadily from 0 to 180 gpm over 6 minutes: (180 − 0) ÷ (6 − 0) = 30 gpm per minute, a steady increase matching Card B's ramp-up description.Answer: -3 gpm per minute.
Card C matches Station 3; rate = -3 gpm/min. Station 3's flow falls steadily from 500 to 410 gpm over 30 minutes: (410 − 500) ÷ (30 − 0) = -90 ÷ 30 = -3 gpm per minute, a steady decline matching Card C's clogging-filter description.Answer: 5 gpm per hour.
Card D matches Station 4; overall rate = 5 gpm/hr, with different rates within the interval. Station 4's overall average rate of change from 0 to 8 hours is (340 − 300) ÷ (8 − 0) = 5 gpm per hour, but this single number hides real variation within the interval: from 0 to 4 hours the rate is (380 − 300) ÷ 4 = 20 gpm per hour (rising), while from 4 to 8 hours the rate is (340 − 380) ÷ 4 = -10 gpm per hour (falling). This matches Card D's description of demand that rises, holds, then falls and partly recovers.
Differentiation
Support (below grade level)
Provide a printed formula card reading "average rate of change = (change in flow) ÷ (change in time)" at each station, and allow teams to use a calculator for every calculation. Consider running the first match as a whole-class demonstration using Station 1 before starting the timed relay.
Extension (above grade level)
Challenge teams that finish early to calculate the average rate of change for Station 4 from 6 to 8 hours, and to explain, using that rate, why the flow at hour 8 ends above its hour 0 value even though it had fallen back to 300 gpm at hour 6.
ELL supports
Use the same scenario cards for every team, translated or paired with simple icons (a flat line for Card A, an upward arrow for Card B, a downward arrow for Card C, a wavy line for Card D) so the matching task does not depend entirely on reading English text quickly during the timed relay. Allow teams to record their calculated rates as numbers on the answer slip without full sentence explanations.
Extensions
Invite a local water or wastewater utility to share a real pump station flow chart from their SCADA system (with any sensitive details removed), and have students identify which of the four relay patterns, constant, rising, falling, or variable, best describes the real data.