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Classroom activity Grade 8 Math

Meadowlark Pump Station Function Match: A Grade 8 Card Sort Relay

A 40-minute relay activity where grade 8 teams race to match equations, tables, graphs, and descriptions of four fictional pump station functions.

Objectives

  1. Students will determine the rate of change and initial value from an equation, table, graph, or verbal description of a linear function.
  2. Students will match different representations of the same linear function.
  3. Students will explain how initial value and rate of change together uniquely identify a linear function.

Vocabulary

Key words: function, rate of change, initial value, linear function

Teacher overview

Meadowlark Water Authority (a fictional water authority used for this activity) operates four pump stations, each modeled by its own linear function relating minutes of pumping to tank volume. This is a relay-style card sort for teams of 3 to 4 students: sixteen cards, four representations (equation, table, graph, and verbal description) for each of the four stations, are shuffled together and spread around the room. Teams physically retrieve cards one at a time and must calculate each card's rate of change and initial value to figure out which four cards belong together, turning a matching game directly into repeated practice identifying a function's key features across different formats.

Activity Directions

  1. Before class, print and cut sixteen cards: one equation, one table, one graph, and one verbal description for each of the four station functions listed in the Student Handout. Mix all sixteen cards together and spread them face-up on a central table or tape them around the room.
  2. Explain how the activity works to the class: each of the four stations has a matching set of four cards showing the same function in different forms. Finding a match requires calculating the rate of change and initial value from each card, not just guessing from appearance.
  3. Divide the class into teams of 3 to 4 students. Each team sets up a home base (a desk cluster or floor space) with four labeled zones: Station A, Station B, Station C, Station D.
  4. Explain the relay rule: one runner from each team may retrieve exactly one card at a time from the central table, bring it back, and place it in the zone their team believes it belongs to, then tag the next runner before returning for another card. Runners walk rather than run between the table and home base.
  5. Start a 20-minute timer. Teams continue sending runners until either all sixteen cards have been placed into the four zones or time runs out.
  6. When the round ends, call time and have every team stop retrieving cards. Teams check their own four zones together, recalculating rate of change and initial value for each card to confirm or fix any misplaced cards, before the class review begins.
  7. As a class, review each of the four stations together. For each one, ask one team to present their matched set of four cards and explain, using the rate of change and initial value, how they know all four belong together.
  8. Close by discussing relay questions 5 and 6 as a class.
Meadowlark Pump Station Function Match: A Grade 8 Card Sort Relay — Grade 8 Math
Name: ____________________________ Date: ______________

Student Handout

Meadowlark Pump Station Functions (fictional data used for this activity)

Station A: Starts with 20,000 gallons stored and pumps in 500 gallons every minute. Equation: V = 20,000 + 500t. Table: t = 0, 10, 20 gives V = 20,000, 25,000, 30,000.

Station B: Starts at 40,000 gallons and releases 800 gallons every minute during a scheduled drawdown test. Equation: V = 40,000 − 800t. Table: t = 0, 10, 20 gives V = 40,000, 32,000, 24,000.

Station C: Starts with 15,000 gallons and adds 250 gallons every minute. Equation: V = 15,000 + 250t. Table: t = 0, 20, 40 gives V = 15,000, 20,000, 25,000.

Station D: Starts at 60,000 gallons and drains 1,200 gallons every minute for an emergency flush. Equation: V = 60,000 − 1,200t. Table: t = 0, 5, 10 gives V = 60,000, 54,000, 48,000.

For each station, prepare a graph card by plotting the three table points and drawing a straight line through them, and a description card by writing the station's situation in a sentence without stating the equation directly (as shown above).

Relay questions. Answer all six on your team's answer slip, and write a falling rate as a negative number.

  1. Station A's table gives V = 20,000 gallons at t = 0 minutes, V = 25,000 at t = 10, and V = 30,000 at t = 20. What is Station A's rate of change, in gallons per minute?
  2. Station B's table gives V = 40,000 gallons at t = 0 minutes, V = 32,000 at t = 10, and V = 24,000 at t = 20. What is Station B's rate of change, in gallons per minute?
  3. Station C's table gives V = 15,000 gallons at t = 0 minutes, V = 20,000 at t = 20, and V = 25,000 at t = 40. What is Station C's rate of change, in gallons per minute?
  4. Station D's table gives V = 60,000 gallons at t = 0 minutes, V = 54,000 at t = 5, and V = 48,000 at t = 10. What is Station D's rate of change, in gallons per minute?
  5. How did you decide two cards showed the same function even though they looked different, such as an equation and a graph?
  6. What is the danger of matching a table to a graph just by its starting number, without checking the rate of change too?

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: 500 gallons per minute.
    Station A: initial value 20,000, rate +500 per minute. The equation, table, graph, and description for Station A all correspond to a line starting at 20,000 gallons and rising by 500 gallons per minute.
  2. Answer: -800 gallons per minute.
    Station B: initial value 40,000, rate −800 per minute. Station B's four cards all correspond to a line starting at 40,000 gallons and falling by 800 gallons per minute.
  3. Answer: 250 gallons per minute.
    Station C: initial value 15,000, rate +250 per minute. Station C's four cards all correspond to a line starting at 15,000 gallons and rising by 250 gallons per minute.
  4. Answer: -1,200 gallons per minute.
    Station D: initial value 60,000, rate −1,200 per minute. Station D's four cards all correspond to a line starting at 60,000 gallons and falling by 1,200 gallons per minute.
  5. Answer: By calculating the rate of change and initial value from each card independently and checking that both values matched, rather than judging by appearance alone.
  6. Answer: Two different functions can share the same starting number (initial value) but have completely different rates of change, so matching by starting point alone can group cards that do not actually represent the same function.

Differentiation

Support

Reduce the activity to two stations (eight cards) instead of four, and provide the rate of change already calculated on each equation card so students focus on matching rather than computing from scratch.

Extension

Add a fifth, unlabeled station card set with the equation left blank, and ask the team that finishes first to write the missing equation themselves using only the table and description cards, then check it against a graph card the teacher provides separately.

ELL supports

Use consistent color-coding across all four representation types for each station (for example, all Station A cards on yellow paper) as a visual backup cue, without revealing the answer outright. Provide a sentence frame for the class review: "Station ___ starts at ___ gallons and changes by ___ gallons per minute."