Classroom activity Grade 8 Math
Function or Not a Function: A Water-System Sorting Relay
A grade 8 movement activity where teams sort water-system relations into function or not a function using the rule that each input has exactly one output.
Objectives
- Students will decide whether a relation between two water-system quantities is a function.
- Students will justify each choice using the rule that each input has exactly one output.
Vocabulary
Key words: function, input, output, relation
Teacher overview
This is a team relay for a class of about 20 to 30 students, working in groups of four or five. Each team gets a stack of cards, and every card names an input and an output from a water system. The team decides whether the relation is a function, meaning each input has exactly one output, and drops the card in the matching bin. The activity maps directly onto the concept: sorting a card forces students to test the one-output-per-input rule on a real pairing rather than an abstract one.
Activity Directions
- Before class, print and cut one set of the eight relation cards for each team, and set out two labeled targets per team: a Function bin and a Not a Function bin. Shuffle each team's cards.
- Explain the rule in one sentence: a relation is a function when every input value gives exactly one output value, and it is not a function when a single input can give two different outputs.
- Model one card with the whole class. Read a card aloud, ask "Could one input here lead to two different outputs?", and place it in the correct bin with a spoken reason.
- Line up each team in a relay. The first student takes the top card, walks or jogs to the bins, decides Function or Not a Function, drops the card, and returns to tag the next teammate.
- Teammates may not talk the runner through the answer while running, but between turns the team may review any card already placed and move it if they agree it is in the wrong bin.
- Play continues until a team has sorted all eight cards. The first team to finish with every card placed correctly wins; a team that finishes first but has errors keeps fixing until its sort is fully correct.
- End the relay when every team has all eight cards placed correctly, or when four minutes have passed, whichever comes first.
- Debrief with two questions: "Which card was hardest to place, and why?" and "How can one repeated input value show that a relation is not a function?" Steer the discussion to the idea that a single input paired with two outputs is what breaks the function rule.
Student Handout
Work as a team. For each relation, write F if it is a function or N if it is not, and give one short reason. The input is listed first and the output second.
- Input: the time of day. Output: the tank's water level at that time.
- Input: the number of hours a pump has run. Output: the total gallons it has pumped.
- Input: the water temperature of a stream. Output: the amount of oxygen the water can hold at that temperature.
- Input: the date. Output: a home water meter's reading taken at midnight on that date.
- Input: a chlorine residual value. Output: the distance from the plant where that residual was measured.
- Input: the description "the tank is half full." Output: the time of day when that happens.
- Input: a monthly water bill amount. Output: the household that received it.
- Input: a pump's flow rate. Output: the pump model that produces 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
- Answer: Function. Each moment in time has exactly one tank level, so every input gives one output.
- Answer: Function. A given number of pumping hours gives exactly one total of gallons pumped at a steady rate.
- Answer: Function. Each water temperature matches exactly one oxygen-holding amount, so it is a function.
- Answer: Function. Each date has one midnight meter reading, so every input has a single output.
- Answer: Not a function. The same chlorine residual can occur at two different distances from the plant, so one input gives two outputs.
- Answer: Not a function. The tank is half full at more than one time of day, once while filling and once while draining, so one input gives two outputs.
- Answer: Not a function. Two different households can have the same bill amount, so a single input maps to more than one output.
- Answer: Not a function. Two different pump models can share the same flow rate, so one input value points to more than one output.
Differentiation
Support
Give these teams cards that are color-coded, with function cards and non-function cards printed on different colored paper for a first sorting round, then switch to all-white cards once the rule is secure. Let a partner read each card aloud.
Extension
Ask these teams to write two new cards of their own, one function and one non-function, from a water system they choose, and have another team sort them and check the reasoning.
ELL supports
Provide each relation as a small paired picture, such as a clock pointing to a tank level, so students can see the input and output before reading. Provide the sentence frame "This is not a function because one ___ gives two ___."
Extensions
Have students revisit cards 5 and 6 and describe how they could restate each relation so that it becomes a function, for example by swapping which quantity is the input and which is the output, then explain why the swap fixes the rule.