The Three-Cup Mystery: Rank the Temperatures by Watching Dye

Investigation question: Three cups of still water look identical, but each is at a different temperature. Can you rank them from coldest to warmest using only how fast a drop of dye spreads, and what does your ranking tell you about the particles in each cup?

Scientific purpose

Groups receive three identical-looking cups of water labeled X, Y and Z at secret temperatures: cold, room and warm. Without touching them, they release one drop of food coloring into each at the same moment, score how far the color has spread at fixed times for twelve minutes, and graph the three spread curves. They must commit to a ranking, backed by evidence, before a thermometer reveals the truth. Pooled class data then link temperature to spreading, and the debrief turns the result into a particle explanation: in warmer water the particles move faster on average.

Why this helps students with this chapter

Students usually explain the warm cup with words like 'thinner' or 'the heat pushes the dye', which treat water as a smooth material. Ranking hidden temperatures from spreading alone makes them treat the dye as a sensor for something invisible, and the reveal rewards careful observation over guessing. Scoring at fixed times turns an impression into a graph, and comparing groups shows that the pattern holds even when individual cups differ by a few degrees. The lab gives the particle model its first piece of evidence: something in still water is always moving, and it moves faster when the water is warmer.

Standards connections

MS-PS1-4 (practice, the particle-motion link: a higher temperature means faster particle motion): Students use dye spreading as evidence that particles in still water are always moving and move faster on average when the water is warmer, one link in the PE's model of particle motion and temperature. No energy is added or removed to change a state, so the lab builds toward the PE rather than assessing it.

MS-PS3-4 (supports, only the idea that temperature measures the average kinetic energy of particles): This is a Grade 6 PE in the California integrated sequence. The lab relies on its core idea that a thermometer reading reflects the average motion of particles, but students do not plan the energy, mass and type-of-matter investigation the PE describes.

Roles (rotate each session)

• Dropper captain: Leads the '3, 2, 1, drop' countdown and, with two teammates, makes sure each cup gets exactly one drop from the same height at the same moment.
• Timekeeper: Runs the stopwatch, calls each check time aloud, and makes sure nobody touches the cups, the tray or the table during the run.
• Scorer: Compares each cup with the spread-score card at every check time and calls a score; the team agrees before it is written down.
• Recorder and thermometer reader: Writes every score, leads the sketch at the 2:00 check, and after the ranking is committed reads each cup's temperature at eye level.

Materials

Estimated cost: 10 to 15 per class (add about 20 if eight alcohol thermometers must be bought) (an estimate; A sleeve of 50 clear cups about $5, a pack of 100 transfer pipettes about $6 and a bottle of food coloring about $3; cups and pipettes can be rinsed and reused. Thermometers, trays and pitchers are usually classroom stock; alcohol thermometers cost about $2 to $3 each. Estimated retail prices, not quotes.)

Safety

• The warm water is no hotter than 50 °C and is prepared and poured only by the teacher; students do not use hot-water taps, kettles or the warm pitcher.
• Use digital or alcohol-filled thermometers, never mercury. If a glass thermometer breaks, step back and tell the teacher; do not pick up the pieces.
• Spilled water is a slip hazard. Keep the cups on the tray and wipe up spills at once.
• Food coloring stains skin, clothing and paper. Roll up sleeves and keep recording sheets off the tray.
• Nothing in this lab is for drinking, not even the plain water.

Teacher preparation and setup

1. The day before, fill one pitcher with tap water and leave it out overnight so it reaches room temperature, and chill a second pitcher in a refrigerator.
2. Just before class, make the warm water by mixing hot tap water with cold until a thermometer reads 40 to 45 °C. Never use water above 50 °C; you pour it, not students.
3. For each group, decide which label (X, Y or Z) gets which temperature, and vary the order between groups so neighbors cannot copy. Write the assignments and the starting temperatures on a key card that you keep out of sight.
4. Pour 200 mL into each cup, set the three cups on white paper on a tray with a white backdrop, and place the tray at the group's table without saying which cup is which. Wipe any fogging off the cold cup.
5. Pre-fill three pipettes per group with food coloring, and practice releasing exactly one drop from about 1 cm above a water surface so you can demonstrate it.
6. Project or print the spread-score card (it is on the recording sheet) and agree with the class what 'most of the water' means before the run starts.

Investigation design

Student procedure

1. Read the spread-score card together. Before any dye goes in, write any clues you notice about the three cups in q1 (for example, fogging on the outside). Your final ranking must rest on the dye evidence, not on these clues.
2. From now until the thermometer step, do not touch the cups, the tray or the table. Wait one minute so the water stops swirling from being poured.
3. Three teammates each hold one pre-filled pipette straight up, about 1 cm above the center of one cup. On the dropper captain's '3, 2, 1, drop', each squeezes out exactly one drop. The timekeeper starts the stopwatch on 'drop'.
4. At 0:30, 1:00, 2:00, 3:00, 4:00, 6:00, 8:00, 10:00 and 12:00, the timekeeper calls the time and the scorer gives each cup a spread score from 0 to 4, looking from the side against the white backdrop. The team agrees on each score before the recorder writes it.
5. At the 2:00 check, every student sketches a side view of all three cups in the sketch box.
6. When a cup first reaches score 4, write that time in the summary table. If a cup has not reached 4 by 12:00, write 'more than 12 min'.
7. At 12:00, stop watching. As a team, rank the cups from coldest to warmest, write the ranking and your strongest evidence in q2, and show it to the teacher, who initials it. The ranking cannot change after this.
8. Reveal: the thermometer reader places the thermometer in each cup in turn, waits 30 seconds, and reads it at eye level. Record each end temperature. The teacher then reads the starting temperatures from the key card; record those too, and answer q3.
9. Plot all three cups on the spread-score graph, score against time, one line per cup, each labeled with its end temperature.
10. Add your group's results to the class table on the board (end temperature and score at 4:00 for each cup), copy the class table onto your sheet, and answer the analysis questions individually.

Expected observations

• Warm cup (about 40 to 45 °C at the start): the drop breaks into curling wisps within seconds; scores of 2 to 3 by 1:00 and usually 4 by about 2:00 to 4:00.
• Room cup (about 20 to 23 °C): the drop sinks as a thread and spreads along the bottom; scores of 1 to 2 at 2:00, about 3 by 4:00 to 6:00, and 4 by about 6:00 to 10:00.
• Cold cup (about 5 to 10 °C): the drop sinks to the bottom and sits as a dark patch; scores of 0 to 1 at 2:00, 1 to 2 at 4:00 and usually only 2 to 3 at 12:00.
• End temperatures drift toward room temperature during the run: the warm cup typically loses a few degrees and the cold cup gains a few.
• These are expected patterns, not measured results. The lab has not been physically tested, and real times depend on the dye brand, the drop size and the room.

Likely difficulties

• Pouring leaves the water swirling, and a drop released too soon is carried around in a spiral. Insist on the one-minute wait.
• Drops differ in size, especially when a pipette is squeezed hard. Practice once on a paper towel; if one drop is clearly larger, note it on the sheet.
• Scorers disagree between 2 and 3. Agree on a team rule before starting, for example that 'most' means more than three quarters of the cup.
• Fogging on the cold cup is common on humid days and gives away which cup is coldest. Wipe it during setup and remind students that clues cannot replace the dye evidence.
• Someone bumps the table and sends a ripple through all three cups. Record it, and if time allows rerun that cup with fresh water.

Structured debrief

1. Reveal the class pattern first: post the class table and ask each group whether its ranking held. Most will; where one did not, the cold and room cups are usually the pair confused, because both start slowly. Ask what scoring rule would separate them better (for example, scoring the top half and the bottom half of the cup separately).
2. Build the cause-and-effect chain on the board: higher temperature, faster particles on average, more frequent and harder bumps on the dye particles, faster spreading. Ask which links the data show directly (temperature and spreading) and which are the model's explanation (the two middle links).
3. Name what else moved the color: the dye sinking because it is a little denser than water, and gentle currents set up by temperature differences inside the cup. Propose the gelatin version as a cleaner test, and point out that a good explanation says how sure we are.
4. Close on the thermometer: it reported the average motion of the water's particles. Preview Lab 2, where students control the 'temperature' of a model directly by how hard they shake it.

Recording sheet: what students fill in

Lab 1 recording sheet: The three-cup mystery

Spread-score card. 0: a tight blob or thread of color. 1: color in less than a quarter of the water. 2: color in about half of the water. 3: color in most of the water, but streaky. 4: evenly tinted, no streaks. Score each cup from the side, against the white backdrop.

Analysis questions: answer key

Individual evidence of learning

Each student submits their own copy of the score table, the 2:00 sketch, the spread graph, the class table and answers to q1 through q10. The graph and q4 show data analysis; q5, q6 and q10 are the evidence that the student links temperature to the average motion of particles; q8 and q9 show that the student can judge the strength and limits of the evidence.

Assessment criteria

Accessibility adaptations

• Tape a picture strip of the five spread scores beside the cups so that scoring is done by matching rather than by reading descriptions.
• Use dark blue dye, large clear cups and a bright white backdrop for students with low vision; the scorer calls every score aloud.
• A student with limited fine-motor control can be the timekeeper or scorer while a partner handles the pipettes and the thermometer.
• Let students call observations aloud while a partner writes, and accept spoken or recorded answers to q5 and q8.
• Offer a sentence frame for q5: 'The dye spread faster in cup ___ because its particles ___.'

Low-cost alternative

If thermometers or pipettes are scarce, run the three cups as one teacher demonstration under a document camera, let groups score from the projection, and reveal the temperatures at the end. A toothpick or cotton swab dipped in food coloring and touched to the surface can replace the pipettes, as long as every cup gets the same method.

Model limitations

Dye spreading in a cup is not pure diffusion. The drop is slightly denser than water and sinks, and temperature differences inside the cup (a warm cup cooling at its surface and sides) set up gentle currents that carry color, more strongly in the warm cup. Faster particle motion is still the main reason warm water mixes sooner, but this test cannot separate it from currents; a gelatin version would. The spread score is a judgment, and the warm and cold cups drift toward room temperature during the run, so each cup's temperature is a range rather than one value. This lab has not been physically tested by the authors; times will vary with the dye brand, drop size and room temperature.

Teacher notes

Keep the key card out of sight until every group's ranking is initialed. Expect the cold and room cups to be the pair most often confused. The score at 4:00 is the most useful class number because every cup has one; plot the class's scores against end temperature on the board so W5 has a real class dataset to compare with its simulated one. If warm cups in your room reach score 4 before 2:00, add a 0:15 check. Remind students that 'spreading' is the observation and 'particle motion' is the explanation.