Roll the Dice: Where Does a Water Molecule Go, and How Long Does It Stay?

Investigation question: If you follow one water molecule through a chance-based model of the water cycle, where does it spend most of its time, which processes move it, and how well does the model match Earth's real reservoirs?

Scientific purpose

Students walk a water molecule through eight stations (ocean, atmosphere, snowpack, river, lake, soil, plant, groundwater) using dice rules that encode which moves are likely from each place. Every roll is recorded with its process and driver, groups pool their tallies, and the class computes how long the model keeps water in each reservoir. Students then compare the model's ranking to approximate real residence times, find where the model is faithful and where it is crude, and propose a rule change for a real scenario such as a warm winter or heavy groundwater pumping.

Why this helps students with this chapter

A diagram of the water cycle shows every pathway at once and gives no sense of likelihood or time. The dice turn pathways into probabilities: from the ocean, four rolls out of six keep you there; from the atmosphere, every roll sends you down. After fifteen moves students have felt that the ocean and groundwater are sticky, that the air is a brief stop, that the river is a corridor, and that no two routes are alike. Pooling the class's tallies produces numbers they can compare to real residence times, which makes the model something to test rather than something to memorize.

Standards connections

MS-ESS2-4 (assesses, developing, using and revising a model of water cycling with multiple pathways driven by sunlight and gravity): Students use the model to generate route data, explain each move as Sun-driven, gravity-driven or cooling, draw their route as a network, evaluate the model against real reservoirs and modify its rules; the route record, class analysis and proposed revision are evidence toward this PE. It is a California Grade 6 expectation that this seventh-grade textbook revisits.

Roles (rotate each session)

• Traveler: Rolls the die at each station, reads the number aloud, and carries the group's token (or bead string) to the next station.
• Recorder: Writes each move in the journey log: station, roll, where the molecule went or that it stayed, the process named on the station sign, and the driver.
• Process checker: Reads the rule for the roll from the station sign, confirms the process and whether it is Sun-driven, gravity-driven or caused by cooling, and keeps the group's tally sheet.

Materials

Estimated cost: 0 to 15 per class (an estimate; Estimate. Printing the signs is free; a pack of 10 dice costs about 5 dollars; pony beads and pipe cleaners add about 8 to 10 dollars and are optional and reusable.)

Safety

• Students move between stations; keep aisles clear, walk, and leave bags under desks.
• Pony beads are a choking hazard for small children; keep them in cups, pick up any that drop, and do not use them in rooms shared with younger students.
• No other hazards; no chemicals, heat or sharp tools are used.

Teacher preparation and setup

1. Print the eight station signs from the station rules table in large type and post them around the room with space to stand at each; put one die (and the optional bead cup) at each.
2. Assign starting stations so that groups begin spread out, not all in the ocean: for eight groups, one per station; for fewer groups, skip the plant and soil as starting points.
3. Draw the class tally chart on the board with the eight stations as rows and the columns total rolls, stays, departures and average stay.
4. Decide the number of moves (15 is the default; 12 if time is short) and the round length (about 30 seconds) so that all groups roll together on your signal.
5. Print or project the approximate real residence-time table from the recording sheet for the comparison step.
6. If you plan the rule-change round, prepare blank station cards so groups can write a modified rule for one station.

Investigation design

Student procedure

1. Before moving, write your prediction in q1: at which station will your molecule spend the most rolls, and which processes will move it most often? Give a reason.
2. Go to your assigned starting station. Record it as move 0 in the journey log and, if using beads, thread one bead of that station's color.
3. On the teacher's signal, the Traveler rolls the die once. The Process checker reads the rule for that number on the station sign and says the process and the driver aloud. The Recorder writes the move: station, roll, 'stayed' or the new station, the process, and the driver (Sun, gravity, cooling, or 'held' for a stay).
4. If the rule says move, walk to the new station and thread a bead of its color; if it says stay, thread another bead of the same color and wait for the next signal. Keep going for 15 moves.
5. After the last move, complete the group tally: for each station, count how many rolls you made there and how many of those were stays. Count the processes by driver.
6. Add your group's numbers to the class tally chart. When all groups are in, compute for each station: departures = total rolls minus stays, and average stay = total rolls ÷ departures (if a station has zero departures, write 'no departures').
7. Draw your route as a network on the recording sheet: a circle for each station you visited, an arrow for each move, labeled with the process, with loops for stays.
8. Compare the class's average-stay ranking to the approximate real residence-time table, and answer the analysis questions individually.
9. If time allows, each group proposes one rule change for one station that models a real scenario (a warm winter with rain instead of snow, a drought, heavy pumping of groundwater, a paved city) and predicts how the class data would change. Play 8 more moves with the changed rule at that station and check the prediction.

Expected observations

• With 90 or more pooled rolls, average stays come out near 3 for Ocean and Groundwater, near 2 for Snowpack and Lake, near 1.2 for River, Soil and Plant, and exactly 1 for Atmosphere; small classes will see noisier values.
• The Ocean collects the most total rolls because it is sticky and many moves lead back to it; the Atmosphere comes second (visited often, one roll each time) and Groundwater third. The Plant and Soil stations get the fewest rolls, and each visit is brief.
• Almost no two groups have the same route; many routes include a stretch that goes up and down between land and air without touching the ocean (for example lake to atmosphere to river), and a few molecules spend nearly all their moves in the ocean or groundwater.
• Students who start in the Atmosphere are moved immediately, which surprises them and anchors the idea that water's stay in the air is short.

Likely difficulties

• Recorders write the destination but not the process; the Process checker must say both aloud before anyone moves. Checking the log for blank process cells is the first thing to do at the end.
• Groups rush ahead between signals, so moves get out of step and tallies are uneven. Use a visible timer and roll only on the signal.
• Students confuse 'moves that began with cooling' with 'moves driven by cooling'; the model never has cooling move water on its own, which is itself a discussion point.
• Average stay is undefined when a station has no departures (possible for Groundwater in a small class). Write 'no departures' and discuss what that implies.
• The ocean's roll 1-4 'stay' can frustrate a group; point out that this boredom is the point of the model.

Structured debrief

1. Fill the class tally together and compute the average stays aloud. Expected pattern: Ocean and Groundwater near 3 rolls, Snowpack and Lake near 2, River, Soil and Plant a little above 1, Atmosphere exactly 1 (it has no stay rule). Ask what rule makes a station sticky and what rule makes it a corridor.
2. Put the real residence-time table beside the class ranking. The ends agree (ocean and groundwater longest, atmosphere shortest) and the middle is compressed. Make the key modeling point: a roll is not a fixed length of time. One roll in the ocean stands for centuries; one roll in the air stands for days. The model gets the order roughly right and the scale completely wrong, which is a limitation students should be able to state.
3. Tally the drivers for the whole class. Gravity usually leads (every exit from the atmosphere and groundwater, most exits from the river and lake, plus infiltration and runoff from the soil), the Sun is second (every evaporation, transpiration, melting and sublimation move), and cooling appears only as the first half of each atmosphere exit. Ask why condensation never appears as a move by itself in this model (the model lumps condensation and precipitation into one step; a more detailed model would add a Cloud station).
4. Hear two or three proposed rule changes and their predictions. A warm-winter rule (atmosphere roll 5 sends water to River instead of Snowpack) empties the snowpack station and shortens the delay between winter storms and river flow, which is the California water-supply story from the presentation. A pumping rule (groundwater roll 4 sends water to Soil via a well) shortens the groundwater stay and is the Lesson 19 bridge.

Recording sheet: what students fill in

Lab 3 recording sheet: Roll the dice through the water cycle

The station rules below are also posted on the station signs. The die decides every move; your job is to record it accurately, name the process and its driver, and then analyze the class's pooled data.

Analysis questions: answer key

Individual evidence of learning

Each student submits their own journey log, group and class tallies, route network drawing, and answers to q1 through q8. The route drawing with labeled processes and drivers, together with q4 and q7, is the primary evidence for developing, using and revising a water cycle model; q3 is the evidence for the data analysis.

Assessment criteria

Accessibility adaptations

• Provide a journey log with the station names as a word bank and the eight drivers pre-printed as circle-one options so recording is a matter of circling rather than writing.
• Allow students with limited mobility to stay seated with a die while a partner moves the bead string, or run the whole model at the desks with the eight signs as cards.
• Give the class tally as a partially completed table and a calculator for q3; accept a verbal explanation for q4 and q7 recorded by the teacher.
• Print station signs with large type and a color band per station that matches the bead color; add icons (sun, down arrow, snowflake) for the three drivers.
• Provide a bilingual word list for the eight stations and the nine processes.

Low-cost alternative

No beads: the journey log is the record. No dice: use a spinner printed from a hexagon, or number slips drawn from a cup and returned. With very few students, each student carries a token and the class pools 4 or 5 journeys of 25 moves each.

Model limitations

A roll is not a unit of time, so the model can show the order of residence times but not their scale; the ocean's three-roll average stands for thousands of years and the atmosphere's one roll for about a week. The rules lump condensation and precipitation into one move and leave out clouds, fog, animals, human use, desalination, wind and the amount of water involved, and the probabilities are chosen to make the order come out sensibly, not measured from Earth. The model treats one molecule at a time, so it cannot show that the ocean holds most of the water or that a drought changes how much water is at a station. This activity has not been physically run by the authors; the expected average stays are computed from the rule probabilities and will be noisier in a real class.

Teacher notes

Check q3 against the actual class tally, not the worked example. The exact long-run average stays from the rules are Ocean 3, Groundwater 3, Snowpack 2, Lake 2, River 1.2, Soil 1.2, Plant 1.2, Atmosphere 1; a class of 100 rolls will scatter around these. In q5, 'cooling' never appears as a stand-alone driver in this model, which is a limitation worth naming aloud rather than a student error. Keep the class tally; the rule-change predictions in q7 make a good warm-up for Lesson 19.