The Missing Moon Data and Marcus's Eclipse Claim
A seventh-grade class spends 30 days recording the Moon's phase and the time of each observation on a shared data table. Priya logs a full moon on Day 8 and again on Day 22; three students log nothing for five consecutive rainy nights; one student records "half moon" on a night when the Moon was below the horizon at the observation time. During the wrap-up, Marcus argues: "The Moon goes around Earth every 29.5 days, so it must line up between Earth and the Sun once a month - we should see a solar eclipse every month." The teacher has a lamp, a globe, and a foam ball, and the district requires students to use evidence to explain why eclipses do not occur monthly. Only two 45-minute periods remain before the unit assessment, and the teacher must decide how much time to spend repairing the data table versus building the model.
1. How should the teacher treat the flawed and missing entries before using the table as evidence, and what distinction should students draw among the three kinds of problems?
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The three problems are not equivalent, and lumping them together would teach the wrong lesson about data. Missing entries from rain are absent data, not wrong data: the phase still occurred, so those nights simply cannot support a claim about timing. The "half moon below the horizon" entry is a procedural error - the student recorded a phase at a time when that phase could not be observed, probably from memory or a website - and should be flagged and set aside, not silently erased. Priya's two full moons are a recording or identification error, since a full moon recurs about every 29.5 days and cannot occur on Day 8 and Day 22 of one cycle. The teacher should keep the raw table intact, annotate it in a second color, and have students count only complete, time-stamped observations when computing phase frequency. That preserves the record, models how scientists handle error, and leaves roughly one period for the lamp-globe-ball model, which is the higher-priority learning goal before the assessment.
2. Describe a lamp-globe-ball sequence that actually tests Marcus's claim, including the feature the model must contain and the evidence students should collect.
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The model must fail first, or students learn nothing. Step 1: with the lamp fixed, orbit the ball around the globe in the plane of the globe's orbit and have students count how often the ball blocks the lamp from the globe's surface. In that setup an alignment happens every revolution, which reproduces Marcus's prediction - that is the point. Step 2: tilt the ball's orbit about 5 degrees relative to that plane (a bent wire hanger or a marked ring works) and repeat. Students now count alignments over twelve revolutions and typically find only two windows per year when the geometry lines up. Step 3: students write the claim-evidence-reasoning statement: "Eclipses are not monthly because the Moon's orbit is inclined about 5 degrees to Earth's orbital plane, so at most new and full moons the shadow misses." Requiring them to record counts before and after the tilt turns the model into a test rather than a demonstration, and directly answers Marcus with data the class generated.
3. Write a three-point scoring guide for a short constructed-response item asking why eclipses do not occur monthly, and justify each point.
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Point 1 - Mechanism (1 pt): Student states the Moon's orbital plane is tilted roughly 5 degrees to Earth's orbital plane, so the three bodies usually do not align. Without this, the response is just a restatement of the question. Point 2 - Use of evidence (1 pt): Student cites specific class evidence, e.g., "in our model, the ball lined up only twice in twelve orbits after we tilted the orbit," rather than a generic reference to "data." This is the domain practice the standard names. Point 3 - Scope and precision (1 pt): Student correctly limits the claim to solar eclipses (new moon) or distinguishes solar from lunar, and does not claim eclipses never occur monthly because the Moon is too small. The size misconception is common and worth detecting. Scoring this way separates content knowledge from evidence use, so a student who knows the tilt but cites nothing still loses a point, and a student who cites the model but says "the Moon's shadow is too small" is caught rather than credited.