Shadow Data on an Irregular Schedule
On a sunny October day, Ms. Rivera's third-grade class (24 students) measures the shadow of a meter stick every 45 minutes. Recess and lunch create gaps, so one group records at 9:20, 10:05, 11:40, and 1:10. Another group's stick is not vertical. The class data show shadows of 95 cm at 9:00, 60 cm at 10:00, 35 cm at 11:30, 40 cm at 12:30, and 70 cm at 1:30. During discussion, a student says, "The Sun moves around Earth, so the shadow changes." Another says, "The shadow gets shorter, then longer, so the Sun goes up and down." Ms. Rivera has a globe and a lamp but limited time to address both the data quality and the explanation.
1. Which pattern in the data is supported, and how should Ms. Rivera address the claim that the Sun moves around Earth?
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The supported pattern is that the shadow shortens toward midday and lengthens again in the afternoon. That pattern is consistent with the Sun appearing higher in the sky around midday and lower in the morning and afternoon. The student's statement that the Sun moves around Earth describes the apparent motion correctly but attributes it to the wrong cause. Ms. Rivera should acknowledge the observation-the Sun does appear to move across the sky-and then distinguish apparent motion from actual motion. A globe and lamp can model Earth rotating while the lamp stays fixed; students can mark where the light hits and see how a stick's shadow would change. She should also name the limits of the model: the lamp is not the Sun, the globe is not to scale, and the model compresses a day into a few seconds. The goal is for students to explain the shadow pattern as evidence of Earth's rotation, not to memorize a definition.
2. How should Ms. Rivera handle the inconsistent measurement times and the non-vertical stick when interpreting the class data?
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She should treat the inconsistencies as a data-quality problem worth solving, not as a reason to discard the investigation. The pattern of shorter midday shadows is still visible across the class data, but the irregular times make it harder to compare shadows directly. She can have students plot shadow length against time of day and notice that points are not evenly spaced. Then they can identify two procedural problems: the stick must be vertical, and measurements should be taken at standard intervals or at least recorded precisely. The group that measured at 9:20, 10:05, 11:40, and 1:10 can still contribute if students use the actual times rather than assumed 45-minute intervals. A quick re-measurement of the vertical stick at 15-minute intervals, or a check with a partner, would improve reliability. This teaches that scientists inspect procedures when data are noisy.
3. What is a concise way to connect the shadow data to the day-night cycle without overloading third graders?
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Ms. Rivera can use one concrete question: "If the Sun appears to move across our sky, what would a friend on the other side of Earth see right now?" With the globe and lamp, students can see that the side facing the lamp is in daylight and the side facing away is in darkness. She can then connect the shadow measurements to Earth's rotation: as the school grounds turn toward and away from the Sun, shadows change and day becomes night. She should keep the explanation at the level of observable consequences-Sun appears higher, shadows shorten, then lengthen, then the Sun sets-rather than introducing orbital mechanics. A short exit ticket asking students to draw and label one position of the globe and lamp would give her evidence of understanding without requiring a lengthy written explanation.