# Moon Phase as a Context for Teaching Scale Factor

## Article excerpt

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As you walk down the halls of many middle schools, you may notice content-specific signs outside of classrooms that say "Science" or "Math." Rarely do you see a classroom with multiple labels such as "Science/Math" to indicate that both subjects are taught concurrently in that classroom. Time and again recommendations are made to integrate teaching across all of the content areas, especially in science and mathematics. Unfortunately, this assimilation is not happening. One reason is that teachers are often specialized in one area while novice in another, and they do not know how to incorporate the different content areas. For this reason we investigated the question, "How can we integrate mathematics and science in a way that supports the learning of concepts in both disciplines?"

To address this question we (university science- and mathematics-education professors) collaborated with a seventh-grade mathematics teacher to develop an inquiry-based, integrated lesson. Middle school standards from the National Science Education Standards (NSES) (NRC 1996) and the National Council of Teachers of Mathematics (NCTM) Principles and Standards (NCTM 2000) were the foundation of this lesson as we combined Earth and space science with scale factors using ratio and proportion (see Figure 1).

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Introduction

The Sun and the Moon are our most visible neighbors in space, yet their distance and size relative to the Earth are often misunderstood. Science textbooks fuel this misconception because they regularly depict linear images of Moon phases without respect to the actual sizes of the Sun, Earth, and Moon, nor their correlated distances from one another. This lesson is designed to help students communicate their ideas of the relative sizes and distances of the Sun, Earth, and Moon and to construct appropriate understandings of how scaling factors can be used to make representations of astronomical distances. To do this, we supplied procedures for students to draw a diagram of the Earth/Sun/Moon relationship as well as demonstrated and solved equations that related the distance measurements to scaled representations of the distances.

We developed this lesson using a learning-cycle model that began with a problem intended to create interest and to determine students' content knowledge before beginning the lesson. Our focus is on students' understandings of proper scale. We use the full Moon aspect of the Earth/Sun/Moon relationship to extend this concept. We do not further the discussion of other Moon phases during this learning cycle. The last phase of our cycle ends with students asking questions that will be addressed in additional learning cycles, beyond the scope of this article (e.g., Why isn't a new Moon a solar eclipse? Why do we not have an eclipse each month in conjunction with the full Moon?). These other aspects of Earth/Sun/Moon relationships can be integrated with other mathematics concepts (e.g., angles, planes) in subsequent cycles.