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Shape and Space in Geometry
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Across the Grades

This activity centers on the difficult process of connecting maps to the way the world looks. In mazes, it's the connection between the "bird's eye view" and the "rat's eye view." Part of the problem is imagining how different something can look from the side as opposed to from above. For some people, this is second nature. Others need more practice.

You can help confused students by having them sketch the map on a larger sheet of paper (or they can print the web page). Then they can set the paper on a table or on the floor, so it's horizontal. (That's one fewer transformation they have to do mentally.) Students can get up and walk around it, imagining themselves on the circle. And you can ask them questions—If you were here [pointing to a position on the circle], would the blue spike be to the right of the red spike or to the left?—and compare their answers with a picture they are trying to locate.

This activity is also unusual in that it is inductive rather than deductive. A deductive activity would be to draw what you see from a given point. Here, you infer the point from the photograph. Thus, this activity relates to logic (and science) as well as to geometry and visualization.

across the grades

In the primary grades, we give students pictures of different parts of a story and ask them to put them in order. Very young children can also begin work with maps. Over the years this map work becomes more and more sophisticated, culminating in complex navigational problems; for example, students triangulating their position based on landmarks or radio beacons.


The NCTM Standards ask us to help students develop their visualization skills. For example, at grades 3–5, they ask that all students "use spatial orientation to navigate to the same point from several different starting positions."

This activity uses the same skill—though imagining a view instead of navigating—with the inductive twist described above: the student has to reason backward to determine the viewpoint from the result.

Back to I Took a Trip on a Train Activity


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