Mapping as a Problem to Solve

This is a follow up to this post - on mapping as inquiry.
http://www.heidisiwak.com/2013/10/class-61-begins-inquiry-world-cafe.html


Grade 6 students continued with their exploration of mapping and the challenge of transferring a 3D world to a 2D surface. After building models of the classroom that included the arched ceiling, students had to think about how to flatten the structure so that all aspects were showing. We observed and discussed how collapsing walls in certain directions would cause different outcomes - walls could turn into straight lines, parts of the room would be no longer visible. Deciding what to do with the ceiling was challenging because simply pushing it to the floor would cause a great deal to disappear.

 Eventually groups realized that the roof could be peeled backward and that collapsing all 4 walls outward would be an elegant solution to the problem.

Students realized, however,  that the walls would become disconnected which led to a discussion of distortion which brought us to the beach ball that had been sitting on my desk all week - a source of on-going speculation. Why was it there?

We reviewed the continents which I drew in marker on the ball and then, to the students surprise, I cut the ball.

Antarctica became stretched out, continents were cut open and the problem of what to do with the now open space became apparent. This astonished students. They realized that the maps they had come to accept as representing the world, were not accurate.


It was time to head to the internet and explore projections. Students were free to follow their interests within the boundaries of our topic to construct their knowledge.

In their reflections students commented on what surprised them and what they understood now about maps, that they didn't know before.

Our next mapping activity, was again presented as a problem for partners to solve. How can you represent the height of a mountain on a 2-Dimensional surface?  Students first had to figure out how to roll a rectangle into a cone - a surprisingly difficult task for some.

Once again I was fascinated by the depth and richness of discussion. It was accountable talk at its finest - all students engaged in focused conversation using higher level thinking skills to analyze and find a solution for a problem.  Their solutions were varied.

Birds Eye View

Once students found their solutions, 1 person from each partnership went to visit others to see how they had solved the problem. They then shared what they had seen.

Finally I introduced the term topographic map and sent them to the iPads to explore. Students were surprised to discover that map-makers used the same solution that the had come to independently. They entered into conversation about the lines and several realized that narrow distances between lines meant steep slopes and wide spaces meant gentler slopes.

Towards the end of class we gathered to confirm our new knowledge. One student volunteered to go to the board and explain how a topographic map works.

Other than providing a rich problem, tools for solving it and facilitating conversations, I did minimal direct instruction. It was a satisfying moment when the class realized that they had taught themselves.