Another interesting problems we solve at the Ateneo Summer Institute is the one in which the teachers created interesting pictures like rat, cat and flowers on geoboard. Later, I asked the teachers to predict which of the picture occupies the largest area. Interestingly, in both groups, teachers suggested counting 'dots left over' as an indicator of area. We later tested this theory by finding the area by counting squares.
Some of the pictures were easily dealt with because they were made up of squares and half-squares. Others were more challenging. I hope the teachers got the idea of how to sequence discussion in students' creation in a way they are kept challenged all the time. We moved from cases which were easy to find the area to cases which demanded more visualization.
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