Joining the Dots...

In our last Low Floor High Ceiling article, we had looked at Squaring the Dots... a series of questions on counting the dots inside squares of different sizes and orientations drawn on dotted paper with the dots as lattice points. The focus of the activity was to tilt squares and try to find a general formula for the number of dots inside the square of a particular tilt, as the side of the square changed.

Naturally, a second question arose. Would it be possible to predict the number of dots inside the square as the tilt changed? Initially it seemed almost impossible, but a change in perspective helped in making sense of this task. And so we moved from counting to generalization.

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