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Grab a box of toothpicks and build a model of a dog pen in a lesson that introduces quadratic functions. Students work in groups to investigate how the area of a rectangle with a fixed perimeter varies with different lengths and widths. They record their observations, look for patterns, and build a function to describe the data. Learners make important connections about maximum, minimum, symmetry, and increasing and decreasing intervals when they use a graphing calculator to graph their data points and the corresponding function. Note that the introduction to the lesson task states the dog pen is to be in the shape of a square. The activity is likely to be more productive if the more general term rectangle is used instead. Pupils may question the need to investigate scenarios with different lengths and widths if they are told in the beginning that the pen is to be a square.

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