![]() ![]() Here is one:Īssume that the students only have to pay for the glass they use and not the scraps that they would cut away. In any case, this task can provide the springboard for a good classroom discussion around issues that students need to think about when modeling with mathematics. Alternatively, the art teacher might already have the materials and just wants his students to stay within a certain budget for the materials they use, knowing that the scraps can be used for future student projects. But exactly how much extra material they would have to buy depends on how the raw materials are sold, so without additional information, it would be hard to determine that without doing some research into how stained glass is sold. In reality, if they had to buy the glass at a store, the glass would likely come in square or rectangular sheets and they would need to buy more than they were going to use. The question of whether the students have to pay for the scraps of glass left over from cutting out the shapes can be dealt with in different ways. What is important is that students recognize they are making this assumption and are explicit about it. Given the precision needed for these estimates, assuming the curves in the design are arcs of a circle is not only reasonable, it is the most expedient assumption to make as well. The shape of the regions in the stained glass window are left purposefully unspecified, as one component skill of modeling with mathematics (MP4) is for students to make simplifying assumptions themselves. ![]() The purpose of this task is for students to find the area and perimeter of geometric figures whose boundaries are segments and fractions of circles and to combine that information to calculate the cost of a project. ![]()
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January 2023
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