This culminating lesson is optional. In this lesson students work on several tasks that combine circumference and area ideas and computations. Students are given a design for a stained-glass window and the prices of the different components. They decide if it would be possible to produce the window for a certain amount of money. Students must make some assumptions about the shapes in the design and about how the different materials are sold.
The second task asks how scaling the window will affect the cost, bringing in ideas from a previous unit. Since measurements of both length and area are involved, the total cost does not simply increase by the scale factor nor by the square of the scale factor. In the last task, students invent their own design for a stained-glass window that could be produced given a cost constraint.
The series of tasks provides many opportunities to engage in different aspects of mathematical modeling (MP4) and strategic use of tools (MP5).
- Apply circumference and area of circles to calculate the cost of a stained-glass window, and explain (orally and in writing) the solution method.
- Design a stained-glass window that could be built for a given dollar amount, and present (orally, in writing, and through other representations) a justification that it costs less than the limit.
- Make simplifying assumptions to solve problems about a stained-glass window.
Let’s use circumference and area to design stained-glass windows.
Four-function calculators are optional but recommended to take the focus off computation.
- I can apply my understanding of area and circumference of circles to solve more complicated problems.
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