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In this lesson, students apply what they have learned about circumference and area of circles to solve problems in context. Both types of problems are mixed together so students have to determine which measurement is called for in each problem situation (MP2). Students continue working with answers expressed in terms of . Also, in previous lessons students were always given one measurement of each circle, but in this lesson they must rely on their own estimations to solve the problems (MP6).
First, students consider eight different situations and determine which situations involve circumference and which involve area. They continue working with these situations throughout the rest of the lesson.
The following three activities are optional, so teachers can choose what best fits the needs of their students. The first optional activity has students create a visual display showing how they solved one of the eight problems. The second optional activity has students critique given solutions to some of the eight problems. The third optional activity uses the Information Gap structure to get students thinking about what information is needed to solve these problems.
Let’s contrast circumference and area.
Be prepared to explain or show images of any of the examples of circles in the sorting activity that may be unfamiliar to your students.