A B C 

a. 

Answers will vary. Some ideas: The lesson is really one of analysis, but students must know and use geometric vocabulary to work with the labels and to communicate with their group about the problems.

b. 

It may not be clear what from the lesson is new to the students, but it seems that some of the logical relationships, and possibly some of the vocabulary, might be.

c. 

Answers will vary. Throughout the lesson, students are thinking analytically to solve problems such as placing the polygons into appropriate Venn diagrams and answering questions about which properties are shared by certain groups of polygons and which ones are not.

d. 

One of the geometric ideas of the course that students encounter in this lesson is the idea of classification. In this lesson, we see how students extend their knowledge of classification of polygons by thinking about categories of shapes and analyzing them in terms of properties that they share. Classification also progresses through grade levels and here we see how the class develops from the more basic ideas and vocabulary towards more complex levels of thinking and problem solving.

Problem A2

People have very different, and often very strong, opinions about the use of context in mathematics clasrooms. It is important to present students with a variety of lessons. Students can be engaged by problems that are not context-based, as well as by those with real-world connections.

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Problem A3

There were lots of adaptations -- the labels and shapes were selected to be more familiar to students in the class. The students used just two loops in the Venn diagram rather than three loops. The activity is more carefully structured in terms of different groups working with different pairs of labels.

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