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What: A Card Sort uses cards or slips of paper that can be manipulated and moved around. It can be done individually or in groups of 2–4. Students put things into categories or groups based on shared characteristics or connections. This routine can be combined with Take Turns, such that each time a student sorts a card into a category or makes a match, she is expected to explain the rationale while the group listens for understanding. The  rst few times students engage in these activities, the teacher should demonstrate how the activity is expected to go. Once students are familiar with these structures, less set-up will be necessary.
Why: A Card Sort provides opportunities to attend to mathematical connections using representations that are already created, instead of expending time and e ort generating representations. It gives students opportunities to analyze representations, statements, and structures closely and make connections (MP2, MP7).
Launch
Arrange students in groups of 2. Display an image of the two circles for all to see. Highlight the radii, diameters, and circumferences in their own colors. Distribute one set of cards to each group of students. Give students time to work with their partner, followed by a whole-class discussion.
Student Task Statement
Here are two circles. The smaller circle has radius  , circumference  , and diameter  . The larger circle has radius  , circumference  , and diameter  .
Your teacher will give you a set of cards. Sort them into groups of equivalent ratios. Be prepared to share your reasoning.
Student Response
Pile (2):    , Pile ( ): , , Pile ( ): , Pile (   ): ,
Unit 7 Lesson 2: Measuring Angles 19


































































































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