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Activity Synthesis
During the activity synthesis, the teacher orchestrates some time for students to synthesize what they have learned. This time is used to ensure that all students have an opportunity to understand the mathematical goal of the activity and situate the new learning within students' previous understanding.
Are You Ready For More?
Note: this feature is limited in the pilot materials. Select classroom activities include an opportunity for diUerentiation for students ready for more of a challenge. Every extension problem is made available to all students with the heading "Are You Ready for More?" These problems go deeper into grade-level mathematics and often make connections between the topic at hand and other concepts at grade level or that are outside of the standard K-12 curriculum. They are intended to be used on an opt-in basis by students if they Rnish the main class activity early or want to do more mathematics on their own. It is not expected that an entire class engages in Are You Ready for More? problems, and it is not expected that any student works on all of them. Are You Ready for More? problems may also be good fodder for a Problem of the Week or similar structure.
Instructional Routines
Anticipate, monitor, select, sequence, connect
What: Fans of 5 Practices for Orchestrating Productive Mathematical Discussions (Smith and Stein, 2011) will recognize these as the 5 Practices. In this curriculum, much of the work of anticipating, sequencing, and connecting is handled by the materials in the activity narrative, launch, and synthesis sections. But teachers will need to take this ball and run with it by developing the capacity to prepare for and conduct whole-class discussions. The book itself would make excellent fodder for a teacher PLC or study group.
Why: In a problem-based curriculum, many activities can be described as “do math and talk about it,” but the 5 Practices lend more structure to these activities so that they more reliably result in students making connections and learning new mathematics.
Card sort
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.
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