Herding Cats
Anchor Papers:
Problem Solving
expert
Problem Solving Rationale
<p>The student provides an effective strategy and a second more efficient strategy to solve the task. The alternative strategy at the end is considered, which shows evidence of the student analyzing the situation and defining a more efficient strategy to solve the task, “but there is a different way…” The student then describes and diagrams this alternative strategy.</p>
Reasoning and Proof
expert
Reasoning Proof Rationale
<p>The student provides a systematic mathematical justification throughout. Because the student also supports their idea mathematically for an alternative strategy on how to solve the task more efficiently, “compensate for the 'dip' of 6 units at the top…” this student achieves Expert level work. Calculations are correct that support the solution.</p>
Communication Level
expert
Communication Rationale
<p>The student uses an organized, sequenced, and labeled response to communicate their work. The student provides insight into the efficiency of their original strategy and defines a more efficient method for reaching the same perimeter. Formal math language is used throughout to communicate their ideas.</p>
Connections Level
expert
Connections RationaleHerding Cats
<p>The student provides a deeper understanding of the mathematics in the task as they describe their alternative strategy to solve the task faster, “compensate for the 'dip' of 6 units at the top…” Experts articulate connections between various strategies for solving the task. </p>
Representation
expert
Representation Rationale
<p>The student constructs a representation that clarifies their idea of using the perimeter of the rectangle “that this shape forms” plus the “the dip.” The construction of the two representations helps to clarify how they can each be used to solve the overall question.</p>