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Work Sample & Commentary: Counting on Frank
The task
Students were asked to read Counting on Frank by Rod Clement and to write a letter to the author commenting on at least one example of the mathematical claims made.

Circumstances of performance
This sample of student work was produced under the following conditions:
alone in a group
in class as homework
with teacher feedback with peer feedback
timed opportunity for revision

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What the work shows
d Writing: The student produces a narrative procedure that:
• engages the reader by establishing a context, creating a persona, and otherwise developing reader interest;
• provides a guide to action that anticipates a reader’s needs; creates expectations through predictable structures, e.g., headings; and provides transitions between steps;
• makes use of appropriate writing strategies such as creating a visual hierarchy and using white space and graphics as appropriate;
• includes relevant information;
• excludes extraneous information;
• anticipates problems, mistakes, and misunderstandings that might arise for the reader;
• provides a sense of closure to the writing.

The detailed steps of the mathematical procedure engage the reader by clearly recounting the steps the student followed.
The context of a letter allows for a constructive critique of several mathematical procedures employed by the author.
Brief anecdotes at the conclusion of each section develop reader interest and support the claims made by the procedures described.
The strategy of announcing that the writer has tried the problems establishes a believable voice for the writer and serves to get the reader’s attention.
This work sample illustrates a standard-setting
performance for the following part of the standards:
d Writing: Produce a narrative procedure.
The headings that begin each of the three sections, along with the appropriate transition words within each section, provide a guide to action for the text.

The letter is written clearly and logically. This avoids the risk of the reader misunderstanding the procedures described and avoids the need to use examples or parallel situations to clarify the points made.
The conclusion of the letter appropriately restates the original claim. The conclusion also exhibits a sensitivity to the author of the book by recognizing the value of the author’s work in an enthusiastic manner and recommending the book to others.