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The tasks
The teacher asked students to respond in their mathematics journals to the following question: What is a mathematical pattern?

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
This work sample illustrates a standard-setting performance for the following parts of the standards:
a Function and Algebra Concepts: Use linear patterns to solve problems.
b Function and Algebra Concepts: Build iterations of simple non-linear patterns.
a Mathematical Communication: Use appropriate mathematical terms, vocabulary, and language.

What the work shows
a Function and Algebra Concepts: The student uses linear patterns to solve problems; that is, shows how one quantity determines another in a linear (“repeating”) pattern, i.e., describes, extends, and recognizes the linear pattern by its rule, such as the total number of legs on a given number of horses can be calculated by counting by fours.
The student explained what patterns are, and noted that a pattern can be linear, i.e., that it “may or may not repeat itself.” The student gave an example of a linear pattern and extended it.

b Function and Algebra Concepts: The student builds iterations of simple non-linear patterns, including multiplicative and squaring patterns (e.g., “growing” patterns) with concrete materials, and recognizes that these patterns are not linear.
The student explained what patterns are, and noted that a pattern can “grow or lower itself,” i.e., be non-linear.

The student went on to give two examples of different kinds of non-linear patterns: one in which the numbers get larger by adding the next odd
number in sequence; the other in which the numbers get larger by adding “numbers in sequence.”

a Mathematical Communication: The student uses appropriate mathematical terms, vocabulary, and language, based on prior conceptual work.
These parts of the work provide evidence of appropriate use of mathematical terms and vocabulary. This evidence is supported throughout the work.