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The tasks
After a discussion about patterns and their use as plans for making various objects (e.g., clothing, model boats, planes, etc.) the students were given the following instructions:

Create a pattern for making a solid. This type of pattern is often called a “net.” The net should be in one piece, and the figure may not have any overlapping sides. As part of your work, you must also:

1. Make the solid figure.
2. Tell how you arrived at your final plan.
3. Explain any rules which you may have discovered during your work.

In order to complete the task, students were given access to the following materials:

• rulers
• markers
• wooden cubes
• graph paper
• construction paper
• scissors
• paper squares, circles, triangles, etc.
• tape

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 Geometry and Measurement Concepts: Give and respond to directions about location.
b Geometry and Measurement Concepts: Visualize and represent two dimensional views of simple rectangular three dimensional shapes.
b Mathematical Skills and Tools: Estimate numerically and spatially.
c Mathematical Skills and Tools: Measure accurately.
e Mathematical Skills and Tools: Refer to geometric shapes and terms correctly.
h Mathematical Skills and Tools: Use measuring devices and manipulatives.
a Mathematical Communication: Use appropriate mathematical terms, vocabulary, and language.
c Mathematical Communication: Explain solutions to problems clearly and logically.

What the work shows
a Geometry and Measurement Concepts: The student gives and responds to directions about location, e.g., by using words such as “in front of,” “right,” and “above.”
The student used location words to explain thinking and understanding, e.g., “right side,” “left side,” “bottom,” and “top.”

b Geometry and Measurement Concepts: The student visualizes and represents two dimensional views of simple rectangular three dimensional shapes, e.g., by showing the front view and side view of a building made of cubes.
The student produced two dimensional views of a three dimensional object—a cube.

b Mathematical Skills and Tools: The student estimates…spatially.

c Mathematical Skills and Tools: The student measures accurately.

The student measured the squares accurately since all the sides were 5 cm. The successful completion of the cube provides further evidence that the student measured correctly.

e Mathematical Skills and Tools: The student refers to geometric shapes and terms correctly.
The student referred correctly to face, square, cube, and pattern.

h Mathematical Skills and Tools: The student uses measuring devices, pencil and paper, and manipulatives.

The student used paper, pencil, and scissors to construct a cube. As part of the construction, the student also had to use a ruler.

a Mathematical Communication: The student uses appropriate mathematical terms, vocabulary, and language, based on prior conceptual work.
The student used location words (e.g., “back,” “front,” and “the left side”) and shape words (e.g., “cube,” and “square”) correctly.

c Mathematical Communication: The student explains solutions to problems clearly and logically, and supports solutions with evidence, in both oral and written work.
The student used examples of nets that work and that do not work as evidence of the solution presented.

There is a small error on the last page (“its” is repeated unnecessarily). This does not detract from the work.