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Performance Tasks

Performance tasks are open-ended, multi-step problems that require students to apply information, understanding, and previous knowledge to create their own learning activity. These tasks should be designed carefully, both to engage students' intellect and to incorporate sound and significant mathematics. Ideally, performance tasks offer students time to investigate and grapple with a problem and to devise their own responses and explanations for how they arrived at an answer. It may be helpful to start with simpler tasks and work up to longer, more complex ones. Assigning students to work on performance tasks in pairs or groups of four will enrich the teacher's observations and notes about strategy, results, and attitude.

Teachers often evaluate performance tasks using a rubric, which is a hierarchy of performance standards and expectations. Whether task-specific or general, the rubric makes it possible to determine a student's score based on overall performance on a task, as opposed to simply the number of correct or incorrect items. A sample rubric could consist of a scale of three to six points that are used to rate performance. Rubrics can be shared with students to help to engage and empower them in the learning process.

Sample performance task

(grades 4-5)

Materials: Pattern blocks, paper, and colored pencils or crayons

Directions:

  1. If the area of the green triangle is one square unit, find the area of the blue rhombus, the red trapezoid, and the yellow hexagon.
  2. Use your pattern blocks to create two different designs with an area that is exactly 15 square units. Draw your patterns on the paper provided.
  3. Write three observations about each of your designs.

Sample rubric for this task:

Points Performance
5 The student correctly determines that the area of the blue rhombus is two square units, the area of the red trapezoid is three square units, and the area of the yellow hexagon is six square units. The two designs have an area of exactly 15 square units, and the student's observations use correct geometric terms.
4 One of the areas is incorrect or the student uses a geometric term incorrectly.
3 Two or three mistakes are made in determining areas or using geometric terminology.
2 Four mistakes are made in determining areas or using geometric terminology.
1 Five or more mistakes are made in determining areas or using geometric terminology.
0 No work is shown or the work is not on task.

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