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FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task can be implemented individually, with small groups, or with the whole class.
- The teacher asks the student to complete the problem on The Meaning of Pi worksheet.
- The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started |
| Misconception/Error The student describes the circumference and diameter of a circle instead of their relationship. |
| Examples of Student Work at this Level Rather than explaining the relationship between the circumference and diameter in terms of pi, the student describes the circumference and diameter of a circle and explains the difference between them.
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| Questions Eliciting Thinking How are the circumference and diameter of a circle related?
What is pi? How is pi related to the circumference and diameter of a circle? |
| Instructional Implications If needed, review the meaning of the diameter and circumference of a circle. Then engage the student in an activity in which the circumferences and diameters of a variety of circles are measured and their ratios computed. Consider implementing CPALMS lesson Apple Pi (resource number 634). Use ratio terminology when talking about the relationship between circumference and diameter. Emphasize that the ratio of the circumference to the diameter of a circle is always the number represented by pi which is approximately 3.14. |
Making Progress |
| Misconception/Error The student describes the relationship between the circumference and diameter of a circle in terms of the circumference formula. |
| Examples of Student Work at this Level The student says the circumference divided by the diameter is pi or the product of pi and the diameter is the circumference.
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| Questions Eliciting Thinking What is the significance of the number that pi represents? How is pi related to circles?
Can pi be described as a ratio? If so, how? |
| Instructional Implications Confirm with the student that he or she is correct. Then guide the student to interpret pi as a ratio. Emphasize that the ratio of the circumference to the diameter of a circle is always the number represented by pi which is approximately 3.14. Explain that it is this fact that gives rise to the familiar formula for finding the circumference of a circle. |
Got It |
| Misconception/Error The student provides complete and correct responses to all components of the task. |
| Examples of Student Work at this Level The student explains that pi is the ratio of the circumference of a circle to its diameter.
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| Questions Eliciting Thinking What happens when you divide the circumference of a circle by its diameter?
Is it possible that there is some circle for which the ratio of its circumference to its diameter is not pi? |
| Instructional Implications Ask the student to write formulas for finding the circumference of a circle given its diameter and given its radius.
Challenge the student to write a formula for the area of a circle in terms of its circumference. |
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
- The Meaning of Pi worksheet
SOURCE AND ACCESS INFORMATION
Contributed by:
MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Access Privileges: Public
* Please note that examples of resources are not intended as complete curriculum.
