Getting Started |
| Misconception/Error The student draws an incomplete or incorrect figure and is unable to precisely define the term circle. |
| Examples of Student Work at this Level The student draws a figure that does not have any important components marked or labeled. The student provides a description rather than a mathematical definition.
The student:
- Draws a circle but does not indicate either a center, radius, or diameter.
- Draws a circle and indicates a center but does not label it.
- Does not understand the meaning of “label.”
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| Questions Eliciting Thinking Can you describe what you have drawn?
What are the important features of a circle?
How are the points on the circle and the center of the circle related? |
| Instructional Implications Provide the student with a precise definition of circle. Guide the student to use the definition to sketch a circle. Consider using a compass to construct a circle, relating the point of the compass to the center of the circle and the radius of the compass to the radius of the circle. Emphasize that each point drawn with the compass is the same distance from the center of the circle. Review terminology related to circles (e.g., center, radius, and diameter). Additionally, instruct the student on conventions in naming circles.
Continue to emphasize the definition of circle and implement this task again with the student at a later time. |
Moving Forward |
| Misconception/Error The student correctly draws a circle but is unable to precisely define the term circle. |
| Examples of Student Work at this Level The student indicates and labels the center, diameter, and radius but does not provide an acceptable definition.
The student labels and relates the radius and diameter.
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| Questions Eliciting Thinking What do you know about circles? How are the diameter and radius related? How are the points on the circle and the center of the circle related?
How would you construct a circle using a compass? At what important point is the point of the compass located? How is the radius of the circle related to the compass? |
| Instructional Implications Ask the student to draw two different radii and to describe the relationship between their lengths. Emphasize that the radius describes the distance between the center of the circle and any point on the circle. Then provide the student with a precise definition of circle. Ask the student to construct a circle with a compass and to indicate how the compass parts and settings relate to the definition of a circle. Ask the student what would happen if the radius of the compass were changed during the construction of the circle.
Continue to emphasize the definition of circle and implement this task again with the student at a later time. |
Almost There |
| Misconception/Error The student’s drawing contains a minor omission or the student uses incorrect terminology in the definition. |
| Examples of Student Work at this Level The student
- Describes the circle as a “line.”
- Indicates a unique property of a circle but does not precisely define the term circle.
- Uses the term “midpoint” rather than “center”.
- Refers to the circle as having sides.
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| Questions Eliciting Thinking What is a line? Is a circle a kind of line?
Do circles have midpoints?
If I gave your definition to someone else, do you think they would recognize it as a definition of the term circle?
Could someone construct a circle from your definition? |
| Instructional Implications Provide direct feedback to the student on how his or her definition could be made more thorough or precise. Ask the student to construct a circle with a compass and to indicate how the compass parts and settings relate to the definition of a circle.
Continue to emphasize the definition of circle and implement this task again with the student at a later time. |
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 accurately draws and labels a circle. The student defines circle as the set of all points in a plane that are equidistant from a given point (called the center). |
| Questions Eliciting Thinking Is the center part of the circle? Is a radius or diameter part of the circle?
What if we replaced the phrase “in the plane” with “in space?” What kind of a figure would we be defining?
What is meant by “area of a circle”? Does a circle really have an area? |
| Instructional Implications Ask the student to experiment with transformations (translations, reflections, rotations, and dilations) of circles in the coordinate plane and to differentiate between those transformations that result in congruence and those that result in similarity. |
