Getting Started |
| Misconception/Error The student does not demonstrate an understanding of a reflection. |
| Examples of Student Work at this Level The student performs another type of transformation on the semicircle such as a translation, reflection, dilation, or stretching (or a combination of these).
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| Questions Eliciting Thinking What does it mean to reflect a figure?
Can you explain how you determined the location of the image? |
| Instructional Implications Be sure the student understands that a reflection is a transformation of the plane. A reflection across line m (the line of reflection) assigns to each point not on line m, a point that is symmetric to itself with respect to line m (e.g., m is the perpendicular bisector of the segment whose endpoints are the point and its image). Also, a reflection assigns to each point on line m the point itself. Use graph paper, tracing paper, or dynamic geometry software to illustrate reflections of points and to demonstrate the relationship between a point, its image, and the line of reflection. Then illustrate reflections of more complex figures such as segments, angles, and polygons. Discuss the basic properties of reflections [e.g., 1) reflections map lines to lines, rays to rays, and segments to segments; 2) reflections are distance preserving; and 3) reflections are degree preserving] and how these properties ensure that the image of a figure under a reflection is always congruent to the preimage.
Provide the student with additional opportunities to reflect polygons. Guide the student to always check the image to ensure that it is congruent to the preimage.
Consider using the MFAS task Demonstrating Reflections (G-CO.1.2) if not previously used. |
Moving Forward |
| Misconception/Error The student makes an error when reflecting the figure. |
| Examples of Student Work at this Level The student attempts a reflection but:
- Reflects across a line other than line l.
- Draws an image that is clearly not congruent to the preimage.
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| Questions Eliciting Thinking What line did you reflect across? Did you use line l?
If a point is on the reflection line, where will its image be located?
Which points on this figure are convenient to transform in order to construct the image?
What is the relationship between the preimage and the image of a figure under a reflection? Do reflections preserve length? Angle measure? |
| Instructional Implications Remind the student that the semicircle is to be reflected across line l. Review the relationship between the preimage of a point, its image, and the reflection line. Ask the student to revise his or her drawing so that the image is a reflection across line l.
Remind the student that reflections preserve both length and angle measure which results in the congruence of the preimage and image. Guide the student to focus on the images of several key points, among them the endpoints of the diameter, the highest point, and the intersection of the semicircle with the reflection line. Be sure the student understands that a reflection assigns to each point on the reflection line the point itself.
Provide feedback on any notational errors (such as not labeling key points of the image or labelling them incorrectly). Allow the student to correct his or her error. Guide the student to always check the image to ensure that it is congruent to the preimage. |
Almost There |
| Misconception/Error The student does not use appropriate notation. |
| Examples of Student Work at this Level The student correctly reflects the semicircle across the given line. However, the student does not label the images of points A and B or labels them incorrectly. For example, the student labels:
- The images of A and B as A and B.
- The image of A as
 and the image of B as  , respectively.
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| Questions Eliciting Thinking Two points, A and B, are labeled on the preimage. How should the images of these points be labeled?
Should a point and its image be labeled with the same letter?
Where is the image of point A in your drawing? Did you label this point correctly? |
| Instructional Implications Review conventions in naming points on the image of a figure, for example as and . Allow the student to correct his or her drawing. Communicate the expectation that correct notation should be used even in the absence of an explicit reminder. |
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 correctly reflects the semicircle across the line l using appropriate notation.
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| Questions Eliciting Thinking What is the symmetry of the figure and how is this symmetry manifested in the image?
How many points do you need to transform before constructing the image?
For what reflection line would the figure and its image completely overlap? |
| Instructional Implications Challenge the student to reflect the figure across a line the makes a 45 degree angle with the given reflection line. |
