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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 Slope Triangles worksheet.
 The teacher asks followup questions, as needed.
TASK RUBRIC
Getting Started 
Misconception/Error The student is unable to explain why the slope is the same regardless of the points chosen to calculate it. 
Examples of Student Work at this Level The student writes a statement about the diagram but fails to to explain why the slope of line k is the same whether the slope is calculated using points A and B or points C and D.

Questions Eliciting Thinking What do you know about slope? How could you represent the slope of line k?
What do you know about similar triangles? Are there any similar triangles in the diagram? How can you show these triangles are similar?
If two triangles are similar, what do you know about corresponding angles? About corresponding sides? 
Instructional Implications If necessary, review the concept of slope and how slope is calculated. Assign coordinates to points A, B, C, and D and ask the student to demonstrate that the slope is the same regardless of which pair of points is used to calculate it.
Review what it means for two triangles to be similar. Then review the AA Similarity Criterion and the consequences of similarity (e.g., corresponding angles are congruent and corresponding sides are proportional). Provide a general outline for the explanation of why the slope of line k is the same whether the slope is calculated using points A and B or points C and D:
 Show that ,
 Use the similarity to deduce that , and
 Show how the slope can be calculated using points A and B and points C and D.
 Conclude the slopes are the same given the proportionality of the sides.
Then assist the student in providing the details of the explanation.

Making Progress 
Misconception/Error The student’s explanation is incomplete. 
Examples of Student Work at this Level The student:
 Does not first establish that the triangles are similar but is able to use this result to complete the explanation.
 Establishes that the triangles are similar but does not relate the proportionality of the sides to the calculation of slope.

Questions Eliciting Thinking How do you know that is similar to ? What is needed to prove two triangles similar?
How is the proportionality of the sides related to the slope of the line? 
Instructional Implications Provide feedback to the student concerning missing elements and allow the student to revise his or her explanation (e.g., remind the student to first establish that the two triangles are similar before using this result to reason about the proportionality of the sides). Assist the student in using the similarity of the triangles to reason about the proportionality of the sides and the relevance to the slope.
Provide the student with a complete explanation and ask the student to compare his or her explanation to the one provided. 
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 since and are both right angles, they are congruent. Since and are both vertical, they are parallel which means that is congruent to (by the Corresponding Angles Theorem). Since two angles of are congruent to two angles of , (by the AA Similarity Theorem). Since these triangles are similar, corresponding sides are proportional so that . But both represent the slope of line k. Since these ratios are equal, the slope of line k can be calculated using either one. 
Questions Eliciting Thinking Could you also find the slope of this line using points B and C?
Is there another way to show the triangles are similar? 
Instructional Implications Ask the student to derive the equation of a line through the origin and the equation of a line that intercepts the yaxis at b.
Consider administering other MFAS tasks for standard 8.EE.2.6. 
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
 Slope Triangles worksheet
SOURCE AND ACCESS INFORMATION
Contributed by:
MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Is this Resource freely Available? Yes
Access Privileges: Public
* Please note that examples of resources are not intended as complete curriculum.