Getting Started 
Misconception/Error The student draws an incomplete or incorrect figure and is unable to precisely define the term angle. 
Examples of Student Work at this Level The student draws:
 A triangle.
 An angle that is composed of segments.

Questions Eliciting Thinking What do you know about angles? What does an angle look like?
Explain what you drew. Where is the angle in your picture? Can you draw just an angle?
What other geometric figure is used to form an angle? 
Instructional Implications Provide the student with a precise definition of an angle. Guide the student to use the definition to sketch an angle. Relate parts of the angle (e.g., sides and vertex) to terms in the definition (e.g., rays and endpoints). Additionally, instruct the student on conventions in naming angles. Provide the student with more complex diagrams that include angles and ask the student to locate specific named angles and justify his or her responses.
Continue to emphasize the definition of an angle and implement this task again with the student at a later time. 
Moving Forward 
Misconception/Error The student correctly draws an angle but is unable to precisely define the term angle. 
Examples of Student Work at this Level Instead of giving a definition of an angle, the student describes how angles are measured or describes angle types.

Questions Eliciting Thinking Can you explain how you drew your angle?
What parts make up your angle?
Can you define your angle by describing its parts? 
Instructional Implications Provide the student with a precise definition of an angle. Relate parts of angles (e.g., sides and vertex) to terms in the definition (e.g., rays and endpoints).
Continue to emphasize the definition of an angle and implement this task again with the student at a later time. 
Almost There 
Misconception/Error The student’s diagram contains a minor omission, or the student uses incorrect terminology in the definition. 
Examples of Student Work at this Level The student defines the angle as two rays meeting at a point.

Questions Eliciting Thinking Where do the two rays that make up an angle meet?
What parts make up your angle? Can you define an angle by describing the parts of an angle?
How would you describe just one side of your angle? Is the side of an angle a finite distance? 
Instructional Implications Provide direct feedback to the student on how his or her definition could be made more thorough or precise.
Give the student a picture of an angle and ask the student to describe the parts of the angle and to write a precise definition in terms of the angle’s parts.
Continue to emphasize the definition of an angle 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 correctly draws and labels an angle. The student defines angle as a figure formed by two rays having a common endpoint called the vertex.

Questions Eliciting Thinking How many ways could you name your angle?
Can you describe different types of angles by their measures?
An angle separates the plane into two regions. Can you imagine what those regions are? 
Instructional Implications Review angle measurement, specifically that an angle is measured with reference to a circle whose center coincides with the vertex of the angle. The angle’s measure is related to the fraction of the circle between the points where its sides intersect the circle. An angle that intersects or turns through of a circle is called a onedegree angle. Consequently, an angle that turns through n onedegree angles is said to have an angle measure of n degrees. Provide opportunities for the student to measure angles on a unit circle. Discuss how a protractor is constructed and enables one to measure angles. 