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Primary Type: Formative Assessment Status: Published This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas! Resource ID#: 66170 This Angle Students are given two angles with the same angle measure but with sides of different lengths and asked to explain which component of an angle determines its measure. Subject(s): Mathematics Grade Level(s): 4 Intended Audience: Educators Freely Available: Yes Keywords: MFAS, angles, rays, turn, angle measures Resource Collection: MFAS Formative Assessments ATTACHMENTS MFAS_ThisAngle_Worksheet.docx FORMATIVE ASSESSMENT TASK Instructions for Implementing the Task This task should be implemented individually. 1. The teacher provides the student with the This Angle worksheet. 2. The teacher says, “Look at these two angles. How do the measures of these two angles compare?” 3. If the student struggles to determine how the angles compare, the teacher should ask, “What could you do to determine how the angles compare? Could you use the tracing paper to help you compare the measures of the angles?” 4. After the student compares the measure of the angles, the teacher asks the student to explain his or her reasoning. TASK RUBRIC Getting Started Misconception/Error The student cannot use angle measurement concepts to correctly compare the angle measures. Examples of Student Work at this Level The student says that the angle with the shorter sides has an angle measure that is less than the angle with longer sides. He or she believes that the length of the sides determines the measure of the angle. page 1 of 3 Questions Eliciting Thinking How are angles measured? What determines the measure of an angle? If you used the tracing paper to trace this angle and then placed it on top of the other angle, would that help you compare their measures? Do the lengths of the sides determine the measure of an angle? Instructional Implications Review the defining attributes of angles (e.g., two rays with a common endpoint). Explain that in the context of angles, the common endpoint is called the vertex of the angle and the rays are called the sides of the angle. Emphasize that the lengths of the sides do not determine the measure of the angle. Explain that since the sides of the angles are rays which extend infinitely in one direction, the sides of all angles are infinitely long. Emphasize that “how open the angle is” that determines its measure. Provide instruction on angle measurement. Be sure to address that angles are measured with reference to a circle whose center is the vertex of the angle. Show the student an angle along with a referent circle. Initially, show the angle as a single ray (with both sides coinciding). Then explain the angle can be formed by keeping one side stationary and rotating the other side through an arc of the circle. Then show the student the angle after one side has been rotated through an arc. Focus the student’s attention on the points where the sides of the angle intersect the circle. Highlight the intercepted arc and explain that the angle’s measure depends on the fraction of the circle this arc represents. Explain that an angle that turns through of a circle is called a “onedegree angle,” and can be used to measure angles. Then explain that an angle that turns through n one-degree angles is said to have an angle measure of n degrees. Explain that when the side of the angle rotates through the entire circle, it rotates 360 degrees. Guide the student to find the measures of angles by taking a fraction of 360 degrees (e.g., the fraction that the arc represents of the entire circle). For example, if the intercepted arc is of the circle, then the angle’s measure is of 360 degrees. Explain that this means that the angle has rotated through 120 one- degree angles. Introduce the student to the protractor. Use the protractor to draw a one-degree angle and explain that this angle is of a circle. Making Progress Misconception/Error The student cannot clearly explain his or her reasoning. Examples of Student Work at this Level The student says that both angles have the same measure but struggles to explain why. The student says, “they look the same” without elaborating. Questions Eliciting Thinking How could you tell the two angles have the same measure? When you think about an angle’s measure, what part of the angle are you considering? Instructional Implications Review angle measurement concepts and model explaining why the two angles appear to have the same measure. Show the student how to use tracing paper to copy one angle, place the copy on top of the other angle aligning the vertices and a side and observing that the other sides coincide as well. Explain that since both pairs of sides coincide, each angle was formed by using the same degree of rotation. Consider using the MFAS task Lawn Sprinkler (4.MD.3.5) to assess a student’s understanding of onedegree turns in angle measurement. 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 explains that both angles have the same measure. The student uses tracing paper to copy one angle, places the copy on top of the other angle aligning the vertices and sides and explains that since both sides coincide, each angle was formed by using the same degree of rotation. Questions Eliciting Thinking How can angles be the same measure but look different? How many onedegree turns are in an angle that has a measure of 63°? How many onedegree turns are in one whole rotation, or circle? Instructional Implications Consider using the MFAS task Determining An Angle’s Measure (4.MD.3.5), which assesses if a student understands how an angle’s measure is determined by considering the fraction of the intercepted arc in relation to the whole circle. Provide instruction on using a protractor to measure angles. Show the student angles in the context of other diagrams such as intersecting lines and polygons. Ask the student to use a protractor to measure specified angles. Challenge the student to find more than one way to measure a given angle using a protractor. ACCOMMODATIONS & RECOMMENDATIONS Special Materials Needed: This Angle worksheet page 2 of 3 Tracing paper 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 License: CPALMS License - no distribution - non commercial Related Standards Name MAFS.4.MD.3.5: Description Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “onedegree angle,” and can be used to measure angles. b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees. page 3 of 3