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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