Standard

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 "one-degree 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.

Explanation

About the Math, Learning Targets, & Rigor

This standard calls for students to explore the connection between angles (measure of rotation) and circular measurement (360 degrees). Students explore an angle as a series of “one-degree turns.” (Angles are geometric shapes composed of two rays that are infinite in length.)

Students should have multiple experiences estimating and comparing angles to the Benchmark 90° or right angle. They should explain their reasoning by deciding first if the angle appears to be an angle that is less than the measure of a right angle (90°) or greater than the measure of a right angle (90°).

• If the angle appears to be less than 90°, it is an acute angle and its measure ranges from 0° to 89°.
• If the angle appears to be an angle that is greater than 90°, it is an obtuse angle and its measures range from 91° to 179°.

Ask questions about the appearance of the angle to help students in deciding which number to use.

Resources

Videos

• Khan Academy (scroll to find 4.MD.5 - click on a skill)
  • Videos (on left side in each skill)
• Learn Zillion
  • Videos
• Virtual Nerd 1
• Virtual Nerd 2

EngageNY Lessons

• Module 4, Topic B, Lesson 5: Use a circular protractor to understand a 1-degree angle as 1/360 of a turn. Explore benchmark angles using the protractor.

Extra Practice

• North Carolina Tasks
• Illustrative Math Tasks
• Howard County Tasks
  • Click on 4th grade at bottom, then 4.MD.5
• Common Core Sheets

Released Assessment Questions

PARCC

4.MD.5

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 "one-degree 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.

STUDENT SAMPLE RESPONSE

Performance Indicators: 4.MD.5

Level 5: Exceeds Expectations

• Recognizes how angles are formed and that angle measures are additive.
• Understands and applies concepts of angle measurement recognizing that angles are measured in reference to a circle.
• Uses a protractor to measure and sketch angles.
• Solves mathematical and realworld problems by composing and decomposing angles.
• Solves mathematical and realworld angle problems, including problems that require the use of equations with a symbol for the unknown angle measure.

Level 4: Meets Expectations

• Understands and applies concepts of angle measurement.
• Uses a protractor to measure and sketch angles.
• Solves mathematical and real-world problems by composing and decomposing angles.

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