4th Grade · Measurement & Data
4.MD.C.5: Understand angles as turns measured in degrees: a full turn is 360°
4.MD.C.5 is a 4th grade Common Core math standard in Measurement & Data. Here’s what it really covers, and how you can help your students learn it.
By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club
The 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.
In plain words
Understand angles as turns measured in degrees: a full turn is 360°.
Sample questions from student practice
These questions from Bobby's Math Club are the kinds of questions your students will see. You can try answering them to see what a student might see.
Question 1 of 3
An angle measures 60°. How many one-degree angles does it turn through?
- 300
- 60
- 6
Where students can get stuck
- Thinking an angle with longer rays is bigger, even when both angles open by the same amount.
- Measuring angles in inches or centimeters, as if the length of the rays were what counts.
- Struggling to connect a quarter turn to 90 degrees and a half turn to 180, out of a full turn of 360.
Effective teaching strategies
- Extend the rays of an angle with a ruler and ask students whether the angle got bigger, so they see that how wide it opens counts, not how long the rays are.
- Have students stand and turn a quarter, a half, and a full turn, and name the turns 90°, 180°, and 360°.
- Ask students to find what fraction of a full turn 90° is, so they connect a quarter turn with 90 out of 360.
Units that teach this standard
Find where 4.MD.C.5 lands in the program you teach. Each unit has a guide written for families. Unit names and order vary between editions and districts, so your school’s own materials have the exact sequence.
Bridges in Mathematics
enVision Mathematics
Everyday Mathematics
Go Math!
i-Ready Classroom Mathematics
Illustrative Mathematics
Math Expressions
Reveal Math
Don’t see your curriculum? Contact Bobby and we’ll see if we can help!
Share it with families
Families can read What angles are and how degrees measure them for a plain-language look at this skill, with three questions to try together and ideas for helping at home.
Help every student practice measurement and data at home
In Bobby's Math Club, students practice at just the right level, with a hint when they need one, a clear explanation after every question, and kid-friendly videos. Unlimited practice is free for every family.
See how it works for teachers
Written by Robert “Bobby” Barnett
Bobby is an award-winning math teacher, the author of Meet Every Learner’s Needs, and the father of two elementary-school math learners. He uses Bobby’s Math Club with his own kids a few times every week. Learn more or contact Bobby.