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Understand Angle Measurement in Degrees Using a Circle

Students understand that angles are measured with reference to a circle, where a full rotation is 360 degrees. A one-degree angle turns through 1/360 of a circle, and an angle of n degrees turns through n one-degree angles. Students connect fraction-of-a-circle thinking to degree measurement.

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Understand Angle Measurement in Degrees Using a Circle

Grade 4 · Understanding Angles · question 1 of 3

0 of 20

20 rungs. A star at the top.

1/10 × 360° = °

How it is taught

0:00 of 3:53

A degree is a tiny slice of a full rotation.

A full rotation is 360 degrees.

?CDO

Read it: An angle is a turn

A full turn is 360°. An angle that turns 1/3 of the circle measures 360 ÷ 3 = 120°.

  1. Find the share of the full turn that the angle makes: 1/3.
  2. Share 360° into that many equal parts: 360 ÷ 3 = 120.
  3. For more than 1 part, multiply: 2/3 of a turn is 2 × 120 = 240°.

A full turn goes all the way around the vertex, and that is 360°.

Equal slices of the turn have equal measures, so each slice is 360° shared out.

The angle is the turn between its rays, so its measure does not change when the rays are drawn longer.

An angle's measure is its share of 360°.

Thinking longer rays make a bigger angle.

Draw the rays longer and the turn between them is still 1/3 of the circle: 120°.

An angle turns 1/6 of a circle. How many degrees is the angle? — 60. A full turn is 360°, and 360 ÷ 6 = 60.

A quarter turn = 90°

Angles measure turning. Picture spinning all the way around — that one full turn traces out a whole circle.

Here's our circle. Every angle we measure is a piece of this turn.

A full circle is split into three hundred sixty equal pieces. Each piece is called one degree.

So a one-degree angle is just one of those tiny slices — exactly one out of three hundred sixty.

An angle of n degrees is simply n of those tiny one-degree slices stacked together.

Let's try one. How many degrees is a quarter of a circle?

A quarter of the circle means one-fourth of three hundred sixty degrees.

One-fourth of three hundred sixty is ninety. So a quarter turn is ninety degrees.

Here it is: two rays meeting at a perfect square corner — that's a ninety degree angle.

Grade 4 · A full circle is 360 degrees

What about half a circle? Half of three hundred sixty is one hundred eighty degrees — a straight line.

A full circle is three hundred sixty degrees, a half is one eighty, and a quarter is ninety. Every angle is a piece of a circle. Awesome!

Now you try. Read this protractor. What is the measure?

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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