Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
An angle forms wherever two rays share a common endpoint, called the vertex. Fourth graders learn to think of an angle as a turn: imagine one ray rotating around the vertex until it lands on the other. The size of the angle is how far the ray turned, not how long the rays are drawn.
To measure that turn, picture a circle centered at the vertex. The angle cuts off a fraction of the circle's arc between the two rays. A turn of 1/360 of a full circle is called a one-degree angle, and an angle that turns through n of those one-degree angles measures n degrees. A quarter turn is 90 degrees, a half turn is 180 degrees and a full turn is 360 degrees. This definition explains why protractors are half circles marked from 0 to 180 and connects angle measurement to fractions, since a quarter of 360 is 90.
Students often think an angle drawn with long rays is larger than one with short rays. The size of the turn, not the length of the sides, determines the angle.
Some students think a degree is a small distance along the arc. A degree is a fraction of a full turn, the same no matter how big the circle is.
Because a quarter is 25 of 100, students may say 25°. A full turn is 360°, so a quarter turn is 360 ÷ 4 = 90°.
An angle turns through 1/6 of a full circle. How many degrees does it measure?
Answer: The angle measures 60°.
Use body turns and a clock face: stand, turn a quarter turn, then a half turn. On a clock, the minute hand turns 30° every five minutes. Paper circles folded into halves, quarters and eighths give students angles of 180°, 90° and 45° to compare.
Assessment items may ask how many degrees are in a fraction of a turn or which angle is larger when the rays are drawn different lengths. Both test the turn idea directly.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 90 (also accepted: 90 degrees, 90°)
A full turn is 360°, so a quarter turn is 360 ÷ 4 = 90°.
Answer: A) A one-degree angle
By definition, an angle that turns through 1/360 of a circle is a one-degree angle.
Answer: 45 (also accepted: 45 degrees, 45°)
360 ÷ 8 = 45, so the angle measures 45°.
Answer: C) They are the same size
Both angles turn through a quarter of a circle, 90°. The length of the rays does not change the size of the turn.
Answer: 90 (also accepted: 90 degrees, 90°)
In 60 minutes the hand turns 360°. 15 minutes is 1/4 of an hour, so it turns 360 ÷ 4 = 90°.
Answer: A) 1/3
120 ÷ 360 = 1/3, so the angle is one third of a full turn.
A full lesson with slides, activities and an exit ticket on understanding angles and degrees, pitched to grade 4 and editable in PowerPoint or Google Slides.
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Make a worksheet →Turn understanding angles and degrees into a quiz students answer online that marks itself, with a class summary for you.
Build a test →Mathematicians chose to divide a full turn into 360 equal parts. Each part is a one-degree angle. The number 360 has many factors, which makes halves, thirds, quarters and sixths whole numbers of degrees.
No. Angle size measures the amount of turn between the two rays. You can extend the rays without changing the angle.