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.
Learning Targets
- I can identify the parts of an angle and define what an angle is.
- I can explain that an angle is measured in degrees.
Other Common Misconceptions
Students may think that the angle size is determined by the length of the rays rather than by the size of the turn. Have them extend the lines of the rays to see that the length of the ray does not change the interior measure.
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.
Enduring Understanding
Angles are measured in degrees.
Essential Questions
How do you measure an angle?
Vocabulary (online dictionary)
angle, ray, endpoint, vertex, degree, acute, obtuse, right, straight
About the Math
An angle is the union of two rays with a common endpoint. The common endpoint is called a vertex.
a. Angles are measured in degrees from 0 to 360. One complete rotation is 360 degrees. Angles have special names based on their degree measures. An acute angle is less than 90 degrees. An obtuse angle is more than 90 degrees. An angle that measures exactly 90 degrees is called a right angle and it looks like a square corner.
b. The measurement of an angle depends upon the fraction of the circle cut off by the rays. The degree measure of an angle can be estimated by comparing it to 90 degrees as more or less than 90 degrees. To find the exact measurement, students need to use a protractor.
MD.6
Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
Learning Targets
- I can measure an angle using a protractor.
- I can sketch angles when given a measurement.
- I can use a protractor to create a give angle.
Enduring UnderstandingProtractors are used to measure angles.
Essential Questions
How do you use a protractor to measure an angle? How do you draw an angle with a given number of degrees?
Vocabulary (online dictionary)
protractor, degree, vertex
About the Math
When using a protractor place the vertex at the center point and place one ray along the horizontal edge. The angle is measured by finding where the second ray intersects the arc of the protractor.
When drawing an angle the process is just the opposite. Draw a ray and place the center of the protractor on the endpoint and mark off the points of the angle measure. Use the straightedge of the protractor to connect point to the vertex.