A protractor measures angles in degrees, a unit defined so that a full rotation is 360 degrees. To measure an angle, place the protractor's center point on the vertex and align the baseline with one ray, then read the degree marking where the other ray crosses the scale. Protractors have two scales (inner and outer); choosing the correct one requires thinking about whether the angle is acute or obtuse. Students also learn to draw angles of a specified size. Angle measurement connects to real applications in navigation, construction, and later in trigonometry.
Provide plenty of hands-on practice with physical protractors. Start by measuring angles that students have already classified as acute or obtuse, so they can check their reading against their classification (an acute angle must be less than 90 degrees). Practice both measuring existing angles and drawing angles of given measures. Use benchmark angles (90, 45, 180) as reference points.
You already know how to classify angles: a right angle is a perfect square corner, an acute angle is smaller than a right angle, and an obtuse angle is bigger. Classification tells you the category; measurement gives you the exact number of degrees. The degree is the unit of angle measurement, and a full rotation around a point is defined as 360 degrees. A right angle is exactly 90 degrees (one quarter of 360), a straight angle is 180 degrees (one half), and a tiny sliver of an angle might be just 5 or 10 degrees.
A protractor is a semicircular tool with two number scales running in opposite directions — one from left to right (0 to 180) and one from right to left (0 to 180). To measure an angle, place the small hole or dot at the center of the protractor exactly on the vertex (the corner point of the angle), and line up the straight baseline of the protractor with one of the rays. Then look at where the other ray crosses the curved scale and read the number. The two-scale design is the main source of confusion: you must choose the scale whose 0 is aligned with the ray you lined up. If you aligned the left ray and used the left-to-right scale, read that scale; do not accidentally read the other one.
Your classification skill is your error-checking tool. Before you read the number, ask yourself: is this angle acute or obtuse? An acute angle must be less than 90 degrees; an obtuse angle must be between 90 and 180. If your protractor reading says 130 for what is clearly an acute angle, you have read the wrong scale — the correct reading is 180 − 130 = 50. This habit of estimating first, measuring second, and checking third makes your measurements reliable. An angle's measure never changes based on how long its rays are drawn — a 40-degree angle drawn with long rays is the same 40 degrees as one drawn with short rays, because degrees measure rotation, not length.