The angles portion of Topic 14 is large and extremely important to the student's future success in geometry (and trigonometry beyond that). I hope to provide you enough information here to get you on the ground running, so you can go into the classroom and have fun with angles. I think you will find that your students will love this unit and start pointing out all of the geometry that they see around your school. Two TEKS address angles and their role in classifying two-dimensional shapes based on their characteristics. Those two TEKS are 4.6C and 4.6D. When you ensure that students have a strong footing in angle attributes (acute, obtuse, right) you will essentially be giving them the tools to correctly identify types of triangles based on the measure of the angles they are composed of. |
Angle Basics
An angle is the amount of turn between two rays/line segments that have a common end point (the vertex). To help students understand the attribute of the spread of the rays, have them compare two angles by tracing one and placing it directly over the other. Be sure to have them compare angles with sides of different lengths. A common misconception for students is that a wide angle with short sides is smaller than a narrow angle with long sides. Students need to be able to tell the difference between large angles and small angles (regardless of the length of the sides) before you move to measuring angles. |
Measuring Angles
Before you ever measure an angle with a protractor you should first compare angles. To help students understand the attribute of the spread of the rays, have them compare two angles by tracing one and placing it directly over the other. Be sure to have them compare angles with sides of different lengths. A common misconception for students is that a wide angle with short sides is smaller than a narrow angle with long sides. Students need to be able to tell the difference between large angles and small angles (regardless of the length of the sides) before you move to measuring angles. Two reasons that cause difficulty in angle measurement: students do not understand the attribute of angle size (the “spread of the angle’s rays”) and protractors are introduced and used without developing understanding. Using a Unit of Angular Measure A unit for measuring angles must be an angle! You can supply the small units (wedge) for your students or have them make their own. If you use a small triangle, students will sometimes get confused as to which angle they are to use as their unit – we suggest that you curve one side and/or mark the angle that is the unit. A piece of cardstock (index card or old file folder) makes a good wedge. Have them use this wedge as a unit of angular measure by counting the number of times it will fit in a given angle. Hand out a worksheet of assorted angles and have each student use their unit to measure the angles. Because the students made their own unit, the results will be different – this is a great discussion! Van de Walle suggests 3 different types of activities before using a protractor: 1. Comparing angles; 2. Using a wedge (small angle) as a unit to measure; 3. Making a protractor. |
Understanding the Protractor
The protractor is one of the most poorly understood measuring tools found in schools. Part of the difficulty is because the units (degrees) are so very small. It is physically impossible to cut out a single degree and use it. A second problem is that there are no visible angles showing on the protractor – just little marks around the outer edge. To add to the confusion, the numbers on most protractors run both directions (clockwise and counter clockwise) along the marked edge. Making a protractor with a larger unit helps to clear up all of these mysterious features. As you watch the video on measuring an angle with a protractor, you will see the idea of the two rays spreading apart and creating an arc that can be measured on the angle demarcations found on the protractor.
Student Resources
These resources are an appropriate way for your students to begin interacting with angles. Measuring angles with the protractor that they made, and discussing the differences in their measurements, and then measuring the same angles with a protractor and discussing their similar findings will help cement the idea of spreads in an angle.