What do you call an angle which is adorable?
Acutie pie!
What do you call a stubborn angle?
Obtuse!
Why was the obtuse angle upset?
Because he was never right!
Why did the obtuse angle go to the beach?
Because it was over 90 degrees!
Last one, I promise!
Seriously though, geometry has the best puns, especially for angles. Not only are they funny, but they can help students remember key features about types of triangles and angles. I particularly like the last three jokes, as they really enforce the idea of a right angle being 90 degrees, and an obtuse angle is more than 90 degrees. Such an important concept and yet, such a simple way to engage students.
In my placement class, certain students are still struggling to grasp the concept of benchmark angles. Benchmark angles are the main angles that one can use to eyeball approximate angles. They are the starting points of angle estimation.
Benchmark angles also help students develop an understanding of angle size. At first, students describe angles qualitatively (less than a right angle, greater than a straight angle); eventually they use a numerical value (“The angle is a little smaller than a right angle, so it’s about 80°”). - Geometry and Spatial Sense, pg 41
The first and most important benchmark is a right angle, or a 90° angle. It looks like an L. Some non-standard tools to help students recognize a right angle is the corner of a piece of paper, the corner of a book, the placement of the hour and minute hand on a clock at 3 pm. An easy tool they always have with them is their hands. If they make an L shape with their thumb and pointer finger, this creates a right angle.
Once they understand the what a right angle looks like, and that it is 90°, they can begin to learn the other benchmarks (45°, 135°, 180°). An simple activity to help students understand the relationship between recognizing benchmark angles and the types of angles is to practice identifying obtuse and acute angles without the use of a protractor. Obtuse angles extend more than 90°, and Acute angles are smaller than a 90°. It was surprising how many students in my placement struggled with this.
An activity that my associate teacher did with her class was to take the students outside, and they recorded and investigated angles and polygons. They looked for right angles, found acute angles on leaves and identified obtuse angles on rocks. Students were engaged and actively looking for different types of angles and shapes around the yard. Some brought back some leaves, and they measured the exact angles with protractors, without being prompted!
Benchmarks are important for students to recognize, especially right angles, so when they start learning about perpendicular lines, they are able to identify the right angle quickly. My grade seven students who hadn’t quite grasped the concept then ran into problems when trying to identify a perpendicular line segment.
1 comments:
The next time I read a blog, I hope that it doesnt disappoint me as much as this one. I mean, I know it was my choice to read, but I actually thought you have something interesting to say. All I hear is a bunch of whining about something that you could fix if you werent too busy looking for attention.
half angle identities
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