Angles as Benchmarks

Our current math emphasis involves using benchmark angles (such as the 90 degree "right" angles found on a square) to find measures of other, unknown angles. Squares (and rectangles) are particularly helpful since they each have FOUR right angles to use as references.

Consider angle "A" in the brown rhombus and angle "B" in the orange scalene right triangle. Most could easily identify that both are acute angles, but what about their angle measures? One could certainly estimate, but to know for sure, another more probable method would be to overlap the two angles to compare each angle against the other.

Overlapping the two acute angles (we do this in class using plastic "Power Polygons" as manipulatives) shows us that angle "A" is half of angle "B" in size. We could also justify this observation by placing two angle "A's" from two different brown rhombi in order to prove that "A + A = B" in this case.

Now we can use this information along with a 90 right angle to learn more.

Angle "A" combined with angle "B" is equivalent to a right angle, which equals 90 degrees. Since angle "A" is half of angle "B", each measure must be 30 degrees and 60 degrees, respectively.

Angle A = 30 degrees
Angle B = 60 degrees

This is just a small sample of the way we are using the Power Polygons to identify and measure unknown angles. This constructivist approach is really helping us make sense of acute, right, obtuse, straight, and reflex angles.

As a further extension, later in the unit, we will also learn to use protractors (rulers for identifying angle measures) for fun!

Students, what has been your most important "lesson learned" as we have been studying angles and their measures? Leave a comment to share your insights with others.