Constructing Angles and Shapes
By folding and examining paper circles, students develop an awareness of the meaning of degree as it relates to angle measurement. A quite accurate (for certain angle measures) protractor can be made by folding a paper circle in half (0o and 180o), into fourths (90o, 270o), into eighths ((45o, 135o, 225o, 315o), and so on, within practical limits. Students use these 'folded paper' protractors as well as standard commercial varieties to measure and construct a variety of angles. Attention is paid to use of a ruler and protractor to create neat, accurate constructions.
Angle types are also discussed, with the following definitions and limits applied:
Another facet of this lesson is the discussion of various polygonal shapes and the number of degrees they contain in their interior angles. This is approached by asking the students to construct, with a ruler and standard protractor, various polygons using the fewest sides possible given certain required angles. For example they must construct a polygon that contains angles of 64o and 37o:
Through discussion and exploration, we find that a triangle always contains 180o, a quadrilateral 360o, a pentagon 540o, and a hexagon 720o.
These first experiences with construction lay some groundwork for classic euclidean compass-and-straight-edge construction in future lessons. The emphasis is on careful, accurate construction of basic angles and polygons.